Small sample inference for probabilistic index models

Probabilistic index models may be used to generate classical and new rank tests, with the additional advantage of supplementing them with interpretable effect size measures. The popularity of rank tests for small sample inference makes probabilistic index models also natural candidates for small sample studies. However, at present, inference for such models relies on asymptotic theory that can deliver poor approximations of the sampling distribution if the sample size is rather small. A bias-reduced version of the bootstrap and adjusted jackknife empirical likelihood are explored. It is shown that their application leads to drastic improvements in small sample inference for probabilistic index models, justifying the use of such models for reliable and informative statistical inference in small sample studies

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

Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference

We propose an approach to lifted approximate inference for first-order probabilistic models, such as Markov logic networks. It is based on performing exact lifted inference in a simplified first-order model, which is found by relaxing first-order constraints, and then compensating for the relaxation. These simplified models can be incrementally improved by carefully recovering constraints that have been relaxed, also at the first-order level. This leads to a spectrum of approximations, with lifted belief propagation on one end, and exact lifted inference on the other. We discuss how relaxation, compensation, and recovery can be performed, all at the firstorder level, and show empirically that our approach substantially improves on the approximations of both propositional solvers and lifted belief propagation.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

Variational Probabilistic Inference and the QMR-DT Network

We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest. They provide alternatives to approximate inference methods based on stochastic sampling or search. We describe a variational approach to the problem of diagnostic inference in the `Quick Medical Reference' (QMR) network. The QMR network is a large-scale probabilistic graphical model built on statistical and expert knowledge. Exact probabilistic inference is infeasible in this model for all but a small set of cases. We evaluate our variational inference algorithm on a large set of diagnostic test cases, comparing the algorithm to a state-of-the-art stochastic sampling method