Computational inference beyond Kingman's coalescent

Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be expressed in terms of families of intractable conditional sampling distributions (CSDs), and rely on principled approximations for accurate inference. Recently, more general Λ- and Ξ- coalescents have been observed to provide better modelling ts to some genetic data sets. We derive families of approximate CSDs for nite sites Λ- and Ξ-coalescents, and use them to obtain "approximately optimal" IS and PAC algorithms for Λ coalescents, yielding substantial gains in efficiency over existing methods

Approximate inference in graphical models

Probability theory provides a mathematically rigorous yet conceptually flexible calculus of uncertainty, allowing the construction of complex hierarchical models for real-world inference tasks. Unfortunately, exact inference in probabilistic models is often computationally expensive or even intractable. A close inspection in such situations often reveals that computational bottlenecks are confined to certain aspects of the model, which can be circumvented by approximations without having to sacrifice the model's interesting aspects. The conceptual framework of graphical models provides an elegant means of representing probabilistic models and deriving both exact and approximate inference algorithms in terms of local computations. This makes graphical models an ideal aid in the development of generalizable approximations. This thesis contains a brief introduction to approximate inference in graphical models (Chapter 2), followed by three extensive case studies in which approximate inference algorithms are developed for challenging applied inference problems. Chapter 3 derives the first probabilistic game tree search algorithm. Chapter 4 provides a novel expressive model for inference in psychometric questionnaires. Chapter 5 develops a model for the topics of large corpora of text documents, conditional on document metadata, with a focus on computational speed. In each case, graphical models help in two important ways: They first provide important structural insight into the problem; and then suggest practical approximations to the exact probabilistic solution.This work was supported by a scholarship from Microsoft Research, Ltd

Approximate Inference in Probabilistic Answer Set Programming for Statistical Probabilities

Type 1 statements were introduced by Halpern in 1990 with the goal to represent statistical information about a domain of interest. These are of the form ''x of the elements share the same property''. The recently proposed language PASTA (Probabilistic Answer set programming for STAtistical probabilities) extends Probabilistic Logic Programs under the Distribution Semantics and allows the definition of this type of statements. To perform exact inference, PASTA programs are converted into probabilistic answer set programs under the Credal Semantics. However, this algorithm is infeasible for scenarios when more than a few random variables are involved. Here, we propose several algorithms to perform both conditional and unconditional approximate inference in PASTA programs and test them on different benchmarks. The results show that approximate algorithms scale to hundreds of variables and thus can manage real world domains