Latent factor density regression models
Jun 30 2012
In this article, we propose a new class of latent factor conditional density regression models with attractive computational and theoretical properties. The proposed approach is based on a novel extension of the recently proposed latent variable density estimation model in which the response variables conditioned on the predictors are modeled as unknown functions of uniformly distributed latent variables and the predictors with an additive Gaussian error. The latent variable specification allows straightforward posterior computation using a uni-dimensional grid via conjugate posterior updates. Moreover, one can center the model on a simple parametric guess facilitating inference. Our approach relies on characterizing the space of conditional densities induced by the above model as kernel convolutions with a general class of continuous predictor-dependent mixing measures. Theoretical properties in terms of rates of convergence are studied.
Keywords:Density regression; Gaussian process; Factor model; Latent variable; Nonparametric Bayes; Rate of convergence