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
