-
Notifications
You must be signed in to change notification settings - Fork 0
/
cs8850_20_model_comparison_1.html
418 lines (363 loc) · 21 KB
/
cs8850_20_model_comparison_1.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/font-awesome/4.5.0/css/font-awesome.min.css">
<!-- <link href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css" rel="stylesheet"/> -->
<script src="lib/colorbrewer.v1.min.js" charset="utf-8"></script>
<script src="lib/colorStringStandalone.js" charset="utf-8"></script>
<script type="text/javascript" src="lib/jquery-2.2.4.min.js"></script>
<title>Advanced Machine Learning</title>
<meta name="description" content="CS8850 GSU class">
<meta name="author" content="Sergey M Plis">
<meta name="apple-mobile-web-app-capable" content="yes">
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
<link rel="stylesheet" href="dist/reset.css">
<link rel="stylesheet" href="dist/reveal.css">
<!-- Code syntax highlighting -->
<link rel="stylesheet" href="plugin/highlight/monokai.css" id="highlight-theme">
<!-- <link rel="stylesheet" href="lib/css/zenburn.css"> -->
<link rel="stylesheet" href="css/custom.css">
<link rel="stylesheet" href="dist/theme/aml.css" id="theme">
<!-- Printing and PDF exports -->
<script>
var link = document.createElement( 'link' );
link.rel = 'stylesheet';
link.type = 'text/css';
link.href = window.location.search.match( /print-pdf/gi ) ? 'css/print/pdf.css' : 'css/print/paper.scss';
document.getElementsByTagName( 'head' )[0].appendChild( link );
</script>
</head>
<body>
<div class="reveal">
<!-- In between the <div="reveal"> and the <div class="slides">-->
<!-- <header style="position: absolute; top: 10px; left: 100px; z-index: 500; font-size:100px;background-color: rgba(0,0,0,0); text-align: center !important"></header> -->
<!-- In between the <div="reveal"> and the <div class="slides">-->
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section>
<section>
<p>
<h2>Advanced Machine Learning</h2>
<h3>20: Model Comparison I</h3>
<p>
</section>
<section>
<h3>Outline for the lecture</h3>
<ul>
<li class="fragment roll-in"> Bias-Variance Trade-off Revisited
<li class="fragment roll-in"> No Free Lunch Theorem
<li class="fragment roll-in"> Problems with Accuracy
<li class="fragment roll-in"> Confusion Matrix
</ul>
</section>
</section>
<!-- --------------------------------------------------------------------------->
<section>
<section>
<h2>Bias-variance trade off revisited</h2>
</section>
<section>
<h2>bandwidth selection for kde</h2>
<ul style="list-style-type: disk; font-size: 22pt">
<li class="fragment roll-in"> Pick $h$ that minimizes the error between
the estimated density and the true density
<li class="fragment roll-in"> Let us use MSE for measuring this error
<li class="fragment roll-in" style="list-style-type: none;"> $E\left[ (\prob{P$_{KDE}$}{\vec{x}} - \prob{P}{\vec{x}})^2 \right] $
<li class="fragment roll-in" style="list-style-type: none;"> $ = E\left[ \prob{P$_{KDE}$}{\vec{x}}^2 - 2 \prob{P$_{KDE}$}{\vec{x}} \prob{P}{\vec{x}} + \prob{P}{\vec{x}}^2\right]$
<li class="fragment roll-in" style="list-style-type: none;"> $ = E\left[ \prob{P$_{KDE}$}{\vec{x}}^2\right] - 2 E\left[\prob{P$_{KDE}$}{\vec{x}}\right] \prob{P}{\vec{x}} + \prob{P}{\vec{x}}^2$
<li class="fragment roll-in" style="list-style-type: none;"> Add and subtract $E^2\left[ \prob{P$_{KDE}$}{\vec{x}} \right]$
<li class="fragment roll-in" style="list-style-type: none;">
\begin{align}
= & E^2\left[ \prob{P$_{KDE}$}{\vec{x}} \right] - 2 E\left[\prob{P$_{KDE}$}{\vec{x}}\right] \prob{P}{\vec{x}} + \prob{P}{\vec{x}}^2 \\
& + E\left[ \prob{P$_{KDE}$}{\vec{x}}^2\right] - E^2\left[ \prob{P$_{KDE}$}{\vec{x}} \right]
\end{align}
<li class="fragment roll-in" style="list-style-type: none;">
\begin{align}
= & (E\left[ \prob{P$_{KDE}$}{\vec{x}} \right] - \prob{P}{\vec{x}})^2 + E\left[ \prob{P$_{KDE}$}{\vec{x}}^2\right] - E^2\left[ \prob{P$_{KDE}$}{\vec{x}}
\right]
\end{align}
<li class="fragment roll-in"> This is an example of <em>bias-variance tradeoff</em>
</ul>
</section>
<section data-fullscreen>
<h2>Bias-variance tradeoff</h2>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="700"
src="figures/bias_variance_targets.png" alt="bias variance">
</section>
<section>
<h2>Bias-Variance Decomposition for MSE </h2>
<row>
<col50>
<ul style="list-style-type: disk; font-size: 26px">
<li class="fragment roll-in"> MSE as an error measure
<li class="fragment roll-in" style="list-style-type: none;"> $E\left[ (\hat{\theta} - \theta)^2 \right] $
<li class="fragment roll-in" style="list-style-type: none;"> $ = E\left[ \hat{\theta}^2 - 2 \hat{\theta}\theta + \theta^2\right]$
<li class="fragment roll-in" style="list-style-type: none;"> $ = E\left[ \hat{\theta}^2\right] - 2 E\left[\hat{\theta}\right] \theta + \theta^2$
<li class="fragment roll-in" style="list-style-type: none;"> Add and subtract $E\left[ \hat{\theta} \right]^2$
<li class="fragment roll-in" style="list-style-type: none;">
\begin{align}
= & E\left[ \hat{\theta} \right]^2 - 2 E\left[\hat{\theta}\right] \theta + \theta^2 \\
& + E\left[ \hat{\theta}^2\right] - E\left[ \hat{\theta} \right]^2
\end{align}
<li class="fragment roll-in" style="list-style-type: none;">
\begin{align}
= & (E\left[ \hat{\theta} \right] - \theta)^2 + E\left[ \hat{\theta}^2\right] - E\left[ \hat{\theta} \right]^2
\end{align}
</ul>
</col50>
<col50>
<ul style="list-style-type: none; font-size: 26px">
<li class="fragment roll-in"> <i class="far fa-grimace"></i> Is not variance $E\left[ (\hat{\theta} - E\left[\hat{\theta}\right])^2\right]$?
<li class="fragment roll-in"> $E\left[ (\hat{\theta} - E\left[\hat{\theta}\right])^2\right]$
<li class="fragment roll-in"> $= E\left[ \hat{\theta}^2 - 2\hat{\theta}E\left[\hat{\theta}\right] + E\left[\hat{\theta}\right]^2 \right]$
<li class="fragment roll-in"> $= E\left[ \hat{\theta}^2 \right] - 2 E\left[ \hat{\theta}\right]E\left[\hat{\theta}\right] + E\left[\hat{\theta}\right]^2$
<li class="fragment roll-in"> $= E\left[ \hat{\theta}^2 \right] - 2 E\left[\hat{\theta}\right]^2 + E\left[\hat{\theta}\right]^2$
<li class="fragment roll-in"> $= E\left[ \hat{\theta}^2 \right] - E\left[\hat{\theta}\right]^2$
</ul>
</col50>
</row>
</section>
<section>
<h2>if data is all we have</h2>
<h3>how do we know if we're doing well?</h3>
<h3>how do we know which model is better?</h3>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="100%"
src="figures/train_validation_test.svg" alt="split">
</section>
<section data-fullscreen>
<h2>Bias-variance tradeoff</h2>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="900"
src="figures/bias_variance_fht.svg" alt="bias variance">
</section>
<section>
<div id="header-right" style="margin-right: -120px; margin-top: -20px;">
<img width="270" src="figures/polyfit.gif" alt="polyfit">
</div>
<h2>Bias-variance tradeoff</h2>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="900"
src="figures/model_complexity.png" alt="model complexity">
</section>
<section>
<h2>Select a model that generalizes best</h2>
<!-- <blockquote style="background-color: #93a1a1; color: #fdf6e3; font-size: 38px; width=100%"> -->
<blockquote dark style="font-size: 34px;">
$E\left[ (g(\theta; {\cal D}) - G(\theta))^2 \right] = \mbox{bias of }g + \mbox{ variance of }g$, <br>
where $g$ is estimated and $G$ is true generalization error
</blockquote>
<row>
<col50>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1); " width="100%" class="fragment" data-fragment-index="0"
src="figures/model_selection_unbiased.svg" alt="unbiased">
</col50>
<col50>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1); " width="100%" class="fragment" data-fragment-index="1"
src="figures/model_selection_low_variance.svg" alt="low variance">
</col50>
</row>
<div class="slide-footer">
<a href="http://www.jmlr.org/papers/volume11/cawley10a/cawley10a.pdf">On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation</a>
</div>
</section>
<section data-vertical-align-top data-background="figures/kde_bias_variance.svg" data-background-size="contain">
<h2>Bias-variance tradeoff</h2>
<!-- <img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="900" -->
<!-- src="figures/kde_bias_variance.svg" alt="kde bias variance"> -->
</section>
<section data-fullscreen>
<h2>Double-descent curve</h2>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="100%"
src="figures/double_descent_curve.svg" alt="double descent">
<div class="slide-footer">
<a href="https://arxiv.org/pdf/1812.11118.pdf">Reconciling modern machine learning practice
and the bias-variance trade-of</a>
</div>
</section>
</section>
<!-- --------------------------------------------------------------------------->
<section>
<section>
<h2>No free lunch theorem</h2>
</section>
<section data-fullscreen>
<img height="100%"
src="figures/universal_remote.png" alt="remote">
</section>
<section data-fullscreen data-background="figures/mousetrap.jpeg">
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1); " width="100%"
src="figures/koshki_myshki_lunch.svg" alt="cats and mice">
<div class="slide-footer">
<a href="https://acomics.ru/~rats-n-cats/254">Кошки-мышки (rat's n cats)</a>
</div>
</section>
<section data-background="figures/Hume.jpg" data-background-size="cover">
<blockquote style="background-color: #93a1a1; color: #fdf6e3; font-size: 36px; width: 100%; margin-top: 150px; text-align: left;">
"Even after the observation of the frequent
conjunction of objects, we have no reason to
draw any inference concerning any object beyond
those of which we have had experience."<p> David
Hume, in A Treatise of Human Nature, Book I,
part 3, Section 12.
</blockquote>
</section>
<section data-fullscreen data-background="figures/wolpertspapers_trans.png">
<div id="header-right">
<img style="border:0; box-shadow: 0px 10px 10px rgba(150, 150, 150, 1); " width="200"
src="figures/David-Wolpert.jpg" alt="David Wolpert">
</div>
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1); " width="100%"
src="figures/wolpertpapers.png" alt="wolperts">
<div class="slide-footer">
<a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.390.9412&rep=rep1&type=pdf">The Lack of A Priori Distinction Between Learning Algorithms</a> and <a href="https://ti.arc.nasa.gov/m/profile/dhw/papers/78.pdf">No Free Lunch Theorems for Optimization</a>
</div>
</section>
<section>
<h2>No free lunch theorem (simply put)</h2>
<blockquote>
There is not a universally good algorithms that's best on all possible test data!
</blockquote>
</section>
</section>
<!-- --------------------------------------------------------------------------->
<section>
<section>
<h2>Problems with accuracy</h2>
</section>
</section>
<!-- --------------------------------------------------------------------------->
<section>
<section>
<h2>Confusion Matrix</h2>
</section>
<section>
<img width="100%" src="figures/confusion_insilico.png" alt="insilico">
</section>
</section>
</div>
</div>
<script src="dist/reveal.js"></script>
<link rel="stylesheet" href="plugin/highlight/monokai.css">
<script src="plugin/highlight/highlight.js"></script>
<script src="plugin/math/math.js"></script>
<script src="plugin/chalkboard/plugin.js"></script>
<script src="plugin/notes/notes.js"></script>
<script src="plugin/zoom/zoom.js"></script>
<script src="plugin/fullscreen/fullscreen.js"></script>
<script src="plugin/menu/menu.js"></script>
<script src="plugin/verticator/verticator.js"></script>
<link rel="stylesheet" href="plugin/verticator/verticator.css">
<script>
// Full list of configuration options available at:
// https://github.com/hakimel/reveal.js#configuration
Reveal.initialize({
// history: true,
hash: true,
margin: 0.01,
minScale: 0.01,
maxScale: 0.93,
menu: {
themes: false,
openSlideNumber: true,
openButton: false,
},
chalkboard: {
boardmarkerWidth: 1,
chalkWidth: 2,
chalkEffect: 1,
toggleNotesButton: false,
toggleChalkboardButton: false,
slideWidth: Reveal.width,
slideHeight: Reveal.height,
// src: "chalkboards/chalkboard_em2.json",
readOnly: false,
theme: "blackboard",
eraser: { src: "plugin/chalkboard/img/sponge.png", radius: 30},
},
math: {
mathjax: 'https://cdn.jsdelivr.net/gh/mathjax/[email protected]/MathJax.js',
config: 'TeX-AMS_SVG-full',
// pass other options into `MathJax.Hub.Config()`
TeX: {
Macros: {
RR: '\\mathbb{R}',
PP: '\\mathbb{P}',
EE: '\\mathbb{E}',
NN: '\\mathbb{N}',
vth: '\\vec{\\theta}',
loss: '{\\cal l}',
hclass: '{\\cal H}',
CD: '{\\cal D}',
def: '\\stackrel{\\text{def}}{=}',
pag: ['\\text{pa}_{{\cal G}^{#1}}(#2)}', 2],
vec: ['\\boldsymbol{\\mathbf #1}', 1],
set: [ '\\left\\{#1 \\; : \\; #2\\right\\}', 2 ],
bm: ['\\boldsymbol{\\mathbf #1}', 1],
argmin: ['\\operatorname\{arg\\,min\\,\}'],
argmax: ['\\operatorname\{arg\\,max\\,\}'],
prob: ["\\mbox{#1$\\left(#2\\right)$}", 2],
},
loader: {load: ['[tex]/color']},
extensions: ["color.js"],
tex: {packages: {'[+]': ['color']}},
svg: {
fontCache: 'global'
}
}
},
plugins: [ Verticator, RevealMath, RevealChalkboard, RevealHighlight, RevealNotes, RevealZoom, RevealMenu ],
});
Reveal.configure({ fragments: true }); // set false when developing to see everything at once
Reveal.configure({ slideNumber: true });
//Reveal.configure({ history: true });
Reveal.configure({ slideNumber: 'c / t' });
Reveal.addEventListener( 'darkside', function() {
document.getElementById('theme').setAttribute('href','dist/theme/aml_dark.css');
}, false );
Reveal.addEventListener( 'brightside', function() {
document.getElementById('theme').setAttribute('href','dist/theme/aml.css');
}, false );
</script>
<style type="text/css">
/* 1. Style header/footer <div> so they are positioned as desired. */
#header-left {
position: absolute;
top: 0%;
left: 0%;
}
#header-right {
position: absolute;
top: 0%;
right: 0%;
}
#footer-left {
position: absolute;
bottom: 0%;
left: 0%;
}
</style>
<!-- // 2. Create hidden header/footer -->
<div id="hidden" style="display:none;">
<div id="header">
<div id="header-left"><h4>CS8850</h4></div>
<div id="header-right"><h4>Advanced Machine Learning</h4></div>
<div id="footer-left">
<img style="border:0; box-shadow: 0px 0px 0px rgba(150, 150, 255, 1);" width="200"
src="figures/valentino.png" alt="robot learning">
</div>
</div>
</div>
<script type="text/javascript">
// 3. On Reveal.js ready event, copy header/footer <div> into each `.slide-background` <div>
var header = $('#header').html();
if ( window.location.search.match( /print-pdf/gi ) ) {
Reveal.addEventListener( 'ready', function( event ) {
$('.slide-background').append(header);
});
}
else {
$('div.reveal').append(header);
}
</script>
</body>
</html>