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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 process. A particular case of this problem is
multivariate regression, which is very difficult when the
underlying mapping is one-to-many. We propose 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 mixture).
Mode selection is determined by a dynamic programming search that
minimises a geometric measure of the reconstructed sequence,
derived from continuity constraints. We illustrate the algorithm
with a toy example and apply it to a real-world inverse problem,
the acoustic-to-articulatory mapping. The results show that the
algorithm outperforms conditional mean imputation and multilayer
perceptrons.
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