Kirthevasan Kandasamy

Query efficient posterior estimation in scientific experiments via Bayesian active learning

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these research domains is to develop methods that can estimate the posterior with few likelihood evaluations.In this paper, we study active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework. We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.

Latent Beta Topographic Mapping

This paper describes Latent Beta Topographic Mapping (LBTM), a generative probability model for non linear dimensionality reduction and density estimation. LBTM is based on Generative Topographic Mapping (GTM) and hence inherits its ability to map complex non linear manifolds. However, the GTM is limited in its ability to reliably estimate sophisticated densities on the manifold. This paper explores the possibilities of learning a probability distribution for the data on the lower dimensional latent space. Learning a distribution helps not only in density estimation but also in maintaining topographic structure. In addition, LBTM provides useful methods for sampling, inference and visualization of high dimensional data. Experimental results indicate that LBTM can reliably learn the structure and distribution of the data and is competitive with existing methods for dimensionality reduction and density estimation.