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Machine Learning - 雪地
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<h1>CS229 学习笔记 Part3</h1>
<div class="a-content">
<div class="a-content-text">
<ul>
<li>
<a href="#toc_0">SVM</a>
<ul>
<li>
<a href="#toc_1">函数间隔和几何间隔 (Functional and geometric margin)</a>
</li>
<li>
<a href="#toc_2">最优间隔分类器 (Optimal margin classifier)</a>
</li>
<li>
<a href="#toc_3">拉格朗日对偶问题</a>
<ul>
<li>
<a href="#toc_4">原始问题</a>
</li>
<li>
<a href="#toc_5">对偶问题</a>
</li>
<li>
<a href="#toc_6">KKT 条件</a>
</li>
</ul>
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<li>
<a href="#toc_7">回到最优间隔分类器问题</a>
</li>
<li>
<a href="#toc_8">核 (Kernels)</a>
</li>
<li>
<a href="#toc_9">正则化</a>
</li>
<li>
<a href="#toc_10">SMO 算法</a>
<ul>
<li>
<a href="#toc_11">坐标上升算法 (Coordinate ascent)</a>
</li>
<li>
<a href="#toc_12">SMO</a>
</li>
</ul>
</li>
</ul>
</li>
</ul>
<h2 id="toc_0">SVM</h2>
<p>CS229 对于 SVM 的理论解释是我学习到的最详细也是最好的一份资料了，对比对象有周志华《机器学习》、《机器学习实战》、Coursera 上的 Machine Learning 等。相当推荐学习 CS229。</p>
<p>分类间隔 (Margin) 和 SVM 的优化目标『最大化分类间隔』这里就不多说了，很好理解，主要还是记录 CS229 中学到的新内容。一个数据点离分类边界 (decision boundary) 越远，则确信度越高。我们的优化目标也相当于寻找一个远离所有数据点的分类边界，当然，前提是这个分类边界得到的分类都正确。</p>
<p>SVM 的一些特殊定义也提及一下，</p>
<ul>
<li>\(y\) 的取值不是 \(\{0,1\}\) 而是 \(\{-1,1\}\)。</li>
<li>假设函数 \(h_{w,b}(x) = g(w^Tx+b)\) 中，我们把截距项单独写出来，便与后续的计算。</li>
<li>我们的分类器输出结果会直接是 1 或 -1，不像 Logistic 回归那样先输出 \(y\) 是某一类的概率。</li>
</ul>
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<a href="14968173531750.html">Read more</a>
<span class="date">2017/6/7 14:35 下午</span>
<span>posted in </span>
<span class="posted-in"><a href='Machine%20Learning.html'>Machine Learning</a></span>
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<h1>CS229 学习笔记 Part2</h1>
<div class="a-content">
<div class="a-content-text">
<ul>
<li>
<a href="#toc_0">判别式和生成式</a>
<ul>
<li>
<a href="#toc_1">判别式</a>
</li>
<li>
<a href="#toc_2">生成式</a>
</li>
</ul>
</li>
<li>
<a href="#toc_3">Gaussian discriminant analysis</a>
</li>
<li>
<a href="#toc_4">讨论：GDA 和 Logistic 回归</a>
</li>
<li>
<a href="#toc_5">朴素贝叶斯</a>
<ul>
<li>
<a href="#toc_6">拉普拉斯平滑</a>
</li>
<li>
<a href="#toc_7">用于文本分类的事件模型</a>
</li>
</ul>
</li>
</ul>
<h2 id="toc_0">判别式和生成式</h2>
<p>对于一个分类任务，判别式和生成式分别代表了两种不同的思路：</p>
<h3 id="toc_1">判别式</h3>
<p>通过直接从输入数据中学习，得到一个『特定输入对应的实际类别』的概率模型，模型的参数为 \(\theta\) 。即学习建模 \(p(y\mid x)\)</p>
<h3 id="toc_2">生成式</h3>
<p>通过对每一个类进行建模，然后就可以通过条件概率算出输入的数据更可能由哪一类生成。即学习建模 \(p(x\mid y)\) 和 \(p(y)\) ，然后计算 \[\arg\max\limits_y\frac{p(x \mid y)p(y)}{p(x)}\]</p>
<p>并且实际计算中，分母 \(p(x)\) 并不会影响各个类别概率的排序，所以最终简化成 \[\arg\max\limits_y p(x \mid y)p(y)\]</p>
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<span class="date">2017/6/5 1:14 上午</span>
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<h1>CS229 学习笔记 Part 1</h1>
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<p>此笔记为我的 CS229 的学习笔记之一，由 Andrew Ng 的 CS229 Lecture notes 和 课堂录像整理而来。用于记录所学到的内容。记录顺序重新编排过，并非是课程原本的教学顺序，并且省略了课程中的一些推导过程，所以适合学习后整理备忘使用，不适合用于同步辅助学习。</p>
<ul>
<li>
<a href="#toc_0">广义线性模型 GLM (Generalized Linear Models)</a>
<ul>
<li>
<a href="#toc_1">具体步骤</a>
</li>
</ul>
</li>
<li>
<a href="#toc_2">优化方法</a>
<ul>
<li>
<a href="#toc_3">梯度下降法</a>
</li>
<li>
<a href="#toc_4">牛顿法</a>
</li>
</ul>
</li>
<li>
<a href="#toc_5">Linear Regression</a>
<ul>
<li>
<a href="#toc_6">Locally weighted linear regression</a>
</li>
</ul>
</li>
</ul>
<h2 id="toc_0">广义线性模型 GLM (Generalized Linear Models)</h2>
<p>广义线性模型是所学到的 Linear Regression 以及 Logistic Regression 的推广形式（更准确的说，这两种模型都属于 GLM 的特殊情况）。它有三个关键假设(Assumptions)构成:</p>
<ol>
<li>\(y \mid x;\theta\sim ExponentialFamily(\eta)\) ：对于固定的参数 \(\theta\) 以及给定 \(x\)， \(y\) 的分布服从某一指数分布族（如高斯分布、伯努利分布、Softmax分布）</li>
<li>对于给定的 \(x\) ，目标是预测 \(T(y)\) 的值。换一种说法就是，我们定义假设函数 \(h(x) = E[y\mid x]\)</li>
<li>natural parameter \(\eta\) 和 输入 \(x\) 是线性相关的， \(\eta = \theta^ \mathrm{ T } x\) （其中，当输入 \(x\) 和 \(\eta\) 是向量的时候， \(\eta_i = \theta_i^ \mathrm{T}x\)）</li>
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<span class="date">2017/5/12 23:14 下午</span>
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