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<!DOCTYPE html>
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<title>1 Introduction | 机器学习白板系列</title>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>简介</a></li>
<li class="chapter" data-level="1" data-path="introduction.html"><a href="introduction.html"><i class="fa fa-check"></i><b>1</b> Introduction</a>
<ul>
<li class="chapter" data-level="1.1" data-path="introduction.html"><a href="introduction.html#频率派的观点"><i class="fa fa-check"></i><b>1.1</b> 频率派的观点</a></li>
<li class="chapter" data-level="1.2" data-path="introduction.html"><a href="introduction.html#贝叶斯派的观点"><i class="fa fa-check"></i><b>1.2</b> 贝叶斯派的观点</a></li>
<li class="chapter" data-level="1.3" data-path="introduction.html"><a href="introduction.html#小结"><i class="fa fa-check"></i><b>1.3</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="mathbasics.html"><a href="mathbasics.html"><i class="fa fa-check"></i><b>2</b> MathBasics</a>
<ul>
<li class="chapter" data-level="2.1" data-path="mathbasics.html"><a href="mathbasics.html#高斯分布"><i class="fa fa-check"></i><b>2.1</b> 高斯分布</a>
<ul>
<li class="chapter" data-level="2.1.1" data-path="mathbasics.html"><a href="mathbasics.html#一维情况-mle"><i class="fa fa-check"></i><b>2.1.1</b> 一维情况 MLE</a></li>
<li class="chapter" data-level="2.1.2" data-path="mathbasics.html"><a href="mathbasics.html#多维情况"><i class="fa fa-check"></i><b>2.1.2</b> 多维情况</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="3" data-path="线性回归.html"><a href="线性回归.html"><i class="fa fa-check"></i><b>3</b> 线性回归</a>
<ul>
<li class="chapter" data-level="3.1" data-path="线性回归.html"><a href="线性回归.html#最小二乘法"><i class="fa fa-check"></i><b>3.1</b> 最小二乘法</a></li>
<li class="chapter" data-level="3.2" data-path="线性回归.html"><a href="线性回归.html#噪声为高斯分布的-mle"><i class="fa fa-check"></i><b>3.2</b> 噪声为高斯分布的 MLE</a></li>
<li class="chapter" data-level="3.3" data-path="线性回归.html"><a href="线性回归.html#权重先验也为高斯分布的-map"><i class="fa fa-check"></i><b>3.3</b> 权重先验也为高斯分布的 MAP</a></li>
<li class="chapter" data-level="3.4" data-path="线性回归.html"><a href="线性回归.html#正则化"><i class="fa fa-check"></i><b>3.4</b> 正则化</a>
<ul>
<li class="chapter" data-level="3.4.1" data-path="线性回归.html"><a href="线性回归.html#l1-lasso"><i class="fa fa-check"></i><b>3.4.1</b> L1 Lasso</a></li>
<li class="chapter" data-level="3.4.2" data-path="线性回归.html"><a href="线性回归.html#l2-ridge"><i class="fa fa-check"></i><b>3.4.2</b> L2 Ridge</a></li>
</ul></li>
<li class="chapter" data-level="3.5" data-path="线性回归.html"><a href="线性回归.html#小结-1"><i class="fa fa-check"></i><b>3.5</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="线性分类.html"><a href="线性分类.html"><i class="fa fa-check"></i><b>4</b> 线性分类</a>
<ul>
<li class="chapter" data-level="4.1" data-path="线性分类.html"><a href="线性分类.html#两分类-硬分类-感知机算法"><i class="fa fa-check"></i><b>4.1</b> 两分类-硬分类-感知机算法</a></li>
<li class="chapter" data-level="4.2" data-path="线性分类.html"><a href="线性分类.html#两分类-硬分类-线性判别分析-lda"><i class="fa fa-check"></i><b>4.2</b> 两分类-硬分类-线性判别分析 LDA</a></li>
<li class="chapter" data-level="4.3" data-path="线性分类.html"><a href="线性分类.html#两分类-软分类-概率判别模型-logistic-回归"><i class="fa fa-check"></i><b>4.3</b> 两分类-软分类-概率判别模型-Logistic 回归</a></li>
<li class="chapter" data-level="4.4" data-path="线性分类.html"><a href="线性分类.html#两分类-软分类-概率生成模型-高斯判别分析-gda"><i class="fa fa-check"></i><b>4.4</b> 两分类-软分类-概率生成模型-高斯判别分析 GDA</a></li>
<li class="chapter" data-level="4.5" data-path="线性分类.html"><a href="线性分类.html#两分类-软分类-概率生成模型-朴素贝叶斯"><i class="fa fa-check"></i><b>4.5</b> 两分类-软分类-概率生成模型-朴素贝叶斯</a></li>
<li class="chapter" data-level="4.6" data-path="线性分类.html"><a href="线性分类.html#小结-2"><i class="fa fa-check"></i><b>4.6</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="降维.html"><a href="降维.html"><i class="fa fa-check"></i><b>5</b> 降维</a>
<ul>
<li class="chapter" data-level="5.1" data-path="降维.html"><a href="降维.html#线性降维-主成分分析-pca"><i class="fa fa-check"></i><b>5.1</b> 线性降维-主成分分析 PCA</a>
<ul>
<li class="chapter" data-level="5.1.1" data-path="降维.html"><a href="降维.html#损失函数"><i class="fa fa-check"></i><b>5.1.1</b> 损失函数</a></li>
<li class="chapter" data-level="5.1.2" data-path="降维.html"><a href="降维.html#svd-与-pcoa"><i class="fa fa-check"></i><b>5.1.2</b> SVD 与 PCoA</a></li>
<li class="chapter" data-level="5.1.3" data-path="降维.html"><a href="降维.html#p-pca"><i class="fa fa-check"></i><b>5.1.3</b> p-PCA</a></li>
</ul></li>
<li class="chapter" data-level="5.2" data-path="降维.html"><a href="降维.html#小结-3"><i class="fa fa-check"></i><b>5.2</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="支撑向量机.html"><a href="支撑向量机.html"><i class="fa fa-check"></i><b>6</b> 支撑向量机</a>
<ul>
<li class="chapter" data-level="6.1" data-path="支撑向量机.html"><a href="支撑向量机.html#约束优化问题"><i class="fa fa-check"></i><b>6.1</b> 约束优化问题</a></li>
<li class="chapter" data-level="6.2" data-path="支撑向量机.html"><a href="支撑向量机.html#hard-margin-svm"><i class="fa fa-check"></i><b>6.2</b> Hard-margin SVM</a></li>
<li class="chapter" data-level="6.3" data-path="支撑向量机.html"><a href="支撑向量机.html#soft-margin-svm"><i class="fa fa-check"></i><b>6.3</b> Soft-margin SVM</a></li>
<li class="chapter" data-level="6.4" data-path="支撑向量机.html"><a href="支撑向量机.html#kernel-method"><i class="fa fa-check"></i><b>6.4</b> Kernel Method</a></li>
<li class="chapter" data-level="6.5" data-path="支撑向量机.html"><a href="支撑向量机.html#小结-4"><i class="fa fa-check"></i><b>6.5</b> 小结</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="指数族分布.html"><a href="指数族分布.html"><i class="fa fa-check"></i><b>7</b> 指数族分布</a>
<ul>
<li class="chapter" data-level="7.1" data-path="指数族分布.html"><a href="指数族分布.html#一维高斯分布"><i class="fa fa-check"></i><b>7.1</b> 一维高斯分布</a></li>
<li class="chapter" data-level="7.2" data-path="指数族分布.html"><a href="指数族分布.html#充分统计量和对数配分函数的关系"><i class="fa fa-check"></i><b>7.2</b> 充分统计量和对数配分函数的关系</a></li>
<li class="chapter" data-level="7.3" data-path="指数族分布.html"><a href="指数族分布.html#充分统计量和极大似然估计"><i class="fa fa-check"></i><b>7.3</b> 充分统计量和极大似然估计</a></li>
<li class="chapter" data-level="7.4" data-path="指数族分布.html"><a href="指数族分布.html#最大熵"><i class="fa fa-check"></i><b>7.4</b> 最大熵</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="概率图模型.html"><a href="概率图模型.html"><i class="fa fa-check"></i><b>8</b> 概率图模型</a>
<ul>
<li class="chapter" data-level="8.1" data-path="概率图模型.html"><a href="概率图模型.html#有向图-贝叶斯网络"><i class="fa fa-check"></i><b>8.1</b> 有向图-贝叶斯网络</a></li>
<li class="chapter" data-level="8.2" data-path="概率图模型.html"><a href="概率图模型.html#无向图-马尔可夫网络马尔可夫随机场"><i class="fa fa-check"></i><b>8.2</b> 无向图-马尔可夫网络（马尔可夫随机场）</a></li>
<li class="chapter" data-level="8.3" data-path="概率图模型.html"><a href="概率图模型.html#两种图的转换-道德图"><i class="fa fa-check"></i><b>8.3</b> 两种图的转换-道德图</a></li>
<li class="chapter" data-level="8.4" data-path="概率图模型.html"><a href="概率图模型.html#更精细的分解-因子图"><i class="fa fa-check"></i><b>8.4</b> 更精细的分解-因子图</a></li>
<li class="chapter" data-level="8.5" data-path="概率图模型.html"><a href="概率图模型.html#推断"><i class="fa fa-check"></i><b>8.5</b> 推断</a>
<ul>
<li class="chapter" data-level="8.5.1" data-path="概率图模型.html"><a href="概率图模型.html#推断-变量消除ve"><i class="fa fa-check"></i><b>8.5.1</b> 推断-变量消除（VE）</a></li>
<li class="chapter" data-level="8.5.2" data-path="概率图模型.html"><a href="概率图模型.html#推断-信念传播bp"><i class="fa fa-check"></i><b>8.5.2</b> 推断-信念传播（BP）</a></li>
<li class="chapter" data-level="8.5.3" data-path="概率图模型.html"><a href="概率图模型.html#推断-max-product-算法"><i class="fa fa-check"></i><b>8.5.3</b> 推断-Max-Product 算法</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="9" data-path="期望最大.html"><a href="期望最大.html"><i class="fa fa-check"></i><b>9</b> 期望最大</a>
<ul>
<li class="chapter" data-level="9.1" data-path="期望最大.html"><a href="期望最大.html#广义-em"><i class="fa fa-check"></i><b>9.1</b> 广义 EM</a></li>
<li class="chapter" data-level="9.2" data-path="期望最大.html"><a href="期望最大.html#em-的推广"><i class="fa fa-check"></i><b>9.2</b> EM 的推广</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="高斯混合模型.html"><a href="高斯混合模型.html"><i class="fa fa-check"></i><b>10</b> 高斯混合模型</a>
<ul>
<li class="chapter" data-level="10.1" data-path="高斯混合模型.html"><a href="高斯混合模型.html#极大似然估计"><i class="fa fa-check"></i><b>10.1</b> 极大似然估计</a></li>
<li class="chapter" data-level="10.2" data-path="高斯混合模型.html"><a href="高斯混合模型.html#em-求解-gmm"><i class="fa fa-check"></i><b>10.2</b> EM 求解 GMM</a></li>
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<li class="chapter" data-level="11" data-path="变分推断.html"><a href="变分推断.html"><i class="fa fa-check"></i><b>11</b> 变分推断</a>
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<li class="chapter" data-level="11.1" data-path="变分推断.html"><a href="变分推断.html#基于平均场假设的变分推断"><i class="fa fa-check"></i><b>11.1</b> 基于平均场假设的变分推断</a></li>
<li class="chapter" data-level="11.2" data-path="变分推断.html"><a href="变分推断.html#sgvi"><i class="fa fa-check"></i><b>11.2</b> SGVI</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html"><i class="fa fa-check"></i><b>12</b> 马尔可夫链蒙特卡洛</a>
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<li class="chapter" data-level="12.1" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#蒙特卡洛方法"><i class="fa fa-check"></i><b>12.1</b> 蒙特卡洛方法</a></li>
<li class="chapter" data-level="12.2" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#mcmc"><i class="fa fa-check"></i><b>12.2</b> MCMC</a></li>
<li class="chapter" data-level="12.3" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#平稳分布"><i class="fa fa-check"></i><b>12.3</b> 平稳分布</a></li>
<li class="chapter" data-level="12.4" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#隐马尔可夫模型"><i class="fa fa-check"></i><b>12.4</b> 隐马尔可夫模型</a></li>
<li class="chapter" data-level="12.5" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#hmm"><i class="fa fa-check"></i><b>12.5</b> HMM</a>
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<li class="chapter" data-level="12.5.1" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#evaluation"><i class="fa fa-check"></i><b>12.5.1</b> Evaluation</a></li>
<li class="chapter" data-level="12.5.2" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#learning"><i class="fa fa-check"></i><b>12.5.2</b> Learning</a></li>
<li class="chapter" data-level="12.5.3" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#decoding"><i class="fa fa-check"></i><b>12.5.3</b> Decoding</a></li>
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<li class="chapter" data-level="12.6" data-path="马尔可夫链蒙特卡洛.html"><a href="马尔可夫链蒙特卡洛.html#小结-5"><i class="fa fa-check"></i><b>12.6</b> 小结</a></li>
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<li class="chapter" data-level="13" data-path="线性动态系统.html"><a href="线性动态系统.html"><i class="fa fa-check"></i><b>13</b> 线性动态系统</a></li>
<li class="chapter" data-level="14" data-path="粒子滤波.html"><a href="粒子滤波.html"><i class="fa fa-check"></i><b>14</b> 粒子滤波</a>
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<li class="chapter" data-level="14.1" data-path="粒子滤波.html"><a href="粒子滤波.html#sis"><i class="fa fa-check"></i><b>14.1</b> SIS</a></li>
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<li class="chapter" data-level="15" data-path="条件随机场.html"><a href="条件随机场.html"><i class="fa fa-check"></i><b>15</b> 条件随机场</a>
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<li class="chapter" data-level="15.1" data-path="条件随机场.html"><a href="条件随机场.html#crf-的-pdf"><i class="fa fa-check"></i><b>15.1</b> CRF 的 PDF</a></li>
<li class="chapter" data-level="15.2" data-path="条件随机场.html"><a href="条件随机场.html#边缘概率"><i class="fa fa-check"></i><b>15.2</b> 边缘概率</a></li>
<li class="chapter" data-level="15.3" data-path="条件随机场.html"><a href="条件随机场.html#参数估计"><i class="fa fa-check"></i><b>15.3</b> 参数估计</a></li>
<li class="chapter" data-level="15.4" data-path="条件随机场.html"><a href="条件随机场.html#译码"><i class="fa fa-check"></i><b>15.4</b> 译码</a></li>
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<li class="chapter" data-level="16" data-path="高斯网络.html"><a href="高斯网络.html"><i class="fa fa-check"></i><b>16</b> 高斯网络</a>
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<li class="chapter" data-level="16.1" data-path="高斯网络.html"><a href="高斯网络.html#高斯贝叶斯网络-gbn"><i class="fa fa-check"></i><b>16.1</b> 高斯贝叶斯网络 GBN</a></li>
<li class="chapter" data-level="16.2" data-path="高斯网络.html"><a href="高斯网络.html#高斯马尔可夫网络-gmn"><i class="fa fa-check"></i><b>16.2</b> 高斯马尔可夫网络 GMN</a></li>
</ul></li>
<li class="chapter" data-level="17" data-path="贝叶斯线性回归.html"><a href="贝叶斯线性回归.html"><i class="fa fa-check"></i><b>17</b> 贝叶斯线性回归</a>
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<li class="chapter" data-level="17.1" data-path="贝叶斯线性回归.html"><a href="贝叶斯线性回归.html#推断-1"><i class="fa fa-check"></i><b>17.1</b> 推断</a></li>
<li class="chapter" data-level="17.2" data-path="贝叶斯线性回归.html"><a href="贝叶斯线性回归.html#预测"><i class="fa fa-check"></i><b>17.2</b> 预测</a></li>
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<li class="chapter" data-level="18" data-path="高斯过程回归.html"><a href="高斯过程回归.html"><i class="fa fa-check"></i><b>18</b> 高斯过程回归</a>
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<li class="chapter" data-level="18.1" data-path="高斯过程回归.html"><a href="高斯过程回归.html#核贝叶斯线性回归"><i class="fa fa-check"></i><b>18.1</b> 核贝叶斯线性回归</a></li>
<li class="chapter" data-level="18.2" data-path="高斯过程回归.html"><a href="高斯过程回归.html#函数空间的观点"><i class="fa fa-check"></i><b>18.2</b> 函数空间的观点</a></li>
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<li class="chapter" data-level="19" data-path="受限玻尔兹曼机.html"><a href="受限玻尔兹曼机.html"><i class="fa fa-check"></i><b>19</b> 受限玻尔兹曼机</a>
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<li class="chapter" data-level="19.1" data-path="受限玻尔兹曼机.html"><a href="受限玻尔兹曼机.html#推断-2"><i class="fa fa-check"></i><b>19.1</b> 推断</a>
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<li class="chapter" data-level="19.1.1" data-path="受限玻尔兹曼机.html"><a href="受限玻尔兹曼机.html#phv"><i class="fa fa-check"></i><b>19.1.1</b> <span class="math inline">\(p(h|v)\)</span></a></li>
<li class="chapter" data-level="19.1.2" data-path="受限玻尔兹曼机.html"><a href="受限玻尔兹曼机.html#pv"><i class="fa fa-check"></i><b>19.1.2</b> <span class="math inline">\(p(v)\)</span></a></li>
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<li class="chapter" data-level="20" data-path="谱聚类.html"><a href="谱聚类.html"><i class="fa fa-check"></i><b>20</b> 谱聚类</a></li>
<li class="chapter" data-level="21" data-path="前馈神经网络.html"><a href="前馈神经网络.html"><i class="fa fa-check"></i><b>21</b> 前馈神经网络</a>
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<li class="chapter" data-level="21.1" data-path="前馈神经网络.html"><a href="前馈神经网络.html#from-pla-to-dl"><i class="fa fa-check"></i><b>21.1</b> From PLA to DL</a></li>
<li class="chapter" data-level="21.2" data-path="前馈神经网络.html"><a href="前馈神经网络.html#非线性问题"><i class="fa fa-check"></i><b>21.2</b> 非线性问题</a></li>
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<li class="chapter" data-level="22" data-path="配分函数.html"><a href="配分函数.html"><i class="fa fa-check"></i><b>22</b> 配分函数</a>
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<li class="chapter" data-level="22.1" data-path="配分函数.html"><a href="配分函数.html#包含配分函数的-mle"><i class="fa fa-check"></i><b>22.1</b> 包含配分函数的 MLE</a></li>
<li class="chapter" data-level="22.2" data-path="配分函数.html"><a href="配分函数.html#对比散度-cd-learning"><i class="fa fa-check"></i><b>22.2</b> 对比散度-CD Learning</a></li>
<li class="chapter" data-level="22.3" data-path="配分函数.html"><a href="配分函数.html#rbm-的学习问题"><i class="fa fa-check"></i><b>22.3</b> RBM 的学习问题</a></li>
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<li class="chapter" data-level="23" data-path="近似推断.html"><a href="近似推断.html"><i class="fa fa-check"></i><b>23</b> 近似推断</a></li>
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<h1><span class="header-section-number">1</span> Introduction<a href="introduction.html#introduction" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<p>对概率的诠释有两大学派，一种是频率派另一种是贝叶斯派。后面我们对观测集采用下面记号：
<span class="math display">\[
X_{N\times p}=(x_{1},x_{2},\cdots,x_{N})^{T},x_{i}=(x_{i1},x_{i2},\cdots,x_{ip})^{T}
\]</span>
这个记号表示有 <span class="math inline">\(N\)</span> 个样本，每个样本都是 <span class="math inline">\(p\)</span> 维向量。其中每个观测都是由 <span class="math inline">\(p(x|\theta)\)</span> 生成的。</p>
<div id="频率派的观点" class="section level2 hasAnchor" number="1.1">
<h2><span class="header-section-number">1.1</span> 频率派的观点<a href="introduction.html#频率派的观点" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p><span class="math inline">\(p(x|\theta)\)</span>中的 <span class="math inline">\(\theta\)</span> 是一个常量。对于 <span class="math inline">\(N\)</span> 个观测来说观测集的概率为 <span class="math inline">\(p(X|\theta)\mathop{=}\limits _{iid}\prod\limits _{i=1}^{N}p(x_{i}|\theta))\)</span> 。为了求 <span class="math inline">\(\theta\)</span> 的大小，我们采用最大对数似然MLE的方法：</p>
<p><span class="math display">\[
\theta_{MLE}=\mathop{argmax}\limits _{\theta}\log p(X|\theta)\mathop{=}\limits _{iid}\mathop{argmax}\limits _{\theta}\sum\limits _{i=1}^{N}\log p(x_{i}|\theta)
\]</span></p>
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<div id="贝叶斯派的观点" class="section level2 hasAnchor" number="1.2">
<h2><span class="header-section-number">1.2</span> 贝叶斯派的观点<a href="introduction.html#贝叶斯派的观点" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>贝叶斯派认为 <span class="math inline">\(p(x|\theta)\)</span> 中的 <span class="math inline">\(\theta\)</span> 不是一个常量。这个 <span class="math inline">\(\theta\)</span> 满足一个预设的先验的分布 <span class="math inline">\(\theta\sim p(\theta)\)</span> 。于是根据贝叶斯定理依赖观测集参数的后验可以写成：</p>
<p><span class="math display">\[
p(\theta|X)=\frac{p(X|\theta)\cdot p(\theta)}{p(X)}=\frac{p(X|\theta)\cdot p(\theta)}{\int\limits _{\theta}p(X|\theta)\cdot p(\theta)d\theta}
\]</span>
为了求 <span class="math inline">\(\theta\)</span> 的值，我们要最大化这个参数后验MAP：</p>
<p><span class="math display">\[
\theta_{MAP}=\mathop{argmax}\limits _{\theta}p(\theta|X)=\mathop{argmax}\limits _{\theta}p(X|\theta)\cdot p(\theta)
\]</span>
其中第二个等号是由于分母和 <span class="math inline">\(\theta\)</span> 没有关系。求解这个 <span class="math inline">\(\theta\)</span> 值后计算<span class="math inline">\(\frac{p(X|\theta)\cdot p(\theta)}{\int\limits _{\theta}p(X|\theta)\cdot p(\theta)d\theta}\)</span> ，就得到了参数的后验概率。其中 <span class="math inline">\(p(X|\theta)\)</span> 叫似然，是我们的模型分布。得到了参数的后验分布后，我们可以将这个分布用于预测贝叶斯预测：
<span class="math display">\[
p(x_{new}|X)=\int\limits _{\theta}p(x_{new}|\theta)\cdot p(\theta|X)d\theta
\]</span>
其中积分中的被乘数是模型，乘数是后验分布。</p>
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<div id="小结" class="section level2 hasAnchor" number="1.3">
<h2><span class="header-section-number">1.3</span> 小结<a href="introduction.html#小结" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>频率派和贝叶斯派分别给出了一系列的机器学习算法。频率派的观点导出了一系列的统计机器学习算法而贝叶斯派导出了概率图理论。在应用频率派的 MLE 方法时最优化理论占有重要地位。而贝叶斯派的算法无论是后验概率的建模还是应用这个后验进行推断时积分占有重要地位。因此采样积分方法如 MCMC 有很多应用。</p>
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