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Ukol.html
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Ukol.html
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<head>
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<body class='typora-export' >
<div id='write' class = 'is-node'><h1><a name='header-c1' class='md-header-anchor '></a>Úkol #1: PFL067 Statistické metody zpracování přirozeného jazyka</h1><h2><a name='header-c6' class='md-header-anchor '></a>1. Entropie textu</h2><p>V tomto experimentu určíte podmíněnou entropii distribuce slov v textu danou předchozím slovem. K tomu budete potřebovat nejprve spočítat <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.349ex" height="2.577ex" viewBox="0 -806.1 2733.7 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E6-MJMATHI-50" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path stroke-width="1" id="E6-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="1" id="E6-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path><path stroke-width="1" id="E6-MJMAIN-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path><path stroke-width="1" id="E6-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path><path stroke-width="1" id="E6-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E6-MJMATHI-50" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E6-MJMAIN-28" x="751" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E6-MJMATHI-69" x="1141" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E6-MJMAIN-2C" x="1486" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E6-MJMATHI-6A" x="1931" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E6-MJMAIN-29" x="2344" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-6">P(i,j)</script>, což je pravděpodobnost, že v jakékoli pozici v textu najdete slovo <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.802ex" height="1.994ex" viewBox="0 -755.9 345.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E15-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E15-MJMATHI-69" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-15">i</script> a bezprostředně za ním slovo <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.985ex" height="2.461ex" viewBox="-11.5 -755.9 424 1059.4" role="img" focusable="false" style="vertical-align: -0.705ex; margin-left: -0.027ex;"><defs><path stroke-width="1" id="E16-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E16-MJMATHI-6A" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-16">j</script> a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.962ex" height="2.577ex" viewBox="0 -806.1 2567 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E9-MJMATHI-50" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path stroke-width="1" id="E9-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path stroke-width="1" id="E9-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path><path stroke-width="1" id="E9-MJMAIN-7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"></path><path stroke-width="1" id="E9-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path><path stroke-width="1" id="E9-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E9-MJMATHI-50" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E9-MJMAIN-28" x="751" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E9-MJMATHI-6A" x="1141" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E9-MJMAIN-7C" x="1553" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E9-MJMATHI-69" x="1832" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E9-MJMAIN-29" x="2177" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-9">P(j|i)</script>, což je pravděpodobnost, že v případě výskytu slova <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.802ex" height="1.994ex" viewBox="0 -755.9 345.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E15-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E15-MJMATHI-69" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-15">i</script> v textu následuje slovo <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.985ex" height="2.461ex" viewBox="-11.5 -755.9 424 1059.4" role="img" focusable="false" style="vertical-align: -0.705ex; margin-left: -0.027ex;"><defs><path stroke-width="1" id="E16-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E16-MJMATHI-6A" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-16">j</script>. Podmíněnou entropii distribuce slov v textu danou předchozím slovem, můžeme spočítat jako:</p><div contenteditable="false" class="mathjax-block md-end-block" id="mathjax-c8" cid="c8" mdtype="math_block"><span class="MathJax_Preview"></span><span class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.903ex" height="5.612ex" viewBox="0 -1007.2 15027.6 2416.4" role="img" focusable="false" style="vertical-align: -3.273ex;"><defs><path stroke-width="1" id="E1-MJMATHI-48" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path><path stroke-width="1" id="E1-MJMAIN-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 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639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path stroke-width="1" id="E1-MJMAIN-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path><path stroke-width="1" id="E1-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="1" id="E1-MJMAIN-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path stroke-width="1" id="E1-MJSZ2-2211" d="M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 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H(J|I) = -\sum_{i\in I,j\in J}P(i,j)log_2 P(j|i)
</script></div><p>Perplexity se spočítá jako:</p><div contenteditable="false" class="mathjax-block md-end-block" id="mathjax-c11" cid="c11" mdtype="math_block"><span class="MathJax_Preview"></span><span class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="21.937ex" height="3.044ex" viewBox="0 -1007.2 9445.3 1310.7" role="img" focusable="false" style="vertical-align: -0.705ex;"><defs><path stroke-width="1" id="E2-MJMATHI-50" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 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y="0"></use></g></g></g></svg></span></span><script type="math/tex; mode=display" id="MathJax-Element-2">
PX(P(J|I)) = 2^{H(J|I)}
</script></div><p>Vypočtěte podmíněnou entropii a perplexity pro <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-41-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.426ex" height="1.877ex" viewBox="0 -705.6 5780.5 808.1" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E41-MJTT-54" d="M129 38Q129 51 129 55T135 65T151 76H220V535H110V501Q110 470 109 464T101 450Q93 442 68 442H60Q37 442 28 461Q26 466 26 527L27 589Q36 607 49 610H55Q61 610 72 610T97 610T131 610T170 611T215 611T264 611H476Q478 609 483 606T489 602T493 598T496 593T497 586T498 576T498 562V526V488Q498 452 480 444Q476 442 456 442Q431 442 423 450Q416 457 415 463T414 501V535H304V76H374Q389 67 392 61T396 38Q396 10 374 1H151Q140 5 135 11T130 21T129 38Z"></path><path stroke-width="1" id="E41-MJTT-45" d="M374 271Q374 241 367 232T332 223Q307 223 299 231Q290 240 290 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422T476 416T480 407T481 393Q481 368 470 362T434 355H425H392L344 290Q295 225 295 223Q294 223 309 203T350 149L405 77L439 76H453Q474 76 484 69T495 38Q495 10 473 1H303Q281 9 281 32V38Q281 49 282 54T290 67T313 76Q324 76 324 77L259 173L197 77Q202 76 209 76Q225 75 233 68T241 55T242 38Q242 28 242 24T236 12T221 1H51Q29 9 29 32V38Q29 48 29 51T31 59T38 67T51 76H117L171 149Q224 222 224 223L124 355H90H78Q54 355 45 361T35 393Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-54"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-45" x="525" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-58" x="1051" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-54" x="1576" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-45" x="2102" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-4E" x="2627" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-31" x="3153" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-2E" x="3678" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-74" x="4204" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-78" x="4729" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E41-MJTT-74" x="5255" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-41">\verb|TEXTEN1.txt|</script>.</p><p>Tento soubor má každé slovo na samostatném řádku. (Interpunkce je považována za slovo, stejně jako v mnoha jiných případech.) <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.802ex" height="1.994ex" viewBox="0 -755.9 345.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E15-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E15-MJMATHI-69" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-15">i</script> a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.985ex" height="2.461ex" viewBox="-11.5 -755.9 424 1059.4" role="img" focusable="false" style="vertical-align: -0.705ex; margin-left: -0.027ex;"><defs><path stroke-width="1" id="E16-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E16-MJMATHI-6A" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-16">j</script> uvedené výše budou také překrývat větné hranice, kde <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.802ex" height="1.994ex" viewBox="0 -755.9 345.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E15-MJMATHI-69" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E15-MJMATHI-69" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-15">i</script> je poslední slovo jedné věty a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.985ex" height="2.461ex" viewBox="-11.5 -755.9 424 1059.4" role="img" focusable="false" style="vertical-align: -0.705ex; margin-left: -0.027ex;"><defs><path stroke-width="1" id="E16-MJMATHI-6A" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E16-MJMATHI-6A" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-16">j</script> je první slovo následující věty (ale zřejmě tam bude tečka na konci většiny vět). </p><p>Dále budete poškozovat text a měřit, jak to změní podmíněnou entropii. Každý znak v textu poškodíme s pravděpodobností <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E57-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E57-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E57-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-57">10\%</script>. Každý vybraný znak změníme na náhodný znak z množiny znaků vyskytujících se v textu. Vzhledem k náhodě v experimentu, spusťte pokus 10 krát a vraťte minimální, maximální a střední hodnotu entropie. Ujistěte se, že nepoužíváte stejné semínko random generátoru, při opakování experimentu a také se ujistěte, že poškozujete originální text a ne již dříve poškozený. Proveďte stejný experiment pro pravděpodobnosti vybrání znaku <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.098ex" height="2.227ex" viewBox="0 -806.1 1334 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E24-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="1" id="E24-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E24-MJMAIN-35" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E24-MJMAIN-25" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-24">5\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.098ex" height="2.227ex" viewBox="0 -806.1 1334 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E25-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E25-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E25-MJMAIN-31" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E25-MJMAIN-25" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-25">1\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-26-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.908ex" height="2.227ex" viewBox="0 -806.1 2113 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E26-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E26-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="1" id="E26-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E26-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-31" x="779" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-25" x="1279" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-26">0.1\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-27-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.07ex" height="2.227ex" viewBox="0 -806.1 2613.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E27-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E27-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="1" id="E27-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E27-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-30" x="779" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-31" x="1279" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-25" x="1780" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-27">0.01\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-28-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.233ex" height="2.227ex" viewBox="0 -806.1 3114 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E28-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E28-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="1" id="E28-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E28-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-30" x="779" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-30" x="1279" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-31" x="1780" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-25" x="2280" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-28">0.001\%</script>.</p><p>Dále pro každé slovo v textu s pravděpodobností <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E57-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E57-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E57-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-57">10\%</script> vyberte slovo a náhodně ho zaměňte za jiné z množiny slov vyskytujících se v textu. Opět spusťte experiment 10 krát a vraťte minimální, maximální a střední hodnotu entropie. Proveďte stejný experiment pro pravděpodobnosti vybrání slova <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.098ex" height="2.227ex" viewBox="0 -806.1 1334 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E24-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="1" id="E24-MJMAIN-25" d="M465 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xlink:href="#E24-MJMAIN-25" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-24">5\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.098ex" height="2.227ex" viewBox="0 -806.1 1334 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E25-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E25-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E25-MJMAIN-31" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E25-MJMAIN-25" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-25">1\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" 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0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-31" x="779" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E26-MJMAIN-25" x="1279" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-26">0.1\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-27-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.07ex" height="2.227ex" viewBox="0 -806.1 2613.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E27-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E27-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="1" id="E27-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E27-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-30" x="779" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-31" x="1279" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E27-MJMAIN-25" x="1780" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-27">0.01\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-28-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.233ex" height="2.227ex" viewBox="0 -806.1 3114 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E28-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E28-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="1" id="E28-MJMAIN-31" d="M213 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200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-30" x="779" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-30" x="1279" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-31" x="1780" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E28-MJMAIN-25" x="2280" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-28">0.001\%</script>.</p><p>Nyní udělejte přesně totéž pro soubor <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-42-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg 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xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-54" x="1576" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-43" x="2102" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-5A" x="2627" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-31" x="3153" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-2E" x="3678" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-74" x="4204" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-78" x="4729" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E42-MJTT-74" x="5255" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-42">\verb|TEXTCZ1.txt|</script>, který obsahuje pobodné množství textu.</p><p>Vytvořte tabulky, graf a vysvětlete své výsledky. Také se pokuste vysvětlit rozdíly mezi těmito dvěma jazyky. K podložení svého vysvětlení bude dobré udělat tabulky se základními charakteristikami těchto dvou textů (počet slov, počet znaků (celkový, na jedno slovo), frekvence nejčastějších slov, počet slov s frekvencí 1, atd).</p><p>Přiložte svůj zdrojový kód komentovaný takovým způsobem, že bude stačit přečtení komentářů na porozumění tomu, co jste udělali a jak jste to udělali.</p><p>Nyní předpokládejme, že dva jazyky <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.227ex" viewBox="0 -755.9 1135.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E33-MJMATHI-4C" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path><path stroke-width="1" id="E33-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E33-MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E33-MJMAIN-31" x="963" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-33">L_1</script> a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-36-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.227ex" viewBox="0 -755.9 1135.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E36-MJMATHI-4C" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path><path stroke-width="1" id="E36-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E36-MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E36-MJMAIN-32" x="963" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-36">L_2</script> nesdílejí žádná slovíčka, a že podmíněná entropie, jak je popsáno výše, textu <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.412ex" height="2.227ex" viewBox="0 -755.9 1038.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E39-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path><path stroke-width="1" id="E39-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMATHI-54" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMAIN-31" x="826" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-39">T_1</script> v jazyce <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.227ex" viewBox="0 -755.9 1135.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E33-MJMATHI-4C" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path><path stroke-width="1" id="E33-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E33-MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E33-MJMAIN-31" x="963" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-33">L_1</script> je <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="1.994ex" viewBox="0 -755.9 764.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E40-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E40-MJMATHI-45" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-40">E</script>, a že podmíněná entropie textu <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-38-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.412ex" height="2.227ex" viewBox="0 -755.9 1038.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E38-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path><path stroke-width="1" id="E38-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMATHI-54" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-32" x="826" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-38">T_2</script> v jazyce <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-36-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.227ex" viewBox="0 -755.9 1135.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E36-MJMATHI-4C" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path><path stroke-width="1" id="E36-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E36-MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E36-MJMAIN-32" x="963" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-36">L_2</script> je také <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="1.994ex" viewBox="0 -755.9 764.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E40-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E40-MJMATHI-45" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-40">E</script>. Nyní vytvořte nový text přidáním <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-38-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.412ex" height="2.227ex" viewBox="0 -755.9 1038.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E38-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path><path stroke-width="1" id="E38-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMATHI-54" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E38-MJMAIN-32" x="826" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-38">T_2</script> za <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.412ex" height="2.227ex" viewBox="0 -755.9 1038.4 958.9" role="img" focusable="false" style="vertical-align: -0.472ex;"><defs><path stroke-width="1" id="E39-MJMATHI-54" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path><path stroke-width="1" id="E39-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMATHI-54" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E39-MJMAIN-31" x="826" y="-213"></use></g></svg></span><script type="math/tex" id="MathJax-Element-39">T_1</script>. Bude podmíněná entropie tohoto nového textu větší, menší nebo rovna hodnotě <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="1.994ex" viewBox="0 -755.9 764.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E40-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E40-MJMATHI-45" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-40">E</script>? Vysvětlete.</p><h2><a name='header-c29' class='md-header-anchor '></a>2. Cross-Entropie a modelování jazyka</h2><p>Tento úkol vám ukáže, že je důležité vyhlazování pro modelování jazyka a v některých detailech vám umožní pocítit jeho účinky.</p><p>Za prvé budete muset připravit data: vezměte stejná data jako v předchozí úloze, tj. <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-41-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.426ex" height="1.877ex" viewBox="0 -705.6 5780.5 808.1" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E41-MJTT-54" d="M129 38Q129 51 129 55T135 65T151 76H220V535H110V501Q110 470 109 464T101 450Q93 442 68 442H60Q37 442 28 461Q26 466 26 527L27 589Q36 607 49 610H55Q61 610 72 610T97 610T131 610T170 611T215 611T264 611H476Q478 609 483 606T489 602T493 598T496 593T497 586T498 576T498 562V526V488Q498 452 480 444Q476 442 456 442Q431 442 423 450Q416 457 415 463T414 501V535H304V76H374Q389 67 392 61T396 38Q396 10 374 1H151Q140 5 135 11T130 21T129 38Z"></path><path stroke-width="1" id="E41-MJTT-45" d="M374 271Q374 241 367 232T332 223Q307 223 299 231Q290 240 290 263V279H173V76H418V118V144Q418 167 426 176T460 186Q491 186 500 166Q502 161 502 93V52Q502 25 499 17T480 1H41Q19 9 19 32V38Q19 63 36 73Q42 76 65 76H89V535H65H55Q44 535 38 537T25 548T19 573Q19 602 41 610H47Q53 610 63 610T88 610T121 610T160 611T204 611T251 611H458Q460 609 465 606T471 602T475 598T478 593T479 586T480 576T480 562V526V488Q480 452 462 444Q458 442 438 442Q413 442 405 450Q398 457 397 463T396 501V535H173V355H290V371Q290 394 299 403T332 412Q363 412 372 392Q374 387 374 317V271Z"></path><path stroke-width="1" id="E41-MJTT-58" d="M39 571Q39 597 49 604T93 611H141H218Q233 602 236 595T239 573Q239 538 210 535Q202 535 202 534T215 507T243 454L257 428L307 535H298Q266 538 266 573Q266 584 267 588T273 598T289 611H366H401Q442 611 454 605T466 573Q466 546 448 538Q442 535 421 535H398L299 327Q299 323 362 201L426 77L449 76Q467 76 475 75T489 65T495 38Q495 11 477 3Q473 1 395 1H317Q295 8 295 38Q295 73 325 76L334 77Q333 78 314 117T276 196L257 235L239 196Q221 157 204 118T186 77Q190 76 196 76Q211 74 218 67T227 55T228 38Q228 28 227 24T221 13T206 1H50Q28 9 28 32V38Q28 63 45 73Q51 76 73 76H96L214 324Q215 327 162 431L108 535H85H79Q67 535 60 536T46 546T39 571Z"></path><path stroke-width="1" id="E41-MJTT-4E" d="M20 571Q20 598 30 604T73 611H105H136Q152 611 160 611T177 607T189 601T198 587T206 568T217 537T231 497Q354 142 365 95L368 84V535H347H342Q314 535 306 552Q304 556 304 573Q304 586 304 590T310 600T326 611H482Q497 602 500 596T504 573Q504 559 501 551T491 540T478 536T460 535H439V25Q432 7 424 4T389 0H374Q334 0 322 31L293 115Q171 468 159 517L156 528V76H177H183Q195 76 202 75T215 64T221 38Q221 10 199 1H43Q32 5 27 11T22 21T21 38V44Q21 66 37 73Q44 76 64 76H85V535H64Q49 535 42 536T28 545T20 571Z"></path><path stroke-width="1" id="E41-MJTT-31" d="M99 461Q99 470 99 474T104 487T120 498T151 502Q213 517 251 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style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.199ex" height="1.994ex" viewBox="0 -755.9 2669.2 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E43-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="1" id="E43-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-32"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-30" x="500" y="0"></use><g transform="translate(1167,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E43-MJMAIN-30" x="1001" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-43">20\,000</script> slov nazvěte testovací data, posledních <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-44-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.199ex" height="1.994ex" viewBox="0 -755.9 2669.2 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E44-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path stroke-width="1" id="E44-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E44-MJMAIN-34"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E44-MJMAIN-30" x="500" y="0"></use><g transform="translate(1167,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E44-MJMAIN-30"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E44-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E44-MJMAIN-30" x="1001" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-44">40\,000</script> slov ze zbytku nazvěte heldout a zbytek budou trénovací data.</p><p>Tady přichází programování: Spočítejte počet trénovacích slov. Nyní jste připraveni na výpočet unigram, bigram a trigram pravděpodobností. Vypočítejte také pravděpodobnost v závislosti na slovní zásobě. 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437H40Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E45-MJMATHI-54" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-45">T</script> je velikost textu a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-46-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.787ex" height="1.994ex" viewBox="0 -755.9 769.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E46-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 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\begin{eqnarray*}
p_0(w_i) &=& \dfrac{1}{V}\\
p_1(w_i) &=& \dfrac{c_1(w_i)}{T}\\
p_2(w_i|w_{i-1}) &=& \dfrac{c_2(w_{i-1},w_i)}{c_1({w_{i-1})}}\\
p_3(w_i|w_{i-2},w_{i-1}) &=& \dfrac{c_3(w_{i-2},w_{i-1},w_i)}{c_2(w_{i-1},w_i)}
\end{eqnarray*}
</script></div><p><strong>Buď opatrný</strong>; Vzpomeň si, jak správně zacházet se začátkem a koncem trénovacích dat s ohledem na počítání bigramu a trigramu.</p><p>Nyní vypočtěte čtyři vyhlazovací parametry (tj. koeficienty, váhy, lambdy, parametry interpolace, nebo cokoli na trigram bigram unigram a uniform distribuci) z heldout dat algoritmem EM. (Pak udělejte totéž s použitím trénovacích dat: jaké vyhlazovací koeficienty jste dostali? Po odpovědi na tuto otázku je zahoďte!). Vzpomeňte si, že vyhlazovací model má následující podobu:</p><div contenteditable="false" class="mathjax-block md-end-block" id="mathjax-c43" cid="c43" mdtype="math_block"><span class="MathJax_Preview"></span><span class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="77.962ex" height="2.577ex" viewBox="-38.5 -806.1 33567 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex; margin-left: -0.089ex;"><defs><path stroke-width="1" id="E4-MJMATHI-70" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 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p_s(w_i|w_{i-2},w_{i-1}) = l_0p_0(w_i) + l_1p_1(w_i) + l_2p_2(w_i|w_{i-1})+l_3p_3(w_i|w_{i-2},w_{i-1})
</script></div><p>kde</p><div contenteditable="false" class="mathjax-block md-end-block" id="mathjax-c46" cid="c46" mdtype="math_block"><span class="MathJax_Preview"></span><span class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.772ex" height="2.344ex" viewBox="0 -755.9 8513 1009.2" role="img" focusable="false" style="vertical-align: -0.588ex;"><defs><path stroke-width="1" id="E5-MJMATHI-6C" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path stroke-width="1" id="E5-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E5-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path stroke-width="1" id="E5-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E5-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="1" id="E5-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path stroke-width="1" id="E5-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMATHI-6C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-30" x="422" y="-213"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-2B" x="974" y="0"></use><g transform="translate(1975,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMATHI-6C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-31" x="422" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-2B" x="2949" y="0"></use><g transform="translate(3950,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMATHI-6C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-32" x="422" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-2B" x="4925" y="0"></use><g transform="translate(5926,0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMATHI-6C" x="0" y="0"></use><use transform="scale(0.707)" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-33" x="422" y="-213"></use></g><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-3D" x="6956" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E5-MJMAIN-31" x="8012" y="0"></use></g></svg></span></span><script type="math/tex; mode=display" id="MathJax-Element-5">
l_0+l_1+l_2+l_3 = 1
</script></div><p>A konečně vypočítat cross-entropii testovacích dat s využitím nově vybudovaného vyhlazeného jazykového modelu. Nyní poupravte parametry vyhlazení následujícím způsobem: přidat <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E57-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E57-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E57-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-57">10\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-48-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E48-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="1" id="E48-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E48-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMAIN-32"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E48-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-48">20\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-56-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.723ex" height="0.71ex" viewBox="0 -203 1172.5 305.6" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E56-MJMAIN-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMAIN-2026" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-56">\ldots</script>,<span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E54-MJMAIN-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path><path stroke-width="1" id="E54-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E54-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-39"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-54">90\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-51-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E51-MJMAIN-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path><path stroke-width="1" id="E51-MJMAIN-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path><path stroke-width="1" id="E51-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E51-MJMAIN-39"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E51-MJMAIN-35" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E51-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-51">95\%</script> a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-52-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E52-MJMAIN-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path><path stroke-width="1" id="E52-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E52-MJMAIN-39"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E52-MJMAIN-39" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E52-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-52">99\%</script> rozdílu mezi trigram vyhlazení a <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-53-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="1.994ex" viewBox="0 -755.9 1279.5 858.4" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E53-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E53-MJMAIN-2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z"></path><path stroke-width="1" id="E53-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E53-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E53-MJMAIN-2E" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E53-MJMAIN-30" x="779" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-53">1.0</script> k jeho hodnotě, proporciálně uprav zbývající tři parametry (připomeňme, že mají součet 1!!). Potom nastavte trigram vyhlazovací parametr na <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E54-MJMAIN-39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path><path stroke-width="1" id="E54-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E54-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-39"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E54-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-54">90\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-55-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E55-MJMAIN-38" d="M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z"></path><path stroke-width="1" id="E55-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E55-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMAIN-38"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E55-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-55">80\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-56-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.723ex" height="0.71ex" viewBox="0 -203 1172.5 305.6" role="img" focusable="false" style="vertical-align: -0.238ex;"><defs><path stroke-width="1" id="E56-MJMAIN-2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E56-MJMAIN-2026" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-56">\ldots</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.261ex" height="2.227ex" viewBox="0 -806.1 1834.5 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E57-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="1" id="E57-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E57-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-31"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-30" x="500" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E57-MJMAIN-25" x="1001" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-57">10\%</script>, <span class="MathJax_Preview"></span><span class="MathJax_SVG" id="MathJax-Element-58-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.098ex" height="2.227ex" viewBox="0 -806.1 1334 958.9" role="img" focusable="false" style="vertical-align: -0.355ex;"><defs><path stroke-width="1" id="E58-MJMAIN-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path stroke-width="1" id="E58-MJMAIN-25" d="M465 605Q428 605 394 614T340 632T319 641Q332 608 332 548Q332 458 293 403T202 347Q145 347 101 402T56 548Q56 637 101 693T202 750Q241 750 272 719Q359 642 464 642Q580 642 650 732Q662 748 668 749Q670 750 673 750Q682 750 688 743T693 726Q178 -47 170 -52Q166 -56 160 -56Q147 -56 142 -45Q137 -36 142 -27Q143 -24 363 304Q469 462 525 546T581 630Q528 605 465 605ZM207 385Q235 385 263 427T292 548Q292 617 267 664T200 712Q193 712 186 709T167 698T147 668T134 615Q132 595 132 548V527Q132 436 165 403Q183 385 203 385H207ZM500 146Q500 234 544 290T647 347Q699 347 737 292T776 146T737 0T646 -56Q590 -56 545 0T500 146ZM651 -18Q679 -18 707 24T736 146Q736 215 711 262T644 309Q637 309 630 306T611 295T591 265T578 212Q577 200 577 146V124Q577 -18 647 -18H651Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E58-MJMAIN-30" x="0" y="0"></use><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#E58-MJMAIN-25" x="500" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-58">0\%</script> z jeho hodnoty a proporciálně uprav zbývající parametry. Vypočítejte cross-entropii na testovacích datech pro těchto 22 příkladů (původní + 11 zvýšení trigram parametru + 10 snížení trigram vyhlazovacího parametru). Vytvořte tabulky a grafy a vysvětlete výsledky. Také se snažte vysvětlit rozdíly mezi těmito dvěma jazyky na základě podobných statistik jako v úloze č.2, plus graf pokrytí (definovaný jako procento slov v testtovacích datech, které byly pozorovány v trénovacích datech).</p><p>Přiložte svůj zdrojový kód komentovaný takovým způsobem, že bude stačit přečtení komentářů na porozumění tomu, co jste udělali a jak jste to udělali.</p></div>
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