From Statistical Physics to Data-Driven Modelling with Applications to Quantitative Biology

The study of most scientific fields now relies on an ever-increasing amount of data, due to instrumental and experimental progress in monitoring and manipulating complex systems made of many microscopic constituents. How can we make sense of such data, and use them to enhance our understanding of biological, physical, and chemical systems? Aimed at graduate students in physics, applied mathematics, and computational biology, the primary objective of this textbook is to introduce the concepts and methods necessary to answer this question at the intersection of probability theory, statistics, optimisation, statistical physics, inference, and machine learning. The second objective of this book is to provide practical applications for these methods, which will allow students to assimilate the underlying ideas and techniques. While readers of this textbook will need basic knowledge in programming (Python or an equivalent language), the main emphasis is not on mathematical rigour, but on the development of intuition and the deep connections with statistical physics.

1 - Introduction to Bayesian inference
2 - Asymptotic inference and information
3 - High-dimensional inference: searching for principal components
4 - Priors, regularisation, sparsity
5 - Graphical models: from network reconstruction to Boltzmann machines
6 - Unsupervised learning: from representations to generative models
7 - Supervised learning: classification with neural networks
8 - Time series: from Markov models to hidden Markov models

Simona Cocco is a research Director at the Ecole Normale Supérieure in Paris, working on statistical physics, biophysics, and inference of models from data. In 2000, she received a double PhD in Physics from the Ecole Normale Supérieure in Lyon and Biophysics from the University of Rome “Sapienza” and was then a postdoc at the ENS in Paris and in Chicago, before joining the CNRS in 2001 as a permanent researcher. Between 2009 and 2011 she was a senior member at the Institute of Advanced Study in Princeton. Rémi Monasson is a research Director at the CNRS and the Ecole Normale Supérieure, and a professor at the Ecole Polytechnique. He did his PhD on the statistical mechanics of neural networks, and was then a postdoc in Rome, working on disordered systems and phase transitions in optimisation problems. He later worked on biophysics and systems biology in Chicago and at the Institute for Advanced Study in Princeton. His research interests lie at the intersection of statistical physics, machine learning and computational biology. Francesco Zamponi received his PhD in Theoretical Physics from the University of Rome “Sapienza” and was then a postdoc at the ENS and the CEA in Paris, before joining the CNRS in 2008 as a permanent researcher. He is currently based at the Physics Department of the ENS in Paris. His research is driven by the application of ideas and methods issued from the statistical mechanics of complex systems, to problems arising in classical and quantum condensed matter, biology, information theory, and mathematics. He has published over 130 research articles, and is the author of a chapter for the Handbook of Satisfiability (IOS Press 2021) and a book on the Theory of Simple Glasses (Cambridge University Press 2019). He was awarded an ERC Consolidator grant (GlassUniversality) and is one of the Principal Investigators of the Simons collaboration on ‘Cracking the glass problem’.