A Classification Framework for Partially Observed Dynamical Systems

TL;DR

This paper introduces a general classification framework for partially observed dynamical systems that leverages posterior distributions over models to account for uncertainty, demonstrating robustness even with simplified model classes.

Contribution

It proposes a novel approach using posterior distributions in model space for classification, improving robustness and handling uncertainty in partially observed systems.

Findings

Classifier performance remains strong with simplified model classes.

The framework effectively handles uncertainty from noise and sampling.

Validated on biological and stochastic systems.

Abstract

We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we employ posterior distributions over models, thus taking into account in a principled manner the uncertainty due to both the generative (observational and/or dynamic noise) and observation (sampling in time) processes. We evaluate the framework on two testbeds - a biological pathway model and a stochastic double-well system. Crucially, we show that the classifier performance is not impaired when the model class used for inferring posterior distributions is much more simple than the observation-generating model class, provided the reduced complexity inferential model class captures the essential characteristics needed for the given classification task.