Probabilistic Machine Learning book – a great free reference for maths of machine learning

At the #universityofoxford I focus a lot on the mathematics aspect of AI

I recommend eight books for the mathematics of AI

The Nature Of Statistical Learning Theory By Vladimir Vapnik.
Pattern Classification By Richard O Duda
Machine Learning: An Algorithmic Perspective, Second Edition By Stephen Marsland
The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition By Trevor Hastie, Robert Tibshirani, Jerome Friedman
Pattern Recognition and Machine Learning (Information Science and Statistics) By Christopher M. Bishop
Machine Learning: The Art and Science of Algorithms that Make Sense of Data By Peter Flach
Deep Learning By Goodfellow, Bengio and Corville
Machine Learning: A Probabilistic Perspective by Kevin Murphy

Now, there is a new version of Machine Learning: A Probabilistic Perspective by Kevin Murphy

This is an amazing book – last published in 2012

The structure below and link to access below

If you can, I recommend you should buy this book, as I will – because this is very generous of Kevin Murphy and MIT press

The structure is very detailed and the book takes a Bayesian perspective

Foundations

Probabilistic inference

Introduction

Bayes’ rule

Bayesian concept learning

Bayesian machine learning

Probabilistic models

Bernoulli and binomial distributions

Categorical and multinomial distributions

Univariate Gaussian (normal) distribution

Some other common univariate distributions

The multivariate Gaussian (normal) distribution

Linear Gaussian systems

Mixture models

Probabilistic graphical models

Parameter estimation

Introduction

Maximum likelihood estimation (MLE)

Empirical risk minimization (ERM)

Regularization

The method of moments

Online (recursive) estimation

Parameter uncertainty

Optimization algorithms

First-order methods

Second-order methods

Stochastic gradient descent

Constrained optimization

Proximal gradient method

Bound optimization

Blackbox and derivative free optimization

Information theory

Entropy

Relative entropy (KL divergence)

Mutual information

Bayesian statistics

Introduction

Conjugate priors

Noninformative priors

Hierarchical priors

Empirical priors

Bayesian model comparison

Approximate inference algorithms

Bayesian decision theory

Bayesian decision theory

A/B testing

Bandit problems

II Linear models

Linear discriminant analysis

Introduction

Gaussian discriminant analysis

Naive Bayes classifiers

Generative vs discriminative classifiers

Logistic regression

Introduction

Binary logistic regression

Multinomial logistic regression

Preprocessing discrete input data

Robust logistic regression

Bayesian logistic regression

Linear regression

Introduction

Standard linear regression

Ridge regression

Robust linear regression

Lasso regression

Bayesian linear regression

Generalized linear models

Introduction

The exponential family

Generalized linear models (GLMs)

Probit regression

III Deep neural networks

Neural networks for unstructured data

Introduction

Multilayer perceptrons (MLPs)

Backpropagation

Training neural networks

Regularization

Other kinds of feedforward networks

Neural networks for images

Introduction

Basics

Image classification using CNNs

Solving other discriminative vision tasks with CNNs

Generating images by inverting CNNs

Adversarial Examples

Neural networks for sequences

Introduction

Recurrent neural networks (RNNs)

1d CNNs

Attention

Transformers

Eﬃcient transformers

IV Nonparametric models

Exemplar-based methods

K nearest neighbor (KNN) classification

Learning distance metrics

Kernel density estimation (KDE)

Kernel methods

Inferring functions from data

Mercer kernels

Gaussian processes

Scaling GPs to large datasets

Support vector machines (SVMs)

Sparse vector machines

Trees, forests, bagging and boosting

Classification and regression trees (CART)

Ensemble learning

Bagging

Random forests

Boosting

Interpreting tree ensembles

V Beyond supervised learning

Learning with fewer labeled examples

Data augmentation

Transfer learning

Meta-learning

Few-shot learning

Word embeddings

Semi-supervised learning

Active learning

Dimensionality reduction

Principal components analysis (PCA)

Factor analysis

Autoencoders

Manifold learning

Clustering

Recommender systems

Graph embeddings

Book link is

https://probml.github.io/pml-book/book1.html

Reference

@book{pml1Book,

author = “Kevin P. Murphy”,

title = “Probabilistic Machine Learning: An introduction”,

publisher = “MIT Press”,

year = 2021,

url = “probml.ai“

}

Image source Wikipedia