Discriminative Learning for Dynamic State Prediction

We consider the problem of predicting a sequence of real-valued multivariate states that are correlated by some unknown dynamics, from a given measurement sequence. Although dynamic systems such as the State-Space Models are popular probabilistic models for the problem, their joint modeling of states and observations, as well as the traditional generative learning by maximizing a joint likelihood may not be optimal for the ultimate prediction goal. In this paper, we suggest two novel discriminative approaches to the dynamic state prediction: 1) learning generative state-space models with discriminative objectives and 2) developing an undirected conditional model. These approaches are motivated by the success of recent discriminative approaches to the structured output classification in discrete-state domains, namely, discriminative training of Hidden Markov Models and Conditional Random Fields (CRFs). Extending CRFs to real multivariate state domains generally entails imposing density integrability constraints on the CRF parameter space, which can make the parameter learning difficult. We introduce an efficient convex learning algorithm to handle this task. Experiments on several problem domains, including human motion and robot-arm state estimation, indicate that the proposed approaches yield high prediction accuracy comparable to or better than state-of-the-art methods.