Statistics and machine learning#
Below are some introductory texts for probability, statistics, machine learning and statistical learning theory. They are sorted roughly according to difficulty, so you can find a book that is suitable for where you are and what you need.
A First Course in Probability (9th Edition)
Sheldon M. Ross
This book covers combinatorics and stuff. For undergraduates. Might be too easy.Introduction to Probability and Statistics for Engineers and Scientists (4th Edition)
Sheldon M. Ross
This book covers more advanced topics. Lots of examples.Probability and Statistics, 4/E
Morris H. DeGroot and Mark J. Schervish
An alternative to (1), (2). More systematic but it doesn’t cover advanced topics like (2). This book was used by MIT for the following course. There are some simplified lecture notes on the course website.Probability, Statistics, Statistical learning
Graphical Models
Shaowei Lin
Here are some introductory slides I made for a summer workshop at Notre Dame University in 2013 to undergraduate math students.An Introduction to Graphical Models (not yet published)
Michael Jordan
The author is my FAVORITE guy on statistical learning. Assumes knowledge of probability and statistics, see (1), (2) and (3). Jordan has some old slides for a tutorial he was teaching.All of Statistics
Larry Wasserman
Good broad graduate or advanced undergraduate textbook.An Introduction to Statistical Learning with Applications in R
Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani
Standard introductory UNDERGRADUATE text for statistical learning. Assumes knowledge of probability and statistics, see (1), (2) and (3).The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd Edition)
Trevor Hastie, Robert Tibshirani and Jerome Friedman
Standard introductory GRADUATE text for statistical learning. Assumes knowledge of probability and statistics, see (1), (2) and (3). If you master this textbook, you can truly be an expert in machine learning.StatLect: Lectures on Probability Theory and Mathematical Statistics
Marco Taboga
An advanced online textbook on Statistics.Probability: Theory and Examples
Rick Durrett
Formal treatment of probability theory.Probability and Measure
Patrick Billingsley
Formal treatment of probability theory.Mathematical Statistics
Jun Shao
Formal treatment of probability theory.
The textbook (8) above covers the most of the topics in machine learning in detail. If you are interested in online machine learning classes, here are some good ones.