Repository: Freie Universität Berlin, Math Department

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

Gerber, S. and Horenko, I. (2017) Toward a direct and scalable identification of reduced models for categorical processes. Proceedings of the National Academy of Sciences, 114 (19). pp. 4863-4868.

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Official URL: http://doi.org/10.1073/pnas.1612619114

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) to obtain a reduced dynamical model for a polypeptide dynamics in water and (ii) 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.

Item Type:Article
Subjects:Biological Sciences
Physical Sciences
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2075
Deposited By: Silvia Hoemke
Deposited On:24 Apr 2017 10:29
Last Modified:03 Jul 2017 15:28

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