Toward a direct and scalable identification of reduced models for categorical processes.

Abstract

The applicability of many computational approaches is dwelling on the identification of reduced models defined on a small set of collective variables (colvars). A methodology for scalable probability-preserving identification of reduced models and colvars directly from the data is derived-not relying on the availability of the full relation matrices at any stage of the resulting algorithm, allowing for a robust quantification of reduced model uncertainty and allowing us to impose a priori available physical information. We show two applications of the methodology: (<i>i</i>) to obtain a reduced dynamical model for a polypeptide dynamics in water and (<i>ii</i>) to identify diagnostic rules from a standard breast cancer dataset. For the first example, we show that the obtained reduced dynamical model can reproduce the full statistics of spatial molecular configurations-opening possibilities for a robust dimension and model reduction in molecular dynamics. For the breast cancer data, this methodology identifies a very simple diagnostics rule-free of any tuning parameters and exhibiting the same performance quality as the state of the art machine-learning applications with multiple tuning parameters reported for this problem.