Segmenting Hybrid Trajectories using Latent ODEs

TL;DR

This paper introduces LatSegODE, a novel method combining Latent ODEs with changepoint detection to effectively model and segment hybrid trajectories with discontinuities, outperforming existing methods on various datasets.

Contribution

The paper presents LatSegODE, a new approach that integrates Latent ODEs with PELT for segmentation and reconstruction of hybrid dynamical systems with discontinuities.

Findings

LatSegODE outperforms baselines in synthetic and real datasets.

Effective detection of changepoints in hybrid trajectories.

Improved reconstruction accuracy for discontinuous dynamics.

Abstract

Smooth dynamics interrupted by discontinuities are known as hybrid systems and arise commonly in nature. Latent ODEs allow for powerful representation of irregularly sampled time series but are not designed to capture trajectories arising from hybrid systems. Here, we propose the Latent Segmented ODE (LatSegODE), which uses Latent ODEs to perform reconstruction and changepoint detection within hybrid trajectories featuring jump discontinuities and switching dynamical modes. Where it is possible to train a Latent ODE on the smooth dynamical flows between discontinuities, we apply the pruned exact linear time (PELT) algorithm to detect changepoints where latent dynamics restart, thereby maximizing the joint probability of a piece-wise continuous latent dynamical representation. We propose usage of the marginal likelihood as a score function for PELT, circumventing the need for model complexity-based penalization. The LatSegODE outperforms baselines in reconstructive and segmentation tasks including synthetic data sets of sine waves, Lotka Volterra dynamics, and UCI Character Trajectories.