The Singular Value Decomposition
If one theorem deserves the title ``fundamental theorem of data science,'' it is the singular value decomposition. The SVD factors matrix --- square or rectangular, full-rank or not --- into a rotation, a scaling, and an
阅读文章 →Matrix Decompositions, Norms, and Numerical Linear Algebra
On a real computer, linear algebra is done in finite-precision arithmetic, where the order of operations and the conditioning of a problem decide how many correct digits survive. This chapter consolidates the major matri
阅读文章 →Tensors and Matrix Calculus
Two ideas carry linear algebra the last mile into deep learning. First, generalize vectors and matrices to higher-order arrays --- the natural container for images, sequences, and batches. Second, extends derivatives to
阅读文章 →Linear Algebra in Machine Learning, Deep Learning, and AI
This final chapter is the payoff. Every concept in the book reappears here as the working machinery of modern AI. The thesis is simple and, by now, earned: Data are tensors; models are matrices; learning is optimization
阅读文章 →Preface: how to use this book
Linear algebra is the mathematics of . The moment you stop thinking about a single quantity and start thinking about lists of quantities --- the pixels of an image, the features of a customer, the weights of a neural net
阅读文章 →Why this phase matters
Math Tooling FoundationsLinear algebra, calculus, probability, statistics, and the scientific Python stack3--5 weeksBuild the mathematical intuition that makes every later algorithm instead of feeling like magic. By the
阅读文章 →Orientation
Core Machine LearningClassical models, evaluation, feature engineering, and tuning --- implemented, not just imported6--8 weeksUnderstand classical ML deeply enough to implement the key algorithms from scratch and to bui
阅读文章 →From linear models to neural networks
Deep Learning FoundationsNeurons, backpropagation, optimization, regularization, and PyTorch --- from first principles6--8 weeksUnderstand neural networks from the ground up --- forward pass, backpropagation, optimizatio
阅读文章 →Why images need special architectures
Computer VisionConvolutions, CNN architectures, transfer learning, detection, segmentation, and ViTs4--6 weeksUnderstand how neural networks see: the convolution operation, the architectural lineage from LeNet to ResNet
阅读文章 →Why this is the highest-leverage phase
Sequence Models, NLP TransformersFrom RNNs to attention to LLMs, tokenization, fine-tuning, and RAG6--8 weeksMaster the architecture behind modern AI. Build a Transformer from first principles, understand tokenization (i
阅读文章 →Discriminative vs. generative
Generative ModelsAutoencoders, VAEs, GANs, and diffusion --- how machines create4--5 weeksUnderstand how models learn to data: the latent-variable view (VAEs), the adversarial game (GANs), and the denoising process (diff
阅读文章 →A different learning paradigm
Reinforcement LearningMDPs, value functions, Q-learning, policy gradients, PPO, and RLHF3--4 weeks (optional)Understand learning by interaction and reward: Markov decision processes, the value/policy duality, deep Q-netw
阅读文章 →Why MLOps is your edge
MLOps, Deployment Production SystemsExperiment tracking, serving, containers, monitoring, optimization, and CI/CD for ML4--6 weeksTurn models into reliable products. Track experiments, package and serve models, monitor f
阅读文章 →The purpose of capstones
Capstone ProjectsCompounding value by building end-to-end systems in your own domainsOngoingConvert knowledge into demonstrable capability. Ship 2--3 end-to-end projects that intersect your existing domains (logistics, b
阅读文章 →Preface: how to use this book
If linear algebra is the language of machine learning and calculus is its engine, then probability and statistics are its . Machine learning is, at its core, the discipline of drawing reliable conclusions from noisy, inc
阅读文章 →Distributions and Identities Reference
A compact reference for the notation, distributions, and identities used throughout the book.
阅读文章 →What Is Probability?
Probability is the mathematics of uncertainty --- a precise language for reasoning about things we cannot predict with certainty. A coin flip, tomorrow's weather, whether an email is spam, what word comes next in a sente
阅读文章 →Conditional Probability and Bayes' Theorem
Almost all useful probability is : we want to know the chance of something what we already know. How likely is disease given a positive test? Spam given the word ``free''? The next word given the sentence so far? Conditi
阅读文章 →Random Variables and Expectation
So far events have been qualitative (``it rained''). A attaches numbers to outcomes, letting us do arithmetic with uncertainty: average it, measure its spread, add independent copies. Random variables and their two summa
阅读文章 →Common Probability Distributions
A handful of distributions describe most of the randomness we ever model. Each arises from a simple, recurring story --- a coin flip, a count of rare events, a sum of many small effects --- and learning those stories let
阅读文章 →Joint Distributions, Covariance, and the Multivariate Gaussian
Real data is rarely one number; it is vectors of many interrelated quantities --- pixels, features, tokens. To model them we need that capture how variables vary , the that quantifies their linear relationship, and the ,
阅读文章 →Inequalities and Limit Theorems
Why does averaging more data give a better answer? Why are so many things bell-shaped? Why can we estimate an expectation by a sample mean --- the move that justifies mini-batch training? The answer these questions. They
阅读文章 →Estimation and Maximum Likelihood
We now cross from probability into statistics --- from ``given the model, predict the data'' to ``given the data, infer the model.'' The central task is : using a sample to guess an unknown parameter. The dominant method
阅读文章 →Confidence Intervals and Hypothesis Testing
A point estimate alone is dangerous: it hides its own uncertainty. This chapter adds the error bars. express how precise an estimate is; decide whether an observed effect is real or could be chance. These frequentist too
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