Course content:
Introduction to Bayesian Inference, Conditional Probability and Bayes Theorem,
Asymptotic inference, Entropy of a distribution, Cross entropy, Posterior Distribution, Kullback Leibler Divergence, Irrelevance of prior distribution, Entropy of a Poisson Proces
Information and Shannon’s Entropy, Mutual Information, The Maximal Entropy Principle
Principal Component Analysis, Most Informative directions and top components ; Retarded learning phase transition.
Clustering, Online PCA
Priors regularisation and Sparsity, Priors for least squared regressions, Cross validation for optimal prior strength
Graphical Inference : Network reconstruction for multivariate Gaussian variables, Ising model and Inverse Ising model, Pseudo Likelihood, Boltzmann Machine Learning, mean field inference, Inference of couplings from neuronal data
Unsupervised learning: Autoencoders, Restricted Boltzmann Machines. Linear and Non LinearActivation functions, Representations
Classification with neural network and perceptron learning algorithm, Multilayer neural networks
Markov models and Hidden Markov Models