Reconstruction of Sequential Data with Probabilistic Models and Continuity Constraints

Abstract

We consider the problem of reconstructing a temporal discrete sequence of multidimensional real vectors when part of the data is missing, under the assumption that the sequence was generated by a continuous pro(cid:173) cess. A particular case of this problem is multivariate regression, which is very difficult when the underlying mapping is one-to-many. We pro(cid:173) pose an algorithm based on a joint probability model of the variables of interest, implemented using a nonlinear latent variable model. Each point in the sequence is potentially reconstructed as any of the modes of the conditional distribution of the missing variables given the present variables (computed using an exhaustive mode search in a Gaussian mix(cid:173) ture). Mode selection is determined by a dynamic programming search that minimises a geometric measure of the reconstructed sequence, de(cid:173) rived from continuity constraints. We illustrate the algorithm with a toy example and apply it to a real-world inverse problem, the acoustic-to(cid:173) articulatory mapping. The results show that the algorithm outperforms conditional mean imputation and multilayer perceptrons.