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斯坦福大学 2014 机器学习教程 个人笔记（V5.4）

目录
第 1 周 ..............................................................................................................................................1
1、 引言(Introduction)....................................................................................................1
1.1 欢迎............................................................................................................................1
1.2 机器学习是什么？....................................................................................................4
1.3 监督学习....................................................................................................................6
1.4 无监督学习..............................................................................................................10
2、 单变量线性回归(Linear Regression with One Variable) ........................................15
2.1 模型表示..................................................................................................................15
2.2 代价函数..................................................................................................................17
2.3 代价函数的直观理解 I............................................................................................19
2.4 代价函数的直观理解 II...........................................................................................20
2.5 梯度下降..................................................................................................................21
2.6 梯度下降的直观理解..............................................................................................24
2.7 梯度下降的线性回归..............................................................................................27
2.8 接下来的内容..........................................................................................................29
3、 线性代数回顾(Linear Algebra Review)...................................................................30
3.1 矩阵和向量..............................................................................................................30
3.2 加法和标量乘法......................................................................................................31
3.3 矩阵向量乘法..........................................................................................................32
3.4 矩阵乘法..................................................................................................................33
3.5 矩阵乘法的性质......................................................................................................34
3.6 逆、转置..................................................................................................................35
第 2 周 ............................................................................................................................................36
4、 多变量线性回归(Linear Regression with Multiple Variables)................................36
4.1 多维特征..................................................................................................................36
4.2 多变量梯度下降......................................................................................................37
4.3 梯度下降法实践 1-特征缩放 .................................................................................39
4.4 梯度下降法实践 2-学习率 .....................................................................................40
4.5 特征和多项式回归..................................................................................................41
4.6 正规方程..................................................................................................................42
4.7 正规方程及不可逆性（选修）..............................................................................44
5、 Octave 教程(Octave Tutorial)..................................................................................47
5.1 基本操作..................................................................................................................47
5.2 移动数据..................................................................................................................54
5.3 计算数据..................................................................................................................62
5.4 绘图数据..................................................................................................................70
5.5 控制语句：for，while，if 语句 .............................................................................76
5.6 向量化......................................................................................................................82
5.7 工作和提交的编程练习..........................................................................................86
第 3 周 ............................................................................................................................................88
6、 逻辑回归(Logistic Regression)................................................................................88
6.1 分类问题..................................................................................................................88
II
6.2 假说表示..................................................................................................................90
6.3 判定边界..................................................................................................................92
6.4 代价函数..................................................................................................................94
6.5 简化的成本函数和梯度下降..................................................................................98
6.6 高级优化................................................................................................................101
6.7 多类别分类：一对多............................................................................................105
7、 正则化(Regularization) .........................................................................................108
7.1 过拟合的问题........................................................................................................108
7.2 代价函数................................................................................................................110
7.3 正则化线性回归....................................................................................................112
7.4 正则化的逻辑回归模型........................................................................................113
第 4 周 ..........................................................................................................................................115
8、 神经网络：表述(Neural Networks: Representation)...........................................115
8.1 非线性假设............................................................................................................115
8.2 神经元和大脑........................................................................................................117
8.3 模型表示 1.............................................................................................................121
8.4 模型表示 2.............................................................................................................124
8.5 特征和直观理解 1.................................................................................................126
8.6 样本和直观理解 II.................................................................................................128
8.7 多类分类................................................................................................................130
第 5 周 ..........................................................................................................................................131
9、 神经网络的学习(Neural Networks: Learning) .....................................................131
9.1 代价函数................................................................................................................131
9.2 反向传播算法........................................................................................................133
9.3 反向传播算法的直观理解....................................................................................136
9.4 实现注意：展开参数............................................................................................138
9.5 梯度检验................................................................................................................139
9.6 随机初始化............................................................................................................141
9.7 综合起来................................................................................................................142
9.8 自主驾驶................................................................................................................143
第 6 周 ..........................................................................................................................................146
10、 应用机器学习的建议(Advice for Applying Machine Learning) ...........................146
10.1 决定下一步做什么..............................................................................................146
10.2 评估一个假设......................................................................................................149
10.3 模型选择和交叉验证集......................................................................................151
10.4 诊断偏差和方差..................................................................................................153
10.5 正则化和偏差/方差............................................................................................155
10.6 学习曲线..............................................................................................................157
10.7 决定下一步做什么..............................................................................................159
11、 机器学习系统的设计(Machine Learning System Design) ...................................161
11.1 首先要做什么......................................................................................................161
11.2 误差分析..............................................................................................................162
11.3 类偏斜的误差度量..............................................................................................165
11.4 查准率和查全率之间的权衡..............................................................................166
III
11.5 机器学习的数据..................................................................................................168
第 7 周 ..........................................................................................................................................172
12、 支持向量机(Support Vector Machines) ...............................................................172
12.1 优化目标..............................................................................................................172
12.2 大边界的直观理解..............................................................................................178
12.3 大边界分类背后的数学（选修）.......................................................................183
12.4 核函数 1...............................................................................................................190
12.5 核函数 2...............................................................................................................192
12.6 使用支持向量机..................................................................................................194
第 8 周 ..........................................................................................................................................197
13、 聚类(Clustering)....................................................................................................197
13.1 无监督学习：简介..............................................................................................197
13.2 K-均值算法 ...........................................................................................................200
13.3 优化目标..............................................................................................................202
13.4 随机初始化..........................................................................................................203
13.5 选择聚类数..........................................................................................................204
14、 降维(Dimensionality Reduction)...........................................................................207
14.1 动机一：数据压缩..............................................................................................207
14.2 动机二：数据可视化..........................................................................................210
14.3 主成分分析问题..................................................................................................211
14.4 主成分分析算法..................................................................................................213
14.5 选择主成分的数量..............................................................................................214
14.6 重建的压缩表示..................................................................................................215
14.7 主成分分析法的应用建议..................................................................................217
第 9 周 ..........................................................................................................................................218
15、 异常检测(Anomaly Detection) .............................................................................218
15.1 问题的动机..........................................................................................................218
15.2 高斯分布..............................................................................................................220
15.3 算法......................................................................................................................221
15.4 开发和评价一个异常检测系统..........................................................................223
15.5 异常检测与监督学习对比..................................................................................224
15.6 选择特征..............................................................................................................225
15.7 多元高斯分布（选修）......................................................................................227
15.8 使用多元高斯分布进行异常检测（选修）......................................................230
16、 推荐系统(Recommender Systems).......................................................................233
16.1 问题形式化..........................................................................................................233
16.2 基于内容的推荐系统..........................................................................................235
16.3 协同过滤..............................................................................................................237
16.4 协同过滤算法......................................................................................................239
16.5 向量化：低秩矩阵分解......................................................................................240
16.6 推行工作上的细节：均值归一化......................................................................242
第 10 周 ........................................................................................................................................243
17、 大规模机器学习(Large Scale Machine Learning).................................................243
17.1 大型数据集的学习..............................................................................................243
IV
17.2 随机梯度下降法..................................................................................................244
17.3 小批量梯度下降..................................................................................................245
17.4 随机梯度下降收敛..............................................................................................246
17.5 在线学习..............................................................................................................248
17.6 映射化简和数据并行..........................................................................................250
18、 应用实例：图片文字识别(Application Example: Photo OCR) ............................251
18.1 问题描述和流程图..............................................................................................251
18.2 滑动窗口..............................................................................................................252
18.3 获取大量数据和人工数据..................................................................................254
18.4 上限分析：哪部分管道的接下去做..................................................................255
19、 总结(Conclusion)...................................................................................................256
19.1 总结和致谢..........................................................................................................256
附件 ..............................................................................................................................................258
机器学习的数学基础...........................................................................................................258
高等数学.......................................................................................................................258
线性代数.......................................................................................................................266
概率论和数理统计.......................................................................................................276