Non-Parametric State-Space Models: Identifiability, Estimation and Forecasting

State-space models (SSMs) provide a standard methodology for time series analysis and prediction. While recent works utilize nonlinear functions to parameterize the transition and emission processes to enhance their expressivity, the form of additive noise still limits their applicability in real-world scenarios. In this work, we propose a general formulation of SSMs with a completely non-parametric transition model and a flexible emission model which can account for sensor distortion. Besides, to deal with more general scenarios (e.g., non-stationary time series), we add a higher level model to capture time-varying characteristics of the process. Interestingly, we find that even though the proposed model is remarkably flexible, the latent processes are generally identifiable. Given this, we further propose the corresponding estimation procedure and make use of it for the forecasting task. Our model can recover the latent processes and their relations from observed sequential data. Accordingly, the proposed procedure can also be viewed as a method for causal representation learning. We argue that forecasting can benefit from causal representation learning, since the estimated latent variables are generally identifiable. Empirical comparisons on various datasets validate that our model could not only reliably identify the latent processes from the observed data, but also consistently outperform baselines in the forecasting task.