Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneck

TL;DR

This paper introduces Time-lagged Information Bottleneck (T-IB), a novel information-theoretic approach for simplifying Markov process simulations by capturing essential temporal features and enabling large time jumps efficiently.

Contribution

The paper proposes T-IB, a new method that learns optimal representations for Markov processes, improving long-term simulation accuracy and efficiency over existing methods.

Findings

T-IB effectively captures relevant temporal features.

T-IB outperforms existing time-lagged dimensionality reduction methods.

T-IB accurately models statistical properties of original processes.

Abstract

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.