A Constrained Latent Variable Model

Latent variable models provide valuable compact representations for learning and inference in many computer vision tasks. However, most existing models cannot directly encode prior knowledge about the specific problem at hand. In this paper, we introduce a constrained latent variable model whose generated output inherently accounts for such knowledge. To this end, we propose an approach that explicitly imposes equality and inequality constraints on the model's output during learning, thus avoiding the computational burden of having to account for these constraints at inference. Our learning mechanism can exploit non-linear kernels, while only involving sequential closed-form updates of the model parameters. We demonstrate the effectiveness of our constrained latent variable model on the problem of non-rigid 3D reconstruction from monocular images, and show that it yields qualitative and quantitative improvements over several baselines

Voice morphing using the generative topographic mapping

In this paper we address the problem of Voice Morphing. We attempt to transform the spectral characteristics of a source speaker's speech signal so that the listener would believe that the speech was uttered by a target speaker. The voice morphing system transforms the spectral envelope as represented by a Linear Prediction model. The transformation is achieved by codebook mapping using the Generative Topographic Mapping, a non-linear, latent variable, parametrically constrained, Gaussian Mixture Model

Usefulness and estimation of proportionality constraints

Stata has for a long time the capability of imposing the constraint that parameters are a linear function of one another. It does not have the capability to impose the constraint that if a set of parameters change (due to interaction terms) they will maintain the relative differences among them. Such a proportionality constraint has a nice interpretation: the constrained variables together measure some latent concept. For instance if a proportionality constraint is imposed on the variables father’s education, mother’s education, father’s occupational status, and mother’s occupational status, than together they might be thought to measure the latent variable family socioeconomic status. With the proportionality constraint one can estimate the effect of the latent variable and how strong each observed variable loads on the latent variable (i.e. does the mother, the father, or the highest status parent matter most). Such a model is a special case of a so called MIMIC model. In principle these models can be estimated using standard ml algorithms, however as the parameters are rather strongly correlated ml has a hard time finding the maximum. An EM algorithm is proposed that will find the maximum. This maximum is than fed into ml to get the right standard errors.