Mehta P., Bukov M., Wang C.-H., Day A.G.R., Richardson C., Fisher C.K., Schwab D.J. A high-bias, low-variance introduction to Machine Learning for physicists

Physics Reports. — 2019. — Vol. 810. — P. 1-124.Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias–variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton–proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.Why is Machine Learning difficult?
Basics of statistical learning theory.
Gradient descent and its generalizations.
Overview of Bayesian inference.
Linear regression.
Logistic regression.
Combining models.
An introduction to feed-forward deep neural networks (DNNs).
Convolutional Neural Networks (CNNS).
High-level concepts in deep neural networks.
Dimensional reduction and data visualization.
Clustering.
Variational methods and mean-field theory (MFT).
Energy based models: Maximum entropy (MaxEnt) principle, generative models, and Boltzmann learning.
Deep generative models: Hidden variables and restricted Boltzmann machines (RBMs).
Variational autoencoders (VAEs) and generative adversarial networks (GANs).
Outlook.Appendix. Overview of the datasets used in the review.