While density estimation appears as one of the simplest and most widely researched nonparametric models, estimating conditional densities, also known as density regression, has posed a far greater challenge. A major effort was needed to uplift the popular Dirichlet processes to Depended Dirichlet processes suitable for modeling conditional distributions that vary smoothly over the conditioning variable. However, a much simpler framework obtains when one models densities by Gaussian processes. A smooth Gaussian process over the product space of the variable of interest and the conditioning variable, when exponentiated and separately normalized over the response variable at each value of the conditioning variables, produces a conditional density process that is smooth over the product space. In this talk, I will explore theoretical properties of such a process used as a prior distribution in a Baesyain analysis of conditional densities. Our work builds on the impressive recent work by Aad van der Vaart, Harry van Zanten and co-authors in characterizing properties of 're-scaled' Gaussian process models. I shall extend this study to deal with local, coordinate re-scaling that is useful for semi-parametric density regression models, such as those where a variable selection is to be performed on a multidimensional conditioning variable.
Keywords: Gaussian processes; Density regression; Posterior consistency; Variable selection
Biography: Surya T Tokdar is an Assistant Professor at Department of Statistical Science in Duke University. He received his Bachelors and Masters degrees in Statistics from Indian Statistics Institute, Kolkata India. He received his Phd in Statistics in 2006 from Purdue University under the supervision of Professor Jayanta K Ghosh, for which he was awarded The Savage Dissertation Award (Theory & Methods). Prior to joining Duke University, Surya has been a Morris H DeGroot Visiting Assistant Professor at Carnegie Mellon University. His research interest spans Nonparametric Bayesian theory and methods, with special emphasis to novel application and computation.