Identification of Intermittent Temporal Latent Process

Identifying time-delayed temporal latent process is crucial for understanding temporal dynamics and enabling downstream reasoning. Although recent methods have made remarkable progress in this field, they cannot address the dynamics in which the influence of some latent factors on both the subsequent latent states and the observed data can become inactive or irrelevant at different time steps. Therefore, we introduce intermittent temporal latent processes, where: (1) any subset of latent factors may be missing during nonlinear data generation at any time step, and (2) the active latent factors at each step are unknown. This framework encompasses both nonstationary and stationary transitions, accommodating changing or consistent active factors over time. Our work shows that under certain assumptions, the latent variables are block-wise identifiable. With further conditional independence assumption, each latent variable can even be recovered up to component-wise transformations. Using this identification theory, we propose an unsupervised approach, InterLatent , to reliably uncover the representations of the intermittent temporal latent process. The experiments on both synthetic and real-world datasets verify our theoretical claims.