Conditional state space models for discriminative motion estimation

We consider the problem of predicting a sequence of real-valued multivariate states from a given measurement sequence. Its typical application in computer vision is the task of motion estimation. State Space Models are widely used generative probabilistic models for the problem. Instead of jointly modeling states and measurements, we propose a novel discriminative undirected graphical model which conditions the states on the measurements while exploiting the sequential structure of the problem. The major benefits of this approach are: (1) It focuses on the ultimate prediction task while avoiding probably unnecessary effort in modeling the measurement density, (2) It relaxes generative models' assumption that the measurements are independent given the states, and (3) The proposed inference algorithm takes linear time in the measurement dimension as opposed to the cubic time for Kalman filtering, which allows us to incorporate large numbers of measurement features. We show that the parameter learning can be cast as an instance of convex optimization. We also provide efficient convex optimization methods based on theorems from linear algebra. The performance of the proposed model is evaluated on both synthetic data and the human body pose estimation from silhouette videos.