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cocco s from statistical physics data driven modelling 2022

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Textbook in PDF format 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. Preface Introduction to Bayesian inference Why Bayesian inference? Notations and deffnitions The German tank problem Laplace's birth rate problem Tutorial 1: diffusion coeffcient from single-particle tracking Asymptotic inference and information Asymptotic inference Notions of information Inference and information: the maximum entropy principle Tutorial 2: entropy and information in neural spike trains High-dimensional inference: searching for principal components Dimensional reduction and principal component analysis The retarded learning phase transition Tutorial 3: replay of neural activity during sleep following task learning Priors, regularisation, sparsity Lp-norm based priors Conjugate priors Invariant priors Tutorial 4: sparse estimation techniques for RNA alternative splicing Graphical models: from network reconstruction to Boltzmann machines Network reconstruction for multivariate Gaussian variables Boltzmann machines Pseudo-likelihood methods Tutorial 5: inference of protein structure from sequence data Unsupervised learning: from representations to generative models Autoencoders Restricted Boltzmann machines and representations Generative models Learning from streaming data: principal component analysis revisited Tutorial 6: online sparse principal component analysis of neural assemblies Supervised learning: classi cation with neural networks The perceptron, a linear classifier Case of few data: overfitting Case of many data: generalisation A glimpse at multi-layered networks Tutorial 7: prediction of binding between PDZ proteins and peptides Time series: from Markov models to hidden Markov models Markov processes and inference Hidden Markov models Tutorial 8: CG content variations in viral genomes References Index

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Cocco S. From Statistical Physics to Data-Driven Modelling..2022.pdf 9.1 MB

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cocco s from statistical physics data driven modelling 2022