Continuous Latent Process Flows

TL;DR

This paper introduces Continuous Latent Process Flows (CLPF), a novel model for continuous time-series data that improves representational power and inference quality by using a time-dependent normalizing flow driven by stochastic differential equations.

Contribution

The paper proposes CLPF, a new architecture that decodes continuous latent processes into observable processes with a novel variational inference method using trajectory re-weighting.

Findings

Effective in various inference tasks on irregular time grids

Outperforms state-of-the-art baselines on synthetic data

Shows favourable performance on real-world time-series data

Abstract

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has practical benefits, including the ability to generate continuous trajectories and to perform inference on previously unseen time stamps. Despite exciting progress in this area, the existing models still face challenges in terms of their representational power and the quality of their variational approximations. We tackle these challenges with continuous latent process flows (CLPF), a principled architecture decoding continuous latent processes into continuous observable processes using a time-dependent normalizing flow driven by a stochastic differential equation. To optimize our model using maximum likelihood, we propose a novel piecewise construction of a variational posterior process and derive the corresponding variational lower bound using trajectory re-weighting. Our ablation studies demonstrate the effectiveness of our contributions in various inference tasks on irregular time grids. Comparisons to state-of-the-art baselines show our model's favourable performance on both synthetic and real-world time-series data.