• Mazza Christian

• Mazza Christian

This course aims at presenting and studying mathematically models from statistical learning theory, by focusing on deep learning algorithms in multi-layer neural networks. Applications to artificial intelligence will be provided. We will also present and study the basic probabilistic and statistical models of machine learning by making links with neural nets. A special emphasis will be given to deep learning processes for Boltzmann machines using methods from probability theory, statistics and statistical mechanics. 

Topics focus on but are not limited to:
Biological neural networks, mathematical models of neural nets, learning algorithms (Hebb rule) for Hop eld neural nets and Boltzmann machines, machine learning and multivariate statistics (discriminant analysis, regression, support vector machines), general statistical learning theory (deterministic and stochastic models, Vapnik-Cervonenkis theory), learning processes
in associative memories, perceptron and multi-layer neural nets, stochastic processes for deep learning in Boltzmann machines, thermodynamic extension (statistical mechanics of learning processes), self-organisation, chemical reaction networks and machine learning. If time permits we will also consider recent methods from topology and geometry like manifold learning and
topological data analysis.

compte pour Mathématiques appliquées