Science of Information, Statistics, and Learning

+ Information Theory basics: Bayes302222 theorem, Random Variables, Independenceand Conditioning, Shannon entropy, Relative entropy, Mutual Information,Markov chains, Sanov302222s theorem.+ Statistics: Linear regression, statistical model, Exponential families,sampling, Monte Carlo, inference, Maximum Likelihood Estimation, Maximum aposteriori, Bayesian Inference.+ Inference: MaxENT algorithm, relation between Bayesian and MaxENTmethods, Statistical Mechanics, Ising models, graphical models,Hammersley-Clifford theorem, EM algorithm, belief propagation.+ Learning: Introduction to neural networks, the single neuron as aclassifier, capacity of a single neuron, learning as inference, Hopfieldnetworks, Boltzmann machines, Supervised learning in multilayered networks,Gaussian processes, Deconvolution.+ Application to Chemical Reaction Networks: Introduction to chemicalreaction networks, Mass-action kinetics, Chemical Master Equation, Birch302222stheorem, Connection to exponential families, the MLE algorithm usingreaction networks, current topics in molecular intelligence.===