计算机科学的概率与统计：数据解析与机器学习
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"Probability and Statistics for Computer Science" 是一本由David Forsyth编写的教材，适合大二或大三计算机科学专业的学生使用。本书涵盖了定性和定量数据分析、概率论、随机变量和统计方法，特别是与机器学习相关的知识。书中强调了离散随机变量和期望的处理，还介绍了实用的模拟方法，尤其是马尔可夫链的应用。此外，书中还讨论了简单的推理策略，如最大似然估计和贝叶斯推理，并扩展到了置信区间的概念、随机抽样和最简单的假设检验。
书中的分类章节阐述了分类的实用性，教授如何使用随机梯度下降训练SVM分类器，以及如何利用随机森林和最近邻等高级方法。回归章节讲解了如何在实际问题中应用线性回归和最近邻回归。主成分分析章节通过实例深入浅出地建立了直觉，同时也提到了多元缩放的主坐标分析。在聚类部分，作者通过聚集方法和k均值算法展示了如何处理复杂信号的矢量量化特征。
全书各章节穿插了各种教学辅助元素，如过程框、定义、有用事实和记忆提示。每章末尾都有问题和编程练习，以帮助巩固学习内容。教师资源包括所有问题的模型解决方案和教师手册，以及配套的演示幻灯片。
这本书的目标是使计算机科学的学生能够理解和应用概率统计原理，以便他们在未来的学术研究或职业生涯中能够有效地处理和分析数据。通过实际例子和练习，本书旨在提高学生的实践技能，使其能够在计算机科学领域中利用这些统计工具解决复杂问题。
xviii Contents
11.4 The Support Vector Machine ................................................................. 260
11.4.1 The Hinge Loss ..................................................................... 261
11.4.2 Regularization ...................................................................... 262
11.4.3 Finding a Classifier with Stochastic Gradient Descent ..................................... 262
11.4.4 Searching for ..................................................................... 264
11.4.5 Example: Training an SVM with Stochastic Gradient Descent .............................. 266
11.4.6 Multi-Class Classification with SVMs .................................................. 268
11.5 Classifying with Random Forests ............................................................. 268
11.5.1 Building a Decision Tree: General Algorithm ............................................ 270
11.5.2 Building a Decision Tree: Choosing a Split.............................................. 270
11.5.3 Forests ............................................................................ 272
11.6 You Should ............................................................................... 274
11.6.1 Remember These Definitions ......................................................... 274
11.6.2 Remember These Terms ............................................................. 274
11.6.3 Remember These Facts .............................................................. 275
11.6.4 Use These Procedures ............................................................... 275
11.6.5 Be Able to ......................................................................... 276
12 Clustering: Models of High Dimensional Data ...................................................... 281
12.1 The Curse of Dimension ..................................................................... 281
12.1.1 Minor Banes of Dimension ........................................................... 281
12.1.2 The Curse: Data Isn’t Where You Think It Is ............................................ 282
12.2 Clustering Data ............................................................................ 283
12.2.1 Agglomerative and Divisive Clustering ................................................. 283
12.2.2 Clustering and Distance .............................................................. 285
12.3 The K-Means Algorithm and Variants ......................................................... 287
12.3.1 How to Choose K ................................................................... 288
12.3.2 Soft Assignment .................................................................... 290
12.3.3 Efficient Clustering and Hierarchical K Means ........................................... 291
12.3.4 K-Mediods ........................................................................ 292
12.3.5 Example: Groceries in Portugal ....................................................... 292
12.3.6 General Comments on K-Means ....................................................... 293
12.4 Describing Repetition with Vector Quantization ................................................. 294
12.4.1 Vector Quantization ................................................................. 296
12.4.2 Example: Activity from Accelerometer Data ............................................ 298
12.5 The Multivariate Normal Distribution .......................................................... 300
12.5.1 Affine Transformations and Gaussians .................................................. 301
12.5.2 Plotting a 2D Gaussian: Covariance Ellipses ............................................. 301
12.6 You Should ............................................................................... 302
12.6.1 Remember These Definitions ......................................................... 302
12.6.2 Remember These Terms ............................................................. 302
12.6.3 Remember These Facts .............................................................. 303
12.6.4 Use These Procedures ............................................................... 303
13 Regression ..................................................................................... 305
13.1 Regression to Make Predictions .............................................................. 305
13.2 Regression to Spot Trends ................................................................... 306
13.3 Linear Regression and Least Squares .......................................................... 308
13.3.1 Linear Regression ................................................................... 308
13.3.2 Choosing ˇ ........................................................................ 309
13.3.3 Solving the Least Squares Problem .................................................... 309
13.3.4 Residuals
.......................................................................... 310
13.3.5 R-Squared ......................................................................... 310
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