Applications of probabilistic programming

Thesis

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte Carlo inference with help of data-driven proposals. The latter is presented with experimental results on a linear Gaussian model and a non-parametric dependent Dirichlet process mixture of objects model for object recognition and tracking.

We begin this work by providing a brief introduction to probabilistic programming.

In the second Chapter we present an approach to automatic discovery of samplers in the form of probabilistic programs. Specifically, we learn the procedure code of samplers for one-dimensional distributions. We formulate a Bayesian approach to this problem by specifying a grammar-based prior over probabilistic program code. We use an approximate Bayesian computation method to learn the programs, whose executions generate samples that statistically match observed data or analytical characteristics of distributions of interest. In our experiments we leverage different probabilistic programming systems, including Anglican and Probabilistic C, to perform Markov chain Monte Carlo sampling over the space of programs. Experimental results have demonstrated that, using the proposed methodology, we can learn approximate and even some exact samplers. Finally, we show that our results are competive with regard to genetic programming methods.

In Chapter 3, we describe a way to facilitate sequential Monte Carlo inference in probabilistic programming using data-driven proposals. In particular, we develop a distance-based proposal for the non-parametric dependant Dirichlet process mixture of objects model. We implement this approach in the probabilitic programming system Anglican, and show that for that model data-driven proposals provide significant perfomance improvements. We also explore the possibility of using neural networks to improve data-driven proposals.

Authors: Perov, Y

• DOI: 10.5287/ora-o01n9jdrp
• Type of award: MSc by Research
• Level of award: Masters
• Awarding institution: University of Oxford
• Language: English
• Keywords: data-driven proposals; automatic programming; program induction; generative models; probabilistic inference; Markov chain Monte Carlo; automatic modelling; model induction; probabilistic programming
• Subjects: Machine learning; Computer science; Artificial intelligence