第 1章 隨機(jī)數(shù)生成技術(shù)..............................................................1

1.1標(biāo)準(zhǔn)分布的隨機(jī)數(shù)生成 ....................................................... 1

1.1.1連續(xù)型隨機(jī)變量仿真生成 ...................................................2

1.1.2離散型隨機(jī)變量仿真生成 ..................................................10

1.2非標(biāo)準(zhǔn)分布的隨機(jī)數(shù)生成 ................................................... 14

1.2.1逆變換法 ............................................................... 14

1.2.2接受-拒絕法與自適應(yīng)拒絕法 ............................................... 16

1.2.3組合法 ................................................................. 22

1.3隨機(jī)過(guò)程的隨機(jī)數(shù)生成 ......................................................26

1.3.1馬爾可夫過(guò)程仿真生成....................................................27

1.3.2泊松過(guò)程仿真生成 ....................................................... 31

1.3.3維納過(guò)程仿真生成 ....................................................... 35

1.4基于變分自編碼器模型的數(shù)據(jù)生成 .......................................... 36

1.4.1 VAE模型基本思想.......................................................37

1.4.2變分自編碼器模型 ....................................................... 37

1.5基于生成式對(duì)抗網(wǎng)絡(luò)的數(shù)據(jù)生成 .............................................46

1.5.1 GANs的基本原理 ....................................................... 46

1.5.2 GANs理論推導(dǎo) ......................................................... 48

1.5.3 GANs算法的近優(yōu)算法 ................................................... 53

1.6習(xí)題 ........................................................................ 57
第 2章 探索性數(shù)據(jù)分析 ............................................................ 61

2.1一維探索性數(shù)據(jù)分析 ........................................................ 61

2.1.1匯總統(tǒng)計(jì)量 ............................................................. 62

2.1.2直方圖 ................................................................. 65

2.1.3莖葉圖 ................................................................. 66

2.1.4箱線圖 ................................................................. 68

2.1.5正態(tài)概率圖 ............................................................. 70

2.1.6 Q-Q圖 .................................................................72

2.2多維探索性數(shù)據(jù)分析 ........................................................ 75

2.2.1多屬性統(tǒng)計(jì)量 ........................................................... 75

2.2.2散點(diǎn)圖 ................................................................. 77

2.2.3邊緣直方圖 ............................................................. 83

2.2.4邊緣箱形圖 ............................................................. 84

2.2.5成對(duì)圖 ................................................................. 86

2.2.6 Box-Cox線性變換圖 ..................................................... 87

2.2.7自相關(guān)圖和偏自相關(guān)圖....................................................90

2.2.8交叉相關(guān)圖 .............................................................94

2.2.9滯后圖 ................................................................. 95

2.3習(xí)題 ........................................................................ 97
第 3章 特征提取與選擇方法 .......................................................100

3.1特征提取方法 ..............................................................100

3.1.1主成分分析 ............................................................ 100

3.1.2因子分析 .............................................................. 109

3.1.3獨(dú)立分量分析 .......................................................... 115

3.1.4線性判別分析 .......................................................... 125

3.2時(shí)間序列的特征提取方法 .................................................. 130

3.2.1 STL分解算法 ..........................................................130

3.2.2經(jīng)驗(yàn)?zāi)�態(tài)分解 .......................................................... 132

3.2.3奇異譜分析方法 ........................................................ 139

3.2.4小波變換 .............................................................. 143

3.3特征選擇方法 ..............................................................160

3.3.1過(guò)濾特征選擇 .......................................................... 161

3.3.2 Wrapper法 ............................................................163

3.3.3 Embedded法 .......................................................... 166

3.3.4貝葉斯統(tǒng)計(jì)和正則化 .................................................... 168

3.4習(xí)題 .......................................................................173
第 4章 期望算法..............................................................176

4.1從極大似然估計(jì)到 EM算法 ............................................... 176

4.2 EM算法原理與實(shí)現(xiàn) ....................................................... 178

4.2.1 EM算法原理 .......................................................... 178

4.2.2 EM算法 .............................................................. 180

4.3 EM算法應(yīng)用 .............................................................. 184

4.3.1 K-Means聚類算法 ......................................................184

4.3.2高斯混合模型聚類算法 .................................................. 187

4.3.3 K-Means和 GMM的關(guān)系 ............................................... 195

4.4習(xí)題 .......................................................................195
第 5章 馬爾可夫鏈蒙特卡羅方法 .................................................. 197

5.1蒙特卡羅方法引入 ......................................................... 197

5.2馬爾可夫鏈蒙特卡羅方法 .................................................. 198

5.3 Metropolis-Hastings采樣 .................................................. 200

5.3.1 Metropolis采樣算法 .................................................... 200

5.3.2 Metropolis-Hastings采樣算法 ............................................ 204

5.3.3多維 Metropolis-Hastings采樣算法 ....................................... 207

5.4 Gibbs采樣 ................................................................ 209

5.5馬爾可夫鏈蒙特卡羅方法應(yīng)用 ..............................................213

5.5.1基于 MCMC的貝葉斯統(tǒng)計(jì)推斷...........................................213

5.5.2可逆跳轉(zhuǎn) MCMC方法 .................................................. 215

5.6習(xí)題 .......................................................................220
第 6章 重采樣技術(shù) ................................................................222

6.1刀切法.....................................................................222

6.1.1刀切法基本原理 ........................................................ 222

6.1.2刀切法算法與實(shí)現(xiàn) ...................................................... 225

6.2自助法.....................................................................225

6.2.1自助法基本原理 ........................................................ 225

6.2.2 Rn的統(tǒng)計(jì)特性 ......................................................... 229

6.3重采樣技術(shù)的應(yīng)用 ......................................................... 230

6.3.1 Bagging算法 .......................................................... 230

6.3.2 Boosting算法 ..........................................................237