Dynamic Bayesian Networks: Representation, Inference and Learning by Kevin Patrick Murphy Doctor of Philosophy in Computer Science University of California, Berkeley Professor Stuart Russell, Chair Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T ) time instead of O(T ), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T ) space instead of O(T ); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

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Dynamic bayesian networks: representation, inference and learning

Image understanding requires not only individually estimating elements of the visual world but also capturing the interplay among them. In this paper, we provide a framework for placing local object detection in the context of the overall 3D scene by modeling the interdependence of objects, surface orientations, and camera viewpoint. Most object detection methods consider all scales and locations in the image as equally likely. We show that with probabilistic estimates of 3D geometry, both in terms of surfaces and world coordinates, we can put objects into perspective and model the scale and location variance in the image. Our approach reflects the cyclical nature of the problem by allowing probabilistic object hypotheses to refine geometry and vice-versa. Our framework allows painless substitution of almost any object detector and is easily extended to include other aspects of image understanding. Our results confirm the benefits of our integrated approach.

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Putting Objects in Perspective

It has been widely observed that there is no single "dominant" SAT solver; instead, different solvers perform best on different instances. Rather than following the traditional approach of choosing the best solver for a given class of instances, we advocate making this decision online on a per-instance basis. Building on previous work, we describe SATzilla, an automated approach for constructing per-instance algorithm portfolios for SAT that use so-called empirical hardness models to choose among their constituent solvers. This approach takes as input a distribution of problem instances and a set of component solvers, and constructs a portfolio optimizing a given objective function (such as mean runtime, percent of instances solved, or score in a competition). The excellent performance of SATzilla was independently verified in the 2007 SAT Competition, where our SATzilla07 solvers won three gold, one silver and one bronze medal. In this article, we go well beyond SATzilla07 by making the portfolio construction scalable and completely automated, and improving it by integrating local search solvers as candidate solvers, by predicting performance score instead of runtime, and by using hierarchical hardness models that take into account different types of SAT instances. We demonstrate the effectiveness of these new techniques in extensive experimental results on data sets including instances from the most recent SAT competition.

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SATzilla: portfolio-based algorithm selection for SAT

Inferring, or ‘reverse-engineering', gene networks can be defined as the process of identifying gene interactions from experimental data through computational analysis. Gene expression data from microarrays are typically used for this purpose. Here we compared different reverse-engineering algorithms for which ready-to-use software was available and that had been tested on experimental data sets. We show that reverse-engineering algorithms are indeed able to correctly infer regulatory interactions among genes, at least when one performs perturbation experiments complying with the algorithm requirements. These algorithms are superior to classic clustering algorithms for the purpose of finding regulatory interactions among genes, and, although further improvements are needed, have reached a discreet performance for being practically useful.

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How to infer gene networks from expression profiles

In this paper, we address the challenging problem of simultaneous pedestrian detection and ground-plane estimation from video while walking through a busy pedestrian zone. Our proposed system integrates robust stereo depth cues, ground-plane estimation, and appearance-based object detection in a principled fashion using a graphical model. Object-object occlusions lead to complex interactions in this model that make an exact solution computationally intractable. We therefore propose a novel iterative approach that first infers scene geometry using belief propagation and then resolves interactions between objects using a global optimization procedure. This approach leads to a robust solution in few iterations, while allowing object detection to benefit from geometry estimation and vice versa. We quantitatively evaluate the performance of our proposed approach on several challenging test sequences showing strolls through busy shopping streets. Comparisons to various baseline systems show that it outperforms both a system using no scene geometry and one just relying on structure-from-motion without dense stereo.

Depth and Appearance for Mobile Scene Analysis

The Bayes Net Toolbox (BNT) is an open-source Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a high-level, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and discuss the nascent OpenBayes e ort.

K. Murphy

Papers

The bayes net toolbox for matlab