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 3), 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.

building block for automated diagnosis and control

Estimating the result size of complex queries that involve selection on multiple attributes and the join of several relations is a difficult but fundamental task in database query processing. It arises in cost-based query optimization, query profiling, and approximate query answering. In this paper, we show how probabilistic graphical models can be effectively used for this task as an accurate and compact approximation of the joint frequency distribution of multiple attributes across multiple relations. Probabilistic Relational Models (PRMs) are a recent development that extends graphical statistical models such as Bayesian Networks to relational domains. They represent the statistical dependencies between attributes within a table, and between attributes across foreign-key joins. We provide an efficient algorithm for constructing a PRM from a database, and show how a PRM can be used to compute selectivity estimates for a broad class of queries. One of the major contributions of this work is a unified framework for the estimation of queries involving both select and foreign-key join operations. Furthermore, our approach is not limited to answering a small set of predetermined queries; a single model can be used to effectively estimate the sizes of a wide collection of potential queries across multiple tables. We present results for our approach on several real-world databases. For both single-table multi-attribute queries and a general class of select-join queries, our approach produces more accurate estimates than standard approaches to selectivity estimation, using comparable space and time.

We show how a conceptually simple search operator called Optimal Reinsertion can be applied to learning Bayesian Network structure from data. On each step we pick a node called the target. We delete all arcs entering or exiting the target. We then find, subject to some constraints, the globally optimal combination of in-arcs and out-arcs with which to reinsert it. The heart of the paper is a new algorithm called ORSearch which allows each optimal reinsertion step to be computed efficiently on large datasets. Our empirical results compare Optimal Reinsertion against a highly tuned implementation of multi-restart hill climbing. The results typically show one to two orders of magnitude speed-up on a variety of datasets. They usually show better final results, both in terms of BDEU score and in modeling of future data drawn from the same distribution. 1. Bayesian Network Structure Search Given a dataset of R records and m categorical attributes, how can we find a Bayesian network structure that provides a good model of the data? Happily, the formulation of this question into a well-defined optimization problem is now fairly well understood (Heckerman et al., 1995; Cooper & Herskovits, 1992). However, finding the optimal solution is an NP-complete problem (Chickering, 1996a). The computational issues in performing heuristic search in this space are also severe, even taking into account the numerous ingenious and effective innovations in recent years (e.g.

Prioritized sweeping is a model-based reinforcement learning method that attempts to focus an agent's limited computational resources to achieve a good estimate of the value of environment states. To choose effectively where to spend a costly planning step, classic prioritized sweeping uses a simple heuristic to focus computation on the states that are likely to have the largest errors. In this paper, we introduce generalized prioritized sweeping, a principled method for generating such estimates in a representation-specific manner. This allows us to extend prioritized sweeping beyond an explicit, state-based representation to deal with compact representations that are necessary for dealing with large state spaces. We apply this method for generalized model approximators (such as Bayesian networks), and describe preliminary experiments that compare our approach with classical prioritized sweeping. 1 Introduction In reinforcement learning, there is a tradeoff between spending time act...

We propose a decision theoretic approach for deciding which interventions to perform so as to learn the causal structure of a model as quickly as possible. Without such interventions, it is impossible to distinguish between Markov equivalent models, even given infinite data. We perform online MCMC to estimate the posterior over graph structures, and use importance sampling to find the best action to perform at each step. We assume the data is discrete-valued and fully observed.

We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n × n, n ≥ 3, positive-definite symmetric matrix of random variables and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if W11 − W12W −1 is independent 22 W ′ 12 of {W12, W22} for every block partitioning

We present a collective approach to learning a Bayesian network from distributed heterogenous data. In this approach, we first learn a local Bayesian network at each site using the local data. Then each site identifies the observations that are most likely to be evidence of coupling between local and non-local variables and transmits a subset of these observations to a central site. Another Bayesian network is learnt at the central site using the data transmitted from the local site. The local and central Bayesian networks are combined to obtain a collective Bayesian network, that models the entire data. Experimental results and theoretical justification that demonstrate the feasibility of our approach are presented.

We consider the task of aggregating beliefs of several experts. We assume that these beliefs are represented as probability distributions. We argue that the evaluation of any aggregation technique depends on the semantic context of this task. We propose a framework, in which we assume that nature generates samples from a `true' distribution and different experts form their beliefs based on the subsets of the data they have a chance to observe. Naturally, the optimal aggregate distribution would be the one learned from the combined sample sets. Such a formulation leads to a natural way to measure the accuracy of the aggregation mechanism. We show that the well-known aggregation operator LinOP is ideally suited for that task. We propose a LinOP-based learning algorithm, inspired by the techniques developed for Bayesian learning, which aggregates the experts' distributions represented as Bayesian networks. We show experimentally that this algorithm performs well in practice. 1

results for performance debugging and failure diagnosis and detection in systems by using approaches based on automatically inducing models and deriving correlations from observed data. We believe that maximizing the potential of this line of research will require surmounting some fundamental challenges arising not from the modeling techniques themselves, but specifically from the application of those techniques to realworld systems. We specifically formulate three challenges. First, as new data is collected from a system, previously-induced models must be continuously assessed and validated, with the ultimate aim of achieving online adaption to system changes. Second, human operators must be able to effectively interact with the models, including interpreting model findings to generate explanations, enabling human feedback to improve the models, and identifying false positives and missed detections. Third, it should be possible to formally manipulate “signatures” of system state as represented by these models, allowing us to query the system’s past to identify recurring problems and manually annotate them with additional information. We contend that the specifics of this problem domain not only raise these challenges, but also provide the knowledge base from which to derive wellengineered solutions to them. We suggest some possible strategies for addressing each challenge and show how they arise in the context of a real example. 1