Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities

The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of a Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finite-dimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and apply it to several real-world data sets.

Probabilistic inference for fast learning in control

A novel framework is provided for very fast model-based reinforcement learning in continuous state and action spaces. It requires probabilistic models that explicitly characterize their levels of condence. Within the framework, exible, non-parametric models are used to describe the world based on previously collected experience. It demonstrates learning on the cart-pole problem in a setting where very limited prior knowledge about the task has been provided. Learning progressed rapidly, and a good policy found after only a small number of iterations.