A high-bias, low-variance introduction to Machine Learning for physicists

A high-bias, low-variance introduction to Machine Learning for physicists

May 29, 2019 | Pankaj Mehta, Ching-Hao Wang, Alexandre G. R. Day, and Clint Richardson, Marin Bukov, Charles K. Fisher, David J. Schwab
This review provides an introduction to machine learning (ML) for physicists, emphasizing its core concepts and tools in a way that is intuitive and accessible. The review begins with fundamental concepts in ML and modern statistics, such as the bias-variance tradeoff, overfitting, regularization, and gradient descent, before moving on to more advanced topics in supervised and unsupervised learning. Topics covered include ensemble models, deep learning and neural networks, clustering, energy-based models, and variational methods. The review highlights the natural connections between ML and statistical physics and uses Python Jupyter notebooks to introduce modern ML/statistical packages with physics-inspired datasets, such as the Ising model and Monte-Carlo simulations of supersymmetric decays. The review concludes with an outlook on the potential of ML for advancing our understanding of the physical world and open problems in ML where physicists may contribute. The review is structured to serve as an introduction to foundational and state-of-the-art techniques in ML for physicists. It balances theoretical foundations with practical applications, providing a middle ground between a short overview and a full-length textbook. The review emphasizes physics-inspired pedagogical approaches, focusing on simple examples before delving into more advanced topics. It includes Jupyter notebooks to help readers apply the concepts to their own areas of interest. The review covers supervised and unsupervised learning, including linear and logistic regression, clustering, dimensionality reduction, and deep learning. It discusses the challenges of high-dimensional data, the importance of data visualization, and the role of regularization in preventing overfitting. The review also explores energy-based models, such as MaxEnt and RBMs, and variational methods, including mean-field theory. It concludes with an outlook on the intersection of physics and ML, highlighting the potential for physicists to contribute to open problems in ML. The review is suitable for graduate students, researchers, and advanced undergraduates with a background in statistical physics and mathematical techniques.This review provides an introduction to machine learning (ML) for physicists, emphasizing its core concepts and tools in a way that is intuitive and accessible. The review begins with fundamental concepts in ML and modern statistics, such as the bias-variance tradeoff, overfitting, regularization, and gradient descent, before moving on to more advanced topics in supervised and unsupervised learning. Topics covered include ensemble models, deep learning and neural networks, clustering, energy-based models, and variational methods. The review highlights the natural connections between ML and statistical physics and uses Python Jupyter notebooks to introduce modern ML/statistical packages with physics-inspired datasets, such as the Ising model and Monte-Carlo simulations of supersymmetric decays. The review concludes with an outlook on the potential of ML for advancing our understanding of the physical world and open problems in ML where physicists may contribute. The review is structured to serve as an introduction to foundational and state-of-the-art techniques in ML for physicists. It balances theoretical foundations with practical applications, providing a middle ground between a short overview and a full-length textbook. The review emphasizes physics-inspired pedagogical approaches, focusing on simple examples before delving into more advanced topics. It includes Jupyter notebooks to help readers apply the concepts to their own areas of interest. The review covers supervised and unsupervised learning, including linear and logistic regression, clustering, dimensionality reduction, and deep learning. It discusses the challenges of high-dimensional data, the importance of data visualization, and the role of regularization in preventing overfitting. The review also explores energy-based models, such as MaxEnt and RBMs, and variational methods, including mean-field theory. It concludes with an outlook on the intersection of physics and ML, highlighting the potential for physicists to contribute to open problems in ML. The review is suitable for graduate students, researchers, and advanced undergraduates with a background in statistical physics and mathematical techniques.
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