Identifying latent state transition in non-linear dynamical systems

Çağlar Hızlı, Çagatay Yildiz, Matthias Bethge, S. T. John, Pekka Marttinen

Keywords: Identifiability, Nonlinear ICA, Dynamical Systems, Sequential Variational Autoencoder

TL;DR: We present the first latent dynamical system that allows for identification of the unknown transition function, and theoretically proved its identifiability based on standard assumptions.

Abstract:

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying low-dimensional latent states and their time evolutions.
Previous work on disentangled representation learning within the realm of dynamical systems focused on the latent states, possibly with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior.
Inspired by advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps past states to the present.
We introduce a practical algorithm based on variational auto-encoders and empirically demonstrate in realistic synthetic settings that we can recover latent state dynamics with high accuracy, and correspondingly achieve high future prediction accuracy.

Submission Number: 28