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

✍ Scribed by Simona Cocco, Rémi Monasson, Francesco Zamponi

• Publisher: Oxford University Press
• Year: 2022
• Tongue: English
• Leaves: 193
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
Titlepage
Copyright
Contents
Preface
1 Introduction to Bayesian inference
1.1 Why Bayesian inference?
1.2 Notations and deffnitions
1.3 The German tank problem
1.4 Laplace's birth rate problem
1.5 Tutorial 1: diffusion coeffcient from single-particle tracking
2 Asymptotic inference and information
2.1 Asymptotic inference
2.2 Notions of information
2.3 Inference and information: the maximum entropy principle
2.4 Tutorial 2: entropy and information in neural spike trains
3 High-dimensional inference: searching for principal components
3.1 Dimensional reduction and principal component analysis
3.2 The retarded learning phase transition
3.3 Tutorial 3: replay of neural activity during sleep following task learning
4 Priors, regularisation, sparsity
4.1 Lp-norm based priors
4.2 Conjugate priors
4.3 Invariant priors
4.4 Tutorial 4: sparse estimation techniques for RNA alternative splicing
5 Graphical models: from network reconstruction to Boltzmann machines
5.1 Network reconstruction for multivariate Gaussian variables
5.2 Boltzmann machines
5.3 Pseudo-likelihood methods
5.4 Tutorial 5: inference of protein structure from sequence data
6 Unsupervised learning: from representations to generative models
6.1 Autoencoders
6.2 Restricted Boltzmann machines and representations
6.3 Generative models
6.4 Learning from streaming data: principal component analysis revisited
6.5 Tutorial 6: online sparse principal component analysis of neural assemblies
7 Supervised learning: classi cation with neural networks
7.1 The perceptron, a linear classifier
7.2 Case of few data: overfitting
7.3 Case of many data: generalisation
7.4 A glimpse at multi-layered networks
7.5 Tutorial 7: prediction of binding between PDZ proteins and peptides
8 Time series: from Markov models to hidden Markov models
8.1 Markov processes and inference
8.2 Hidden Markov models
8.3 Tutorial 8: CG content variations in viral genomes
References
Index