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<!DOCTYPE html>
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<title>21 前馈神经网络 | 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>
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<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>
<ul>
<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>
</ul></li>
<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>
</ul></li>
<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>
</ul></li>
<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>
<ul>
<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>
<ul>
<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>
</ul></li>
<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>
<ul>
<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>
<ul>
<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>
</ul></li>
</ul></li>
<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">21</span> 前馈神经网络<a href="前馈神经网络.html#前馈神经网络" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<p>机器学习我们已经知道可以分为两大流派：</p>
<ol style="list-style-type: decimal">
<li><p>频率派，这个流派的方法叫做统计学习，根据具体问题有下面的算法：</p>
<ol style="list-style-type: decimal">
<li><p>正则化，L1，L2 等</p></li>
<li><p>核化，如核支撑向量机</p></li>
<li><p>集成化，AdaBoost，RandomForest</p></li>
<li><p>层次化，神经网络，神经网络有各种不同的模型，有代表性的有：</p>
<ol style="list-style-type: decimal">
<li>多层感知机</li>
<li>Autoencoder</li>
<li>CNN</li>
<li>RNN</li>
</ol>
<p>这几种模型又叫做深度神经网络。</p></li>
</ol></li>
<li><p>贝叶斯派，这个流派的方法叫概率图模型，根据图特点分为：</p>
<ol style="list-style-type: decimal">
<li>有向图-贝叶斯网络，加入层次化后有深度有向网络，包括
<ol style="list-style-type: decimal">
<li>Sigmoid Belief Network</li>
<li>Variational Autoencoder</li>
<li>GAN</li>
</ol></li>
<li>无向图-马尔可夫网络，加入层次化后有深度玻尔兹曼机。</li>
<li>混合，加入层次化后有深度信念网络</li>
</ol>
<p>这几个加入层次化后的模型叫做深度生成网络。</p></li>
</ol>
<p>从广义来说，深度学习包括深度生成网络和深度神经网络。</p>
<div id="from-pla-to-dl" class="section level2 hasAnchor" number="21.1">
<h2><span class="header-section-number">21.1</span> From PLA to DL<a href="前馈神经网络.html#from-pla-to-dl" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<ul>
<li>1958，PLA</li>
<li>1969，PLA 不能解决 XOR 等非线性数据</li>
<li>1981，MLP，多层感知机的出现解决了上面的问题</li>
<li>1986，BP 算法应用在 MLP 上，RNN</li>
<li>1989，CNN，Univeral Approximation Theorem，但是于此同时，由于深度和宽度的相对效率不知道，并且无法解决 BP 算法的梯度消失问题</li>
<li>1993，1995，SVM + kernel，AdaBoost，RandomForest，这些算法的发展，DL 逐渐没落</li>
<li>1997，LSTM</li>
<li>2006，基于 RBM 的 深度信念网络和深度自编码</li>
<li>2009，GPU的发展</li>
<li>2011，在语音方面的应用</li>
<li>2012，ImageNet</li>
<li>2013，VAE</li>
<li>2014，GAN</li>
<li>2016，AlphaGo</li>
<li>2018，GNN</li>
</ul>
<p>DL 不是一个新的东西，其近年来的大发展主要原因如下：</p>
<ol style="list-style-type: decimal">
<li>数据量变大</li>
<li>分布式计算的发展</li>
<li>硬件算力的发展</li>
</ol>
</div>
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<h2><span class="header-section-number">21.2</span> 非线性问题<a href="前馈神经网络.html#非线性问题" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>对于非线性的问题，有三种方法：</p>
<ol style="list-style-type: decimal">
<li>非线性转换，将低维空间转换到高维空间（Cover 定理），从而变为一个线性问题。</li>
<li>核方法，由于非线性转换是变换为高维空间，因此可能导致维度灾难，并且可能很难得到这个变换函数，核方法不直接寻找这个转换，而是寻找一个内积。</li>
<li>神经网络方法，将复合运算变为基本的线性运算的组合。</li>
</ol>
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