Incremental Static Analysis of Probabilistic Programs

Probabilistic models are used successfully in a wide range of fields, including machine learning, data mining, pattern recognition, and robotics. Probabilistic programming languages are designed to express probabilistic models in high-level programming languages and to conduct automatic inference to compute posterior distributions. A key obstacle to the wider adoption of probabilistic programming languages in practice is that general-purpose efficient inference is computationally difficult. This thesis aims to improve the efficiency of inference through incremental analysis, while preserving precision when a probabilistic program undergoes small changes. For small changes to probabilistic knowledge (i.e., prior probability distributions and observations), the probabilistic model represented by a probabilistic program evolves. In this thesis, we first present a new approach, Icpp, which is a data-flow-based incremental inference approach. By capturing the probabilistic dependence of each data-flow fact and updating changed probabilities sparsely, Icpp can incrementally compute new posterior distributions and thus enable previously computed results to be reused. For small changes at observed array data, upon which their probabilistic models are conditioned, the probabilistic models remain unchanged. In this thesis, we also present ISymb, which is a novel incremental symbolic inference framework. By conducting an intra-procedurally path-sensitive analysis, except for "meets-over-all-paths" analysis within an iteration of a loop (conditioned on some observed array data), ISymb captures the probability distribution for each path and only recomputes the probability distributions for the affected paths. Further, ISymb enables a precision-preserving incremental symbolic inference to run significantly faster than its non-incremental counterparts. In this thesis, we evaluate both Icpp and ISymb against the state-of-the-art data-flow-based inference and symbolic inference, respectively. The results demonstrate that both Icpp and ISymb meet their design goals. For example, Icpp succeeds in making data-flow-based incremental inference possible in probabilistic programs when some probabilistic knowledge undergoes small yet frequent changes. Additionally, ISymb enables symbolic inference to perform one or two orders of magnitude faster than non-incremental inference when some observed array dat

Bayesian robot Programming

We propose a new method to program robots based on Bayesian inference and learning. The capacities of this programming method are demonstrated through a succession of increasingly complex experiments. Starting from the learning of simple reactive behaviors, we present instances of behavior combinations, sensor fusion, hierarchical behavior composition, situation recognition and temporal sequencing. This series of experiments comprises the steps in the incremental development of a complex robot program. The advantages and drawbacks of this approach are discussed along with these different experiments and summed up as a conclusion. These different robotics programs may be seen as an illustration of probabilistic programming applicable whenever one must deal with problems based on uncertain or incomplete knowledge. The scope of possible applications is obviously much broader than robotics

Inference with Constrained Hidden Markov Models in PRISM

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference. Defining HMMs with side-constraints in Constraint Logic Programming have advantages in terms of more compact expression and pruning opportunities during inference. We present a PRISM-based framework for extending HMMs with side-constraints and show how well-known constraints such as cardinality and all different are integrated. We experimentally validate our approach on the biologically motivated problem of global pairwise alignment