Bayesian Networks and Graphical Models
Real problems have many interacting variables. (directed graphical models) make such joint distributions tractable by drawing the dependencies as a graph: an arrow means ``directly influences,'' a missing arrow means ``c
閱讀文章 →Computational Bayes: MCMC and Variational Inference
Conjugacy is a luxury; most real posteriors have no closed form because the evidence integral p(D)= p(D)p(),d is intractable. The modern Bayesian toolkit sidesteps it two ways: draws samples from the posterior without ev
閱讀文章 →Bayesian Regression and Hierarchical Models
Now we put the machinery to work on the models practitioners use every day. replaces point-estimate coefficients with full posteriors, delivering principled uncertainty on every prediction. go further, sharing informatio
閱讀文章 →Model Comparison, Evidence, and Occam's Razor
Inference within a model assumes the model is right. But which model should we use? Bayesian model comparison answers this with the very quantity we worked so hard to avoid — the p(D) — which turns out to automatically e
閱讀文章 →Bayes in Machine Learning, Deep Learning, and AI
This capstone gathers the threads into one claim: . The loss is a likelihood. Regularization is a prior. Training finds a posterior mode. Ensembles approximate posterior averaging. Uncertainty estimates are posteriors. F
閱讀文章 →Notation and Formula Reference
A compact reference for the symbols, rules, and formulas used throughout the book.
閱讀文章 →Functions and the Idea of Calculus
Calculus studies how things change and how things accumulate. Before we can speak of change, we need the object that changes: the . This chapter sets up functions and the handful of ``essential'' ones that appear everywh
閱讀文章 →Limits and Continuity
The limit is the idea that makes calculus rigorous. ``Instantaneous'' rate of change and ``infinitely thin'' rectangles both hide a limit: a quantity we approach but may never reach. This chapter builds limits intuitivel
閱讀文章 →The Derivative
The derivative is the central object of differential calculus and the single most important concept for machine learning. It answers the tangent problem: the instantaneous rate at which a function changes. Once we have i
閱讀文章 →Differentiation Rules
Computing every derivative from the limit definition would be exhausting. Fortunately, a small set of rules lets us differentiate almost any function mechanically. The most important of these — the — is the mathematical
閱讀文章 →Applications of the Derivative
Now that we can compute derivatives, we put them to work. Derivatives find the highest and lowest points of a function (), approximate complicated functions by simple ones ( and Newton's method), and resolve stubborn lim
閱讀文章 →The Integral and the Fundamental Theorem
Integration is the second pillar of calculus: the mathematics of . Where the derivative chops a curve into instantaneous rates, the integral sums infinitely many tiny pieces into a total — an area, a distance, a probabil
閱讀文章 →Techniques of Integration
Differentiation is mechanical; integration is an art. There is no universal algorithm, so we build a toolkit of techniques — each one reversing a differentiation rule — plus numerical methods for the (many) integrals wit
閱讀文章 →Applications of Integration
Integration is far more than ``area under a curve.'' Any quantity built by accumulating infinitely many infinitesimal pieces is an integral: areas between curves, volumes of solids, lengths of arcs, averages, and — most
閱讀文章 →Sequences, Series, and Taylor Series
Can you add up infinitely many numbers and get a finite total? Sometimes — and when you can, the result is one of the most powerful tools in mathematics: the ability to represent complicated functions as infinite polynom
閱讀文章 →Multivariable Calculus: Partial Derivatives and the Gradient
Machine-learning models depend on millions of parameters at once, so single-variable calculus is not enough. This chapter extends differentiation to functions of several variables. The star object is the — the vector of
閱讀文章 →Multiple Integrals and a Glimpse of Vector Calculus
Just as differentiation extended to many variables, so does integration. accumulate a quantity over a region of two, three, or more dimensions — the natural setting for probabilities over several variables. The formula i
閱讀文章 →Optimization and Differential Equations
This chapter gathers the calculus that most directly becomes machine learning: how to find minima of functions of many variables (with and without constraints), the gradient-descent dynamics that training uses, and the d
閱讀文章 →Calculus in Machine Learning, Deep Learning, and AI
Here is the payoff. Linear algebra gives AI its — vectors, matrices, transformations. Calculus gives it the ability to . At the heart of almost every modern machine-learning system is one computational pattern: compute a
閱讀文章 →Preface: how to use this book
If linear algebra is the language of machine learning, calculus is its . Calculus is the mathematics of things that vary — how a quantity responds to a small nudge in another (the derivative), and how countless tiny piec
閱讀文章 →Notation and Formula Reference
A compact reference for the symbols and identities used throughout the book.
閱讀文章 →Vectors and the Geometry of Space
Everything in linear algebra is built from one object: the . Before we can multiply matrices or diagonalize transformations, we need to be completely comfortable with what a vector is, how to combine vectors, and how to
閱讀文章 →Systems of Linear Equations
A asks: which values of the unknowns satisfy several linear constraints at once? This is the oldest problem in the subject and still its computational core — training a linear model, balancing a chemical equation, and so
閱讀文章 →Matrices and Matrix Algebra
A matrix is the workhorse object of linear algebra. This chapter develops the algebra of matrices — how to add, multiply, transpose, and invert them — always keeping sight of the three views from the preface: a matrix is
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