Two-Layer Linear Auto-Regressive Models Estimate Latent States

This work presents a theoretical framework for two-layer linear auto-regressive models, demonstrating that they can approximate Kalman filtering when trained on data from partially observed linear dynamical systems. Key findings include the establishment of finite-sample guarantees on prediction and parameter estimation errors, and the optimization landscape showing global minima, which is significant for practitioners as it offers insights into the latent state recovery capabilities of auto-regressive models in sequential data applications. The results suggest that these models can effectively learn complex state dynamics without explicit knowledge of the underlying processes, enhancing their utility in various AI applications.