Event Details

MARS seminar series | Speaker: Gabriel Stoltz (Ecole des Ponts & Inria Paris) | Title: A mathematical analysis of autoencoders for (un)supervised dimensionality reduction

Abstract: Sampling high dimensional probability measures is often made difficult by the multimodality of the target probability distribution. Markov chain Monte Carlo methods need to pass through low probability regions to switch from one mode to another, which is a rare event. An approach to making these transitions less rare is to identify a few selected (nonlinear) degrees of freedom of the system, which are at the origin of the slow mixing behavior, compute the associated free energies, and perform some importance sampling based on the latter function. Various tools have now recently been developed in molecular simulation to automatically find the most relevant nonlinear degrees of freedom hindering sampling, based on machine learning tools such as autoencoders. I will present a methodology to leverage these models for better sampling, and will also provide a mathematical analysis of the approach, relating it to principal manifolds and providing an interpretation based on conditional expectations. I will also discuss recent work in combining these techniques with supervised dimensionality reduction approaches such as Fisher's LDA. The results will be illustrated on biologically relevant systems such as HSP90.