Segmenting Hybrid Trajectories using Latent ODEs
This addresses the challenge of segmenting hybrid trajectories for applications in time series analysis, though it appears incremental as it builds on existing latent ODE methods.
The authors tackled the problem of modeling hybrid systems with smooth dynamics interrupted by discontinuities by proposing LatSegODE, which uses latent ODEs for reconstruction and changepoint detection, outperforming baselines on synthetic datasets like sine waves and UCI Character Trajectories.
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.