Machine Learning in Geomechanics 1

5Artificial Neural Networks: Learning the Optimum Statistical Model from Data

Filippo GATTI

Laboratoire de Mécanique Paris-Saclay, UMR 9026, CentraleSupélec, CNRS, ENS Paris-Saclay, Université Paris-Saclay, Gif-sur-Yvette, France

The objective of this chapter is to provide a general background on machine learning basics to a non-expert readership with a strong background in computational science. Major theoretical aspects are outlined and supported by detailed examples and tutorials (along with the corresponding code snippets) to boost the learning process of both basic and advanced concepts with the help of practical and commented hands-on sessions, accessible to everybody. In particular, the chapter rephrases the machine learning problem according to an information theory paradigm that highlights the tight entanglement between two perspectives on data science: the statistic versus the optimization ones. Hereafter, sampling theory is firstly presented, including an introduction on the Fisher approach to statistical learning and by an introduction to the principle of maximum entropy for conditional probability laws. The remainder of the chapter is devoted to present the optimization framework in which major machine learning problems are cast, consisting of minimizing the empirical risk over a class of parametric statistical models. This framework is presented in connection with the Fisher information and the MaxEnt principle presented at the beginning of the chapter. First- ...