From 926d0b37a01cf5e54deca8065bf9bc411c4850ef Mon Sep 17 00:00:00 2001
From: Rickustc <1072105344@qq.com>
Date: Sat, 27 Apr 2024 19:57:44 +0800
Subject: [PATCH] Site updated: 2024-04-27 19:57:44

---
 .../index.html"                                            | 5 ++++-
 2024/GAN/index.html                                        | 5 ++++-
 .../index.html"                                            | 5 ++++-
 .../index.html"                                            | 5 ++++-
 archives/2023/09/index.html                                | 5 ++++-
 archives/2023/index.html                                   | 5 ++++-
 archives/2024/04/index.html                                | 5 ++++-
 archives/2024/index.html                                   | 5 ++++-
 archives/index.html                                        | 5 ++++-
 categories/index.html                                      | 7 +++++--
 content.json                                               | 2 +-
 curriculum/index.html                                      | 5 ++++-
 index.html                                                 | 5 ++++-
 rick/cv.html                                               | 5 ++++-
 rick/index.html                                            | 5 ++++-
 rick/temp.html                                             | 5 ++++-
 tags/DGM/index.html                                        | 5 ++++-
 tags/LVM/index.html                                        | 5 ++++-
 tags/VAE/index.html                                        | 5 ++++-
 tags/index.html                                            | 7 +++++--
 .../index.html"                                            | 5 ++++-
 "tags/\346\255\243\345\210\231\345\214\226/index.html"     | 5 ++++-
 22 files changed, 87 insertions(+), 24 deletions(-)

diff --git "a/2023/\346\267\261\345\272\246\345\255\246\344\271\240\344\270\255\347\232\204\346\255\243\345\210\231\345\214\226/index.html" "b/2023/\346\267\261\345\272\246\345\255\246\344\271\240\344\270\255\347\232\204\346\255\243\345\210\231\345\214\226/index.html"
index c855a81..b78f8f4 100644
--- "a/2023/\346\267\261\345\272\246\345\255\246\344\271\240\344\270\255\347\232\204\346\255\243\345\210\231\345\214\226/index.html"
+++ "b/2023/\346\267\261\345\272\246\345\255\246\344\271\240\344\270\255\347\232\204\346\255\243\345\210\231\345\214\226/index.html"
@@ -84,7 +84,10 @@ <h1 id="reference">Reference</h1>
             s.src = '//' + 'nothing' + '.disqus.com/embed.js';
             s.setAttribute('data-timestamp', +new Date());
             (d.head || d.body).appendChild(s);
-        })();</script></div></div></div><div class="column column-left is-4-tablet is-4-desktop is-3-widescreen  order-1"><div class="card widget" data-type="profile"><div class="card-content"><nav class="level"><div class="level-item has-text-centered flex-shrink-1"><div><figure class="image is-128x128 mx-auto mb-2"><img class="avatar" src="/img/avatar.png" alt="Rick Wang"></figure><p class="title is-size-4 is-block" style="line-height:inherit;">Rick Wang</p><p class="is-size-6 is-block">AI Engineering ComputerVision MachineLearning</p><p class="is-size-6 is-flex justify-content-center"><i class="fas fa-map-marker-alt mr-1"></i><span>Shanghai China</span></p></div></div></nav><nav class="level is-mobile"><div class="level-item has-text-centered is-marginless"><div><p class="heading">Posts</p><a href="/archives"><p class="title">4</p></a></div></div><div class="level-item has-text-centered is-marginless"><div><p class="heading">Categories</p><a href="/categories"><p class="title">0</p></a></div></div><div class="level-item has-text-centered is-marginless"><div><p class="heading">Tags</p><a href="/tags"><p class="title">5</p></a></div></div></nav><div class="level"><a class="level-item button is-primary is-rounded" href="https://github.com/Rickustc" target="_blank" rel="noopener">Follow</a></div><div class="level is-mobile is-multiline"><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="Github" href="https://github.com/Rickustc"><i class="fab fa-github"></i></a><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="Twitter" href="https://twitter.com/rick_drb"><i class="fab fa-twitter"></i></a><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="RSS" href="/"><i class="fas fa-rss"></i></a></div></div></div><!--!--><!--!--><div class="card widget" data-type="subscribe-email"><div class="card-content"><div class="menu"><h3 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class="input" name="email" type="email" placeholder="Email"><span class="icon is-small is-left"><i class="fas fa-envelope"></i></span></div><div class="control"><input class="button" type="submit" value="Subscribe"></div></div></form></div></div></div><div class="column-right-shadow is-hidden-widescreen"></div></div><div class="column column-right is-4-tablet is-4-desktop is-3-widescreen is-hidden-touch is-hidden-desktop-only order-3"><div class="card widget" data-type="recent-posts"><div class="card-content"><h3 class="menu-label">Recents</h3><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-26T08:11:47.000Z">2024-04-26</time></p><p class="title"><a href="/2024/GAN/">GAN</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/">深度学习中的正则化</a></p></div></article></div></div><div class="card widget" data-type="archives"><div class="card-content"><div class="menu"><h3 class="menu-label">Archives</h3><ul class="menu-list"><li><a class="level is-mobile" href="/archives/2024/"><span class="level-start"><span class="level-item">2024</span></span><span class="level-end"><span class="level-item tag">3</span></span></a></li><li><a class="level is-mobile" href="/archives/2023/"><span class="level-start"><span class="level-item">2023</span></span><span class="level-end"><span class="level-item tag">1</span></span></a></li></ul></div></div></div><div class="card widget" data-type="tags"><div class="card-content"><div class="menu"><h3 class="menu-label">Tags</h3><div class="field is-grouped is-grouped-multiline"><div class="control"><a class="tags has-addons" href="/tags/DGM/"><span class="tag">DGM</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/LVM/"><span class="tag">LVM</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/VAE/"><span class="tag">VAE</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/%E6%A6%82%E7%8E%87%E8%AE%BA-ML%E6%95%B0%E5%AD%A6/"><span class="tag">概率论 ML数学</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/%E6%AD%A3%E5%88%99%E5%8C%96/"><span class="tag">正则化</span><span class="tag">1</span></a></div></div></div></div></div></div></div></div></section><footer class="footer"><div class="container"><div class="level"><div class="level-start"><a class="footer-logo is-block mb-2" href="/"><img src="/img/agumon.svg" alt="Rick Universe" height="28"></a><p class="is-size-7"><span>&copy; 2024 Rick Wang</span>  Powered by <a href="https://hexo.io/" target="_blank" rel="noopener">Hexo</a> &amp; <a href="https://github.com/ppoffice/hexo-theme-icarus" target="_blank" rel="noopener">Icarus</a><br><span id="busuanzi_container_site_uv">Visited by <span id="busuanzi_value_site_uv">0</span> users</span></p><p class="is-size-7">© 2019</p></div><div class="level-end"><div class="field has-addons"><p class="control"><a 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{
+        })();</script></div></div></div><div class="column column-left is-4-tablet is-4-desktop is-3-widescreen  order-1"><div class="card widget" data-type="profile"><div class="card-content"><nav class="level"><div class="level-item has-text-centered flex-shrink-1"><div><figure class="image is-128x128 mx-auto mb-2"><img class="avatar" src="/img/avatar.png" alt="Rick Wang"></figure><p class="title is-size-4 is-block" style="line-height:inherit;">Rick Wang</p><p class="is-size-6 is-block" style="white-space: pre-line">AI Engineering     
+ComputerVision
+MachineLearning
+</p><p class="is-size-6 is-flex justify-content-center"><i class="fas fa-map-marker-alt mr-1"></i><span>Shanghai China</span></p></div></div></nav><nav class="level is-mobile"><div class="level-item has-text-centered is-marginless"><div><p class="heading">Posts</p><a href="/archives"><p class="title">4</p></a></div></div><div class="level-item has-text-centered is-marginless"><div><p class="heading">Categories</p><a href="/categories"><p class="title">0</p></a></div></div><div class="level-item has-text-centered is-marginless"><div><p class="heading">Tags</p><a href="/tags"><p class="title">5</p></a></div></div></nav><div class="level"><a class="level-item button is-primary is-rounded" href="https://github.com/Rickustc" target="_blank" rel="noopener">Follow</a></div><div class="level is-mobile is-multiline"><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="Github" href="https://github.com/Rickustc"><i class="fab fa-github"></i></a><a 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class="menu-label">Recents</h3><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-26T08:11:47.000Z">2024-04-26</time></p><p class="title"><a href="/2024/GAN/">GAN</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/">深度学习中的正则化</a></p></div></article></div></div><div class="card widget" data-type="archives"><div class="card-content"><div class="menu"><h3 class="menu-label">Archives</h3><ul class="menu-list"><li><a class="level is-mobile" href="/archives/2024/"><span class="level-start"><span class="level-item">2024</span></span><span class="level-end"><span class="level-item tag">3</span></span></a></li><li><a class="level is-mobile" href="/archives/2023/"><span class="level-start"><span class="level-item">2023</span></span><span class="level-end"><span class="level-item tag">1</span></span></a></li></ul></div></div></div><div class="card widget" data-type="tags"><div class="card-content"><div class="menu"><h3 class="menu-label">Tags</h3><div class="field is-grouped is-grouped-multiline"><div class="control"><a class="tags has-addons" href="/tags/DGM/"><span class="tag">DGM</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/LVM/"><span class="tag">LVM</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/VAE/"><span class="tag">VAE</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/%E6%A6%82%E7%8E%87%E8%AE%BA-ML%E6%95%B0%E5%AD%A6/"><span class="tag">概率论 ML数学</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/%E6%AD%A3%E5%88%99%E5%8C%96/"><span class="tag">正则化</span><span class="tag">1</span></a></div></div></div></div></div></div></div></div></section><footer class="footer"><div class="container"><div class="level"><div class="level-start"><a class="footer-logo is-block mb-2" href="/"><img src="/img/agumon.svg" alt="Rick Universe" height="28"></a><p class="is-size-7"><span>&copy; 2024 Rick Wang</span>  Powered by <a href="https://hexo.io/" target="_blank" rel="noopener">Hexo</a> &amp; <a href="https://github.com/ppoffice/hexo-theme-icarus" target="_blank" rel="noopener">Icarus</a><br><span id="busuanzi_container_site_uv">Visited by <span id="busuanzi_value_site_uv">0</span> users</span></p><p class="is-size-7">© 2019</p></div><div class="level-end"><div class="field has-addons"><p class="control"><a class="button is-transparent is-large" target="_blank" rel="noopener" title="Creative Commons" href="https://creativecommons.org/"><i class="fab fa-creative-commons"></i></a></p><p class="control"><a class="button is-transparent is-large" target="_blank" rel="noopener" title="Attribution 4.0 International" href="https://creativecommons.org/licenses/by/4.0/"><i class="fab fa-creative-commons-by"></i></a></p><p class="control"><a class="button is-transparent is-large" target="_blank" rel="noopener" title="Download on GitHub" href="https://github.com/ppoffice/hexo-theme-icarus"><i class="fab 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             article: {
                 highlight: {
                     clipboard: true,
diff --git a/2024/GAN/index.html b/2024/GAN/index.html
index a8d302e..c99f349 100644
--- a/2024/GAN/index.html
+++ b/2024/GAN/index.html
@@ -44,7 +44,10 @@
             s.src = '//' + 'nothing' + '.disqus.com/embed.js';
             s.setAttribute('data-timestamp', +new Date());
             (d.head || d.body).appendChild(s);
-        })();</script></div></div></div><div class="column column-left is-4-tablet is-4-desktop is-3-widescreen  order-1"><div class="card widget" data-type="profile"><div class="card-content"><nav class="level"><div class="level-item has-text-centered flex-shrink-1"><div><figure class="image is-128x128 mx-auto mb-2"><img class="avatar" src="/img/avatar.png" alt="Rick Wang"></figure><p class="title is-size-4 is-block" style="line-height:inherit;">Rick Wang</p><p class="is-size-6 is-block">AI Engineering ComputerVision MachineLearning</p><p class="is-size-6 is-flex justify-content-center"><i class="fas fa-map-marker-alt mr-1"></i><span>Shanghai China</span></p></div></div></nav><nav class="level is-mobile"><div class="level-item has-text-centered is-marginless"><div><p class="heading">Posts</p><a href="/archives"><p class="title">4</p></a></div></div><div class="level-item has-text-centered is-marginless"><div><p class="heading">Categories</p><a href="/categories"><p class="title">0</p></a></div></div><div class="level-item has-text-centered is-marginless"><div><p class="heading">Tags</p><a href="/tags"><p class="title">5</p></a></div></div></nav><div class="level"><a class="level-item button is-primary is-rounded" href="https://github.com/Rickustc" target="_blank" rel="noopener">Follow</a></div><div class="level is-mobile is-multiline"><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="Github" href="https://github.com/Rickustc"><i class="fab fa-github"></i></a><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="Twitter" href="https://twitter.com/rick_drb"><i class="fab fa-twitter"></i></a><a class="level-item button is-transparent is-marginless" target="_blank" rel="noopener" title="RSS" href="/"><i class="fas fa-rss"></i></a></div></div></div><!--!--><!--!--><div class="card widget" data-type="subscribe-email"><div class="card-content"><div class="menu"><h3 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class="menu-label">Recents</h3><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-26T08:11:47.000Z">2024-04-26</time></p><p class="title"><a href="/2024/GAN/">GAN</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a 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diff --git "a/2024/VAE\357\274\232\345\217\230\345\210\206\346\216\250\346\226\255\343\200\201MC\344\274\260\350\256\241\345\222\214\351\207\215\350\246\201\346\200\247\351\207\207\346\240\267/index.html" "b/2024/VAE\357\274\232\345\217\230\345\210\206\346\216\250\346\226\255\343\200\201MC\344\274\260\350\256\241\345\222\214\351\207\215\350\246\201\346\200\247\351\207\207\346\240\267/index.html"
index cf1c5ab..ee915ba 100644
--- "a/2024/VAE\357\274\232\345\217\230\345\210\206\346\216\250\346\226\255\343\200\201MC\344\274\260\350\256\241\345\222\214\351\207\215\350\246\201\346\200\247\351\207\207\346\240\267/index.html"
+++ "b/2024/VAE\357\274\232\345\217\230\345\210\206\346\216\250\346\226\255\343\200\201MC\344\274\260\350\256\241\345\222\214\351\207\215\350\246\201\346\200\247\351\207\207\346\240\267/index.html"
@@ -137,7 +137,10 @@ <h1 id="变分推断">变分推断</h1>
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index 622876d..6ffdf65 100644
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class="menu-label">Recents</h3><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-26T08:11:47.000Z">2024-04-26</time></p><p class="title"><a href="/2024/GAN/">GAN</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a 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diff --git a/content.json b/content.json
index 66d076b..e1793d5 100644
--- a/content.json
+++ b/content.json
@@ -1 +1 @@
-{"posts":[{"title":"GAN","text":"","link":"/2024/GAN/"},{"title":"VAE：变分推断、MC估计和重要性采样","text":"本文将从表征学习的角度以及隐变量模型的角度探讨VAE模型，重点讲述VAE的三个技术 隐变量的意义 高斯混合模型 VAE从概率密度估计的角度来说是一种mixture model 基本的高斯混合模型写做： \\(p(x) = \\sum_{i=1}^{k} w_i \\mathcal{N}(x | \\mu_i, \\Sigma_i)\\) 其中的i是指第i个高斯分布，\\(u_i\\)和\\(\\Sigma_i\\)​指的是第i个高斯分布的均值和方差 但是高斯混合模型的拟合能力是有限的，假如我们用一簇无穷多的高斯分布来拟合最终的分布, 那这个拟合能力不久非常好了吗？怎么去建模这个无穷多(infinite)的分布呢? 这图摘自S9868 Deep learning课程，非常形象的展示了混合模型做了什么：用高斯分布把数据流形填满 怎么做无限混合呢？VAE给出的解答是把累加变成了积分 \\(p_{\\theta}(x) = \\int_{z} \\mathcal{N}(x; g_{\\theta}(z), \\Sigma_{\\theta}(z)) \\mathcal{N}(z; 0, I) dz\\) 也即是假设混合高斯的权重符合一个分布，属于隐变量\\(z\\)，并且我们的高斯分布是隐变量参数化的结果,即式中的条件分布,分别参数化了高斯分布的均值\\(g_{\\theta}\\)和方差\\(\\Sigma_{\\theta}(z))\\) S9868 也给出了无限混合的感性可视化，参数化帮助我们的mixture model更加的flexible了，能自己学习怎么去填满这个数据流形。 这里的\\(P(z)\\)和\\(P_\\theta(x|z)\\)​都假设的高斯分布，当然我们也能make an infinite mixture of the autoregressive distribution and so on. ,从这个角度来说mixture分布是meta model 可以用其他的密度估计模型替代 这个概率摸底建模是一个积分的无穷项，这里我们需要用到统计学的一个基本技术，用MC采样来估计这个积分 \\(p_{\\theta}(x) = \\int p_{\\theta}(x|z)p_z(z)dz = \\mathbb{E}_{z \\sim p_z(z)}[p_{\\theta}(x|z)] \\approx \\frac{1}{M} \\sum_{i=1}^{M} p_{\\theta}(x|z^{(i)}), \\quad z^{(i)} \\sim p_z\\) MC采样的直观理解是求平均值的这个过程本身就蕴含了采样过程 当我们概率建模有了，接下来就是计算极大似然来优化参数！ \\(E_{x \\sim p_{data} }log P_{\\theta}(x)\\)​ 极大似然认为最优的分布参数是一个定值，因此我们把数据扔进去优化一个maximal的似然值 \\(\\theta^* = \\underset{\\theta}{\\arg\\min} \\frac{1}{M} \\sum_{i=1}^{N} \\log \\left( \\sum_{j=1}^{M} \\mathcal{N}\\left(x^{(i)}; g_{\\theta}^{\\mu}\\left(z^{(j)}\\right), g_{\\theta}^{\\Sigma}\\left(z^{(j)}\\right)\\right) \\right)\\) 以上都是在拟合概率，但是对于神经网络而言我们有的标签不是概率这太抽象了，我们只有从Pdata中获得的样本,如何优化这个混合模型？ 把方差固定，优化这个似然值就变成优化\\(||x-g_{\\theta}^{\\mu}||\\),训练的步骤是我们采样一堆隐变量z，扔进网络\\(g_{\\theta}\\)中产生一堆高斯分布的均值，然后在和一个batch的样本\\(x\\)​ 计算L2norm，这就是我们要的似然值. 重要性采样 我们在建模概率的时候是利用的MC采样来估计积分 \\(p_{\\theta}(x) \\approx \\frac{1}{M} \\left( p_{\\theta}(x|z^{(1)}) + p_{\\theta}(x|z^{(2)}) + p_{\\theta}(x|z^{(3)}) + \\ldots \\right)\\) 遇到一个问题，往往高维空间MC采样的效率很低，往往会变成这样： \\(p_{\\theta}(x) \\approx \\frac{1}{M} \\left( 0 + p_{\\theta}(x|z^{(2)}) + 0 + \\ldots \\right)\\)​ 这意味着要想精确的估计概率，必须要大量的采样，采样效率很低 这里引出本文的第二个技术，重要性采样： \\(p_{\\theta}(x) = \\mathbb{E}_{z \\sim p_z}[p_{\\theta}(x|z)] = \\int p_z(z)p_{\\theta}(x|z)dz = \\int \\frac{p_z(z)}{q_z(z)} p_{\\theta}(x|z)q_z(z)dz = \\mathbb{E}_{z \\sim q_z}\\left[\\frac{p_z(z)}{q_z(z)} p_{\\theta}(x|z)\\right]\\) 重要性采样给出一种不用在原始分布p中采样，而在新的分布q中采样，这是一种减少方差的采样技术 最优的\\(q(z)\\)正比于\\(p(z)P_{\\theta}(x|z)\\) 后者正比于\\(P(x,z)\\) 它又正比于\\(p_{\\theta}(z|x)\\)，所以可以证明最优的\\(q(z)\\)等于\\(p_{\\theta}(z|x)\\) \\(p_{\\theta}(x) \\approx \\frac{1}{M} \\sum_{j=1}^{M} \\frac{p_z(z^{(j)})}{p_{\\theta}(z^{(j)}|x)} p_{\\theta}(x|z^{(j)})\\), \\(z^{(j)} \\sim p_{\\theta}(Z|x)\\) 最开始的 在重要性采样的语境下，\\(p_{\\theta}(z|x)\\) 这个z就是和建模\\(p_{\\theta}(x)\\)最相关的z 变分推断 高斯混合模型的有点是隐变量分布是高斯分布，重要性采样的效率更高但是这里又出现了一个难以采样的分布\\(P_{\\theta}(z|x)\\)​​ 这个时候引入最后一个重要的技巧，变分推断(Variational inference) 顺便吐槽一句，很多的教程都从变分推断出发，丝毫不讨论生成的过程，这和我生成模型又有什么关系呢 :D","link":"/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/"},{"title":"贝叶斯的两个理解角度","text":"When you have eliminated the impossible, whatever remains, however improbable, must be the truth... 时间线： 托马斯·贝叶斯（Thomas Bayes）在1763提出，用来解决逆概率问题 贝叶斯： 根据证据修正先验 推断因子 下面具体解释这两个角度 怎么理解修正先验？ \\(P(A|B) = P(A)\\frac{P(B|A)}{P(B)}\\) P(A)是先验概率。 P(B|A)/P(B)称为\"可能性函数\"（Likelyhood），这是一个调整因子，也就是新信息B带来的调整，作用是将先验概率（之前的主观判断）调整到更接近真实概率。 如果\"可能性函数\"P(B|A)/P(B)&gt;1，意味着\"先验概率\"被增强，事件A的发生的可能性变大； 如果\"可能性函数\"=1，意味着B事件无助于判断事件A的可能性； 如果\"可能性函数\"&lt;1，意味着\"先验概率\"被削弱，事件A的可能性变小。 怎么理解推断因子？ \\(P(z_j|x) = \\frac{P(z_j,x)}{\\sum_z P(x|z_i)P(z_i)}\\) 事实上，当初统计学家在回归问题中引入L2正则，只是出于防止矩阵病态造成不可求逆矩阵，后来才发现结果居然更好了。 当我们对抛硬币做做参数估计的时候，加入10次都是正的那很容易得到一个很不准的MLE 参数估计： 点估计:MLE，MAP(通常是优化问题)，矩估计，贝叶斯估计 reference： 极大似然估计、极大后验估计和贝叶斯估计 https://www.zhihu.com/question/61298823/answer/1545994922","link":"/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/"},{"title":"深度学习中的正则化","text":"最近在看集成学习，集成学习中对基学习器的要求是和而不同，及满足两个条件：误差 \\(\\epsilon &lt;0.5\\)且具有多样性，由此引出一系列多样性方法，其和正则化非常类似。借助课上提到的框架对正则化进行梳理。并且试图统一绝大部分ml和dl的正则化方法 1.正则化的定义 正则化：旨在通过对学习算法的修改，减少泛化误差（而不是训练误差，并且可能以提高训练误差为代价） 2.正则化的背景：方差与偏差，欠拟合与过拟合 统计学中的过拟合欠拟合：对应模型的小偏差大方差 方差偏差 模型训练中的过拟合：训练刚开始的时候，训练误差和测试误差都下降。在到达一个临界点之后，训练集的误差下降，测试集的误差上升了，这个时候就进入了过拟合区域 过拟合欠拟合 3.正则化的分类 3.1 对输入样本 对输入样本扰动敏感的学习器：神经网络，决策树等 对输入样本扰动不敏感的学习器：线性学习器，支持向量机（这俩都是线性分类器），朴素贝叶斯，k近邻 数据增强： 数据扰动（噪声） 3.2 对输入属性 Bagging 降维：PCA，SVD，AutoEncoder，LDA 特征选择 3.3 对输出属性 label smooth Dropout 3.4 对模型参数 L1正则化 L2正则化 SVM中的松弛变量 参数共享（CNN，RNN） 3.5 对模型训练 半监督学习 多任务学习 提前终止 对抗训练 知识蒸馏 多级别监督loss Reference 正则化详解 正则化总结的比较好比较全面的文章","link":"/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/"}],"tags":[{"name":"DGM","slug":"DGM","link":"/tags/DGM/"},{"name":"LVM","slug":"LVM","link":"/tags/LVM/"},{"name":"VAE","slug":"VAE","link":"/tags/VAE/"},{"name":"概率论 ML数学","slug":"概率论-ML数学","link":"/tags/%E6%A6%82%E7%8E%87%E8%AE%BA-ML%E6%95%B0%E5%AD%A6/"},{"name":"正则化","slug":"正则化","link":"/tags/%E6%AD%A3%E5%88%99%E5%8C%96/"}],"categories":[],"pages":[]}
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+{"posts":[{"title":"GAN","text":"","link":"/2024/GAN/"},{"title":"VAE：变分推断、MC估计和重要性采样","text":"本文将从表征学习的角度以及隐变量模型的角度探讨VAE模型，重点讲述VAE的三个技术 隐变量的意义 高斯混合模型 VAE从概率密度估计的角度来说是一种mixture model 基本的高斯混合模型写做： \\(p(x) = \\sum_{i=1}^{k} w_i \\mathcal{N}(x | \\mu_i, \\Sigma_i)\\) 其中的i是指第i个高斯分布，\\(u_i\\)和\\(\\Sigma_i\\)​指的是第i个高斯分布的均值和方差 但是高斯混合模型的拟合能力是有限的，假如我们用一簇无穷多的高斯分布来拟合最终的分布, 那这个拟合能力不久非常好了吗？怎么去建模这个无穷多(infinite)的分布呢? 这图摘自S9868 Deep learning课程，非常形象的展示了混合模型做了什么：用高斯分布把数据流形填满 怎么做无限混合呢？VAE给出的解答是把累加变成了积分 \\(p_{\\theta}(x) = \\int_{z} \\mathcal{N}(x; g_{\\theta}(z), \\Sigma_{\\theta}(z)) \\mathcal{N}(z; 0, I) dz\\) 也即是假设混合高斯的权重符合一个分布，属于隐变量\\(z\\)，并且我们的高斯分布是隐变量参数化的结果,即式中的条件分布,分别参数化了高斯分布的均值\\(g_{\\theta}\\)和方差\\(\\Sigma_{\\theta}(z))\\) S9868 也给出了无限混合的感性可视化，参数化帮助我们的mixture model更加的flexible了，能自己学习怎么去填满这个数据流形。 这里的\\(P(z)\\)和\\(P_\\theta(x|z)\\)​都假设的高斯分布，当然我们也能make an infinite mixture of the autoregressive distribution and so on. ,从这个角度来说mixture分布是meta model 可以用其他的密度估计模型替代 这个概率摸底建模是一个积分的无穷项，这里我们需要用到统计学的一个基本技术，用MC采样来估计这个积分 \\(p_{\\theta}(x) = \\int p_{\\theta}(x|z)p_z(z)dz = \\mathbb{E}_{z \\sim p_z(z)}[p_{\\theta}(x|z)] \\approx \\frac{1}{M} \\sum_{i=1}^{M} p_{\\theta}(x|z^{(i)}), \\quad z^{(i)} \\sim p_z\\) MC采样的直观理解是求平均值的这个过程本身就蕴含了采样过程 当我们概率建模有了，接下来就是计算极大似然来优化参数！ \\(E_{x \\sim p_{data} }log P_{\\theta}(x)\\)​ 极大似然认为最优的分布参数是一个定值，因此我们把数据扔进去优化一个maximal的似然值 \\(\\theta^* = \\underset{\\theta}{\\arg\\min} \\frac{1}{M} \\sum_{i=1}^{N} \\log \\left( \\sum_{j=1}^{M} \\mathcal{N}\\left(x^{(i)}; g_{\\theta}^{\\mu}\\left(z^{(j)}\\right), g_{\\theta}^{\\Sigma}\\left(z^{(j)}\\right)\\right) \\right)\\) 以上都是在拟合概率，但是对于神经网络而言我们有的标签不是概率这太抽象了，我们只有从Pdata中获得的样本,如何优化这个混合模型？ 把方差固定，优化这个似然值就变成优化\\(||x-g_{\\theta}^{\\mu}||\\),训练的步骤是我们采样一堆隐变量z，扔进网络\\(g_{\\theta}\\)中产生一堆高斯分布的均值，然后在和一个batch的样本\\(x\\)​ 计算L2norm，这就是我们要的似然值. 重要性采样 我们在建模概率的时候是利用的MC采样来估计积分 \\(p_{\\theta}(x) \\approx \\frac{1}{M} \\left( p_{\\theta}(x|z^{(1)}) + p_{\\theta}(x|z^{(2)}) + p_{\\theta}(x|z^{(3)}) + \\ldots \\right)\\) 遇到一个问题，往往高维空间MC采样的效率很低，往往会变成这样： \\(p_{\\theta}(x) \\approx \\frac{1}{M} \\left( 0 + p_{\\theta}(x|z^{(2)}) + 0 + \\ldots \\right)\\)​ 这意味着要想精确的估计概率，必须要大量的采样，采样效率很低 这里引出本文的第二个技术，重要性采样： \\(p_{\\theta}(x) = \\mathbb{E}_{z \\sim p_z}[p_{\\theta}(x|z)] = \\int p_z(z)p_{\\theta}(x|z)dz = \\int \\frac{p_z(z)}{q_z(z)} p_{\\theta}(x|z)q_z(z)dz = \\mathbb{E}_{z \\sim q_z}\\left[\\frac{p_z(z)}{q_z(z)} p_{\\theta}(x|z)\\right]\\) 重要性采样给出一种不用在原始分布p中采样，而在新的分布q中采样，这是一种减少方差的采样技术 最优的\\(q(z)\\)正比于\\(p(z)P_{\\theta}(x|z)\\) 后者正比于\\(P(x,z)\\) 它又正比于\\(p_{\\theta}(z|x)\\)，所以可以证明最优的\\(q(z)\\)等于\\(p_{\\theta}(z|x)\\) \\(p_{\\theta}(x) \\approx \\frac{1}{M} \\sum_{j=1}^{M} \\frac{p_z(z^{(j)})}{p_{\\theta}(z^{(j)}|x)} p_{\\theta}(x|z^{(j)})\\), \\(z^{(j)} \\sim p_{\\theta}(Z|x)\\) 最开始的 在重要性采样的语境下，\\(p_{\\theta}(z|x)\\) 这个z就是和建模\\(p_{\\theta}(x)\\)最相关的z 变分推断 高斯混合模型的有点是隐变量分布是高斯分布，重要性采样的效率更高但是这里又出现了一个难以采样的分布\\(P_{\\theta}(z|x)\\)​​ 这个时候引入最后一个重要的技巧，变分推断(Variational inference) 顺便吐槽一句，很多的教程都从变分推断出发，丝毫不讨论生成的过程，这和我生成模型又有什么关系呢 :D","link":"/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/"},{"title":"深度学习中的正则化","text":"最近在看集成学习，集成学习中对基学习器的要求是和而不同，及满足两个条件：误差 \\(\\epsilon &lt;0.5\\)且具有多样性，由此引出一系列多样性方法，其和正则化非常类似。借助课上提到的框架对正则化进行梳理。并且试图统一绝大部分ml和dl的正则化方法 1.正则化的定义 正则化：旨在通过对学习算法的修改，减少泛化误差（而不是训练误差，并且可能以提高训练误差为代价） 2.正则化的背景：方差与偏差，欠拟合与过拟合 统计学中的过拟合欠拟合：对应模型的小偏差大方差 方差偏差 模型训练中的过拟合：训练刚开始的时候，训练误差和测试误差都下降。在到达一个临界点之后，训练集的误差下降，测试集的误差上升了，这个时候就进入了过拟合区域 过拟合欠拟合 3.正则化的分类 3.1 对输入样本 对输入样本扰动敏感的学习器：神经网络，决策树等 对输入样本扰动不敏感的学习器：线性学习器，支持向量机（这俩都是线性分类器），朴素贝叶斯，k近邻 数据增强： 数据扰动（噪声） 3.2 对输入属性 Bagging 降维：PCA，SVD，AutoEncoder，LDA 特征选择 3.3 对输出属性 label smooth Dropout 3.4 对模型参数 L1正则化 L2正则化 SVM中的松弛变量 参数共享（CNN，RNN） 3.5 对模型训练 半监督学习 多任务学习 提前终止 对抗训练 知识蒸馏 多级别监督loss Reference 正则化详解 正则化总结的比较好比较全面的文章","link":"/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/"},{"title":"贝叶斯的两个理解角度","text":"When you have eliminated the impossible, whatever remains, however improbable, must be the truth... 时间线： 托马斯·贝叶斯（Thomas Bayes）在1763提出，用来解决逆概率问题 贝叶斯： 根据证据修正先验 推断因子 下面具体解释这两个角度 怎么理解修正先验？ \\(P(A|B) = P(A)\\frac{P(B|A)}{P(B)}\\) P(A)是先验概率。 P(B|A)/P(B)称为\"可能性函数\"（Likelyhood），这是一个调整因子，也就是新信息B带来的调整，作用是将先验概率（之前的主观判断）调整到更接近真实概率。 如果\"可能性函数\"P(B|A)/P(B)&gt;1，意味着\"先验概率\"被增强，事件A的发生的可能性变大； 如果\"可能性函数\"=1，意味着B事件无助于判断事件A的可能性； 如果\"可能性函数\"&lt;1，意味着\"先验概率\"被削弱，事件A的可能性变小。 怎么理解推断因子？ \\(P(z_j|x) = \\frac{P(z_j,x)}{\\sum_z P(x|z_i)P(z_i)}\\) 事实上，当初统计学家在回归问题中引入L2正则，只是出于防止矩阵病态造成不可求逆矩阵，后来才发现结果居然更好了。 当我们对抛硬币做做参数估计的时候，加入10次都是正的那很容易得到一个很不准的MLE 参数估计： 点估计:MLE，MAP(通常是优化问题)，矩估计，贝叶斯估计 reference： 极大似然估计、极大后验估计和贝叶斯估计 https://www.zhihu.com/question/61298823/answer/1545994922","link":"/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/"}],"tags":[{"name":"DGM","slug":"DGM","link":"/tags/DGM/"},{"name":"LVM","slug":"LVM","link":"/tags/LVM/"},{"name":"VAE","slug":"VAE","link":"/tags/VAE/"},{"name":"正则化","slug":"正则化","link":"/tags/%E6%AD%A3%E5%88%99%E5%8C%96/"},{"name":"概率论 ML数学","slug":"概率论-ML数学","link":"/tags/%E6%A6%82%E7%8E%87%E8%AE%BA-ML%E6%95%B0%E5%AD%A6/"}],"categories":[],"pages":[]}
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diff --git a/index.html b/index.html
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@@ -39,7 +39,10 @@
 <strong>impossible</strong>, whatever remains, however
 <strong>improbable</strong>, must be the truth...</p></div><a class="article-more button is-small is-size-7" href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/#more">Read more</a></article></div><div class="card"><article class="card-content article" role="article"><div class="article-meta is-size-7 is-uppercase level is-mobile"><div class="level-left"><span class="level-item">Posted&nbsp;<time dateTime="2024-04-25T16:00:00.000Z" title="2024/4/26上午12:00:00">2024-04-26</time></span><span class="level-item">Updated&nbsp;<time dateTime="2024-04-27T11:45:24.883Z" title="2024/4/27下午7:45:24">2024-04-27</time></span><span class="level-item">9 minutes read (About 1411 words)</span></div></div><p class="title is-3 is-size-4-mobile"><a class="link-muted" href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p><div class="content"><p>本文将从表征学习的角度以及隐变量模型的角度探讨VAE模型，重点讲述VAE的三个技术</p></div><a class="article-more button is-small is-size-7" href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/#more">Read more</a></article></div><div class="card"><article class="card-content article" role="article"><div class="article-meta is-size-7 is-uppercase level is-mobile"><div class="level-left"><span class="level-item">Posted&nbsp;<time dateTime="2023-09-12T19:11:35.000Z" title="2023/9/13上午3:11:35">2023-09-13</time></span><span class="level-item">Updated&nbsp;<time dateTime="2024-04-27T05:46:07.172Z" title="2024/4/27下午1:46:07">2024-04-27</time></span><span class="level-item">3 minutes read (About 511 words)</span></div></div><p class="title is-3 is-size-4-mobile"><a class="link-muted" href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/">深度学习中的正则化</a></p><div class="content"><p>最近在看集成学习，集成学习中对基学习器的要求是和而不同，及满足两个条件：误差
 <span class="math inline">\(\epsilon
-&lt;0.5\)</span>且具有多样性，由此引出一系列多样性方法，其和正则化非常类似。借助课上提到的框架对正则化进行梳理。并且试图统一绝大部分ml和dl的正则化方法</div><a class="article-more button is-small is-size-7" href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/#more">Read more</a></article></div></div><div class="column column-left is-4-tablet is-4-desktop is-3-widescreen  order-1"><div class="card widget" data-type="profile"><div class="card-content"><nav class="level"><div class="level-item has-text-centered flex-shrink-1"><div><figure class="image is-128x128 mx-auto mb-2"><img class="avatar" src="/img/avatar.png" alt="Rick Wang"></figure><p class="title is-size-4 is-block" style="line-height:inherit;">Rick Wang</p><p class="is-size-6 is-block">AI Engineering ComputerVision MachineLearning</p><p class="is-size-6 is-flex justify-content-center"><i class="fas fa-map-marker-alt mr-1"></i><span>Shanghai China</span></p></div></div></nav><nav class="level is-mobile"><div class="level-item has-text-centered 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class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/">深度学习中的正则化</a></p></div></article></div></div><div class="card widget" data-type="archives"><div class="card-content"><div class="menu"><h3 class="menu-label">Archives</h3><ul class="menu-list"><li><a class="level is-mobile" href="/archives/2024/"><span class="level-start"><span class="level-item">2024</span></span><span class="level-end"><span class="level-item tag">3</span></span></a></li><li><a class="level is-mobile" href="/archives/2023/"><span class="level-start"><span class="level-item">2023</span></span><span class="level-end"><span class="level-item tag">1</span></span></a></li></ul></div></div></div><div class="card widget" data-type="tags"><div class="card-content"><div class="menu"><h3 class="menu-label">Tags</h3><div class="field is-grouped is-grouped-multiline"><div class="control"><a class="tags has-addons" href="/tags/DGM/"><span class="tag">DGM</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/LVM/"><span class="tag">LVM</span><span class="tag">1</span></a></div><div class="control"><a class="tags has-addons" href="/tags/VAE/"><span 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diff --git a/rick/index.html b/rick/index.html
index 439a9ac..98ef694 100644
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class="menu-label">Recents</h3><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-26T08:11:47.000Z">2024-04-26</time></p><p class="title"><a href="/2024/GAN/">GAN</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/">深度学习中的正则化</a></p></div></article></div></div><div class="card widget" data-type="archives"><div class="card-content"><div class="menu"><h3 class="menu-label">Archives</h3><ul class="menu-list"><li><a class="level is-mobile" href="/archives/2024/"><span class="level-start"><span class="level-item">2024</span></span><span class="level-end"><span class="level-item tag">3</span></span></a></li><li><a class="level is-mobile" href="/archives/2023/"><span class="level-start"><span class="level-item">2023</span></span><span class="level-end"><span class="level-item tag">1</span></span></a></li></ul></div></div></div><div class="card widget" data-type="tags"><div class="card-content"><div class="menu"><h3 class="menu-label">Tags</h3><div class="field is-grouped is-grouped-multiline"><div class="control"><a class="tags has-addons" href="/tags/DGM/"><span class="tag">DGM</span><span 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diff --git a/rick/temp.html b/rick/temp.html
index 2f83e79..0db042f 100644
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class="menu-label">Recents</h3><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-26T08:11:47.000Z">2024-04-26</time></p><p class="title"><a href="/2024/GAN/">GAN</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T17:00:35.000Z">2024-04-26</time></p><p class="title"><a href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/">贝叶斯的两个理解角度</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2024-04-25T16:00:00.000Z">2024-04-26</time></p><p class="title"><a href="/2024/VAE%EF%BC%9A%E5%8F%98%E5%88%86%E6%8E%A8%E6%96%AD%E3%80%81MC%E4%BC%B0%E8%AE%A1%E5%92%8C%E9%87%8D%E8%A6%81%E6%80%A7%E9%87%87%E6%A0%B7/">VAE：变分推断、MC估计和重要性采样</a></p></div></article><article class="media"><div class="media-content"><p class="date"><time dateTime="2023-09-12T19:11:35.000Z">2023-09-13</time></p><p class="title"><a href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/">深度学习中的正则化</a></p></div></article></div></div><div class="card widget" data-type="archives"><div class="card-content"><div class="menu"><h3 class="menu-label">Archives</h3><ul class="menu-list"><li><a class="level is-mobile" href="/archives/2024/"><span class="level-start"><span class="level-item">2024</span></span><span class="level-end"><span class="level-item tag">3</span></span></a></li><li><a class="level is-mobile" href="/archives/2023/"><span class="level-start"><span class="level-item">2023</span></span><span class="level-end"><span class="level-item tag">1</span></span></a></li></ul></div></div></div><div class="card widget" data-type="tags"><div class="card-content"><div class="menu"><h3 class="menu-label">Tags</h3><div class="field is-grouped is-grouped-multiline"><div class="control"><a class="tags has-addons" href="/tags/DGM/"><span class="tag">DGM</span><span 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index 3a8dfc7..9f9b3f7 100644
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+++ "b/tags/\346\246\202\347\216\207\350\256\272-ML\346\225\260\345\255\246/index.html"
@@ -36,7 +36,10 @@
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 <strong>impossible</strong>, whatever remains, however
-<strong>improbable</strong>, must be the truth...</p></div><a class="article-more button is-small is-size-7" href="/2024/%E8%B4%9D%E5%8F%B6%E6%96%AF%E7%9A%84%E4%B8%A4%E7%A7%8D%E7%90%86%E8%A7%A3%E8%A7%92%E5%BA%A6/#more">Read more</a></article></div></div><div class="column column-left is-4-tablet is-4-desktop is-3-widescreen  order-1"><div class="card widget" data-type="profile"><div class="card-content"><nav class="level"><div class="level-item has-text-centered flex-shrink-1"><div><figure class="image is-128x128 mx-auto mb-2"><img class="avatar" src="/img/avatar.png" alt="Rick Wang"></figure><p class="title is-size-4 is-block" style="line-height:inherit;">Rick Wang</p><p class="is-size-6 is-block">AI Engineering ComputerVision MachineLearning</p><p class="is-size-6 is-flex justify-content-center"><i class="fas fa-map-marker-alt mr-1"></i><span>Shanghai China</span></p></div></div></nav><nav class="level is-mobile"><div class="level-item has-text-centered is-marginless"><div><p 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+&lt;0.5\)</span>且具有多样性，由此引出一系列多样性方法，其和正则化非常类似。借助课上提到的框架对正则化进行梳理。并且试图统一绝大部分ml和dl的正则化方法</div><a class="article-more button is-small is-size-7" href="/2023/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E4%B8%AD%E7%9A%84%E6%AD%A3%E5%88%99%E5%8C%96/#more">Read more</a></article></div></div><div class="column column-left is-4-tablet is-4-desktop is-3-widescreen  order-1"><div class="card widget" data-type="profile"><div class="card-content"><nav class="level"><div class="level-item has-text-centered flex-shrink-1"><div><figure class="image is-128x128 mx-auto mb-2"><img class="avatar" src="/img/avatar.png" alt="Rick Wang"></figure><p class="title is-size-4 is-block" style="line-height:inherit;">Rick Wang</p><p class="is-size-6 is-block" style="white-space: pre-line">AI Engineering     
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