Books and documentation
The chapter notes develop the module’s main material. These books and official documentation provide alternative explanations, fuller proofs, and details of numerical interfaces.
Mathematical references
| Source | Relevant material |
|---|---|
| Deisenroth, Faisal, and Ong, Mathematics for Machine Learning | Part I: linear algebra, geometry, decompositions, vector calculus, probability, and optimization. The local notes specify their numerator-layout derivative convention explicitly. |
| Mitchell, Machine Learning | Chapter 1: tasks, experience, and performance measures. |
| Härdle, Smoothing Techniques: With Implementation in S | Kernel density estimation and smoothing; the source cited for the Old Faithful waiting times in chapter 1. |
| Blitzstein and Hwang, Introduction to Probability | Probability laws, conditioning, random variables, distribution families, and expectation. |
| Durrett, Probability: Theory and Examples | Chapter 1: measure-theoretic foundations, including σ-algebras, the construction of Lebesgue measure, random variables as measurable maps, and the integral behind expectation. |
| Wasserman, All of Statistics | Statistical inference, empirical distributions, estimation, confidence intervals, and testing. |
| Murphy, Probabilistic Machine Learning: An Introduction | Probability, statistics, decision theory, and information-theoretic foundations of probabilistic models. |
| Cover and Thomas, Elements of Information Theory | Entropy, typical sequences, source coding, entropy rates, channels, differential entropy, and rate–distortion. |
| MacKay, Information Theory, Inference, and Learning Algorithms | Connections among coding, probabilistic inference, and learning. |
| Shalev-Shwartz and Ben-David, Understanding Machine Learning | Chapters 2–8 for statistical learning; further chapters on stability, online learning, and Rademacher complexity. |
| Mohri, Rostamizadeh, and Talwalkar, Foundations of Machine Learning | Growth functions, Rademacher complexity, margins, and generalization. |
Numerical libraries
| Documentation | Relevant material |
|---|---|
| NumPy array object | Shape, axes, arithmetic types, and the array representation. |
| NumPy copies and views | Shared storage, indexing, reshaping, and mutation. |
| NumPy broadcasting | Alignment of axes and singleton dimensions. |
| NumPy matrix multiplication | Matrix products, vector special cases, and batch dimensions. |
| NumPy least squares | Least-squares solutions, numerical rank, and singular values. |
| NumPy linear algebra | Factorizations, solves, eigenvalues, singular values, norms, and condition numbers used in chapter 2. |
| SciPy log-sum-exp | Stable logarithmic probability calculations. |
| PyTorch autograd mechanics | Recorded dependencies, leaf gradients, accumulation, and gradient modes. |
PyTorch torch.autograd | grad, backward, and the tensor attributes used in chapter 3’s backpropagation example. |
| PyTorch JVP and VJP | Derivative products with explicit input directions and output seeds. |
| PyTorch Linear | Output-by-input parameter storage and the batched affine map. |
| PyTorch cross-entropy | Logits, target representations, weighting, and reductions. |
| PyTorch optimizers | Gradient clearing, parameter updates, and optimizer state. |
| PyTorch data utilities | Dataset indexing, batching, and sampling order. |
The computing examples notebook accompanies chapter 6. Additional API links appear beside the corresponding definitions in that chapter. Chapters 2 and 3 link each NumPy and PyTorch function where the text first discusses it and list every function their examples use in a final collapsed appendix.