Learning to Smooth with Bidirectional Predictive State Inference Machines

We present the Smoothing Machine (SMACH, pronounced "smash"), a dynamical system learning algorithm based on chain Conditional Random Fields (CRFs) with latent states. Unlike previous methods, SMACH is designed to optimize prediction performance when we have information from both past and future observations. By leveraging Predictive State Representations (PSRs), we model beliefs about latent states through predictive states—an alternative but equivalent representation that depends directly on observable quantities. Predictive states enable the use of well-developed supervised learning approaches in place of local-optimum-prone methods like EM: we learn regressors or classifiers that can approximate message passing and marginalization in the space of predictive states. We provide theoretical guarantees on smoothing performance and we empirically verify the efficacy of SMACH on several dynamical system benchmarks.