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181
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... 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 biosequence analysis, and KFMs have bee ..."
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Cited by 770 (3 self)
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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 biosequence 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) linearGaussian. 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 RaoBlackwellised 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.
Bucket Elimination: A Unifying Framework for Reasoning
"... Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination ..."
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Cited by 298 (58 self)
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Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucketelimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and space exponential in the inducedwidth of the problem's interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called "conditioning search" require only linear space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucketelimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade space for time.
Representing and querying correlated tuples in probabilistic databases
 In ICDE
, 2007
"... Probabilistic databases have received considerable attention recently due to the need for storing uncertain data produced by many real world applications. The widespread use of probabilistic databases is hampered by two limitations: (1) current probabilistic databases make simplistic assumptions abo ..."
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Cited by 142 (11 self)
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Probabilistic databases have received considerable attention recently due to the need for storing uncertain data produced by many real world applications. The widespread use of probabilistic databases is hampered by two limitations: (1) current probabilistic databases make simplistic assumptions about the data (e.g., complete independence among tuples) that make it difficult to use them in applications that naturally produce correlated data, and (2) most probabilistic databases can only answer a restricted subset of the queries that can be expressed using traditional query languages. We address both these limitations by proposing a framework that can represent not only probabilistic tuples, but also correlations that may be present among them. Our proposed framework naturally lends itself to the possible world semantics thus preserving the precise query semantics extant in current probabilistic databases. We develop an efficient strategy for query evaluation over such probabilistic databases by casting the query processing problem as an inference problem in an appropriately constructed probabilistic graphical model. We present several optimizations specific to probabilistic databases that enable efficient query evaluation. We validate our approach by presenting an experimental evaluation that illustrates the effectiveness of our techniques at answering various queries using real and synthetic datasets. 1
A differential approach to inference in Bayesian networks
 Journal of the ACM
, 2000
"... We present a new approach to inference in Bayesian networks which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it ca ..."
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Cited by 140 (20 self)
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We present a new approach to inference in Bayesian networks which is based on representing the network using a polynomial and then retrieving answers to probabilistic queries by evaluating and differentiating the polynomial. The network polynomial itself is exponential in size, but we show how it can be computed efficiently using an arithmetic circuit that can be evaluated and differentiated in time and space linear in the circuit size. The proposed framework for inference subsumes one of the most influential methods for inference in Bayesian networks, known as the tree–clustering or jointree method, which provides a deeper understanding of this classical method and lifts its desirable characteristics to a much more general setting. We discuss some theoretical and practical implications of this subsumption. 1.
UCPnetworks: A directed graphical representation of conditional utilities
 In Proceedings of UAI’01
, 2001
"... We propose a directed graphical representation of utility functions, called UCPnetworks, that combines aspects of two existing preference models: generalized additive models and CPnetworks. The network decomposes a utility function into a number of additive factors, with the directionality of the ..."
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Cited by 117 (21 self)
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We propose a directed graphical representation of utility functions, called UCPnetworks, that combines aspects of two existing preference models: generalized additive models and CPnetworks. The network decomposes a utility function into a number of additive factors, with the directionality of the arcs reflecting conditional dependence in the underlying (qualitative) preference ordering under a ceteris paribus interpretation. The CPsemantics ensures that computing optimization and dominance queries is very efficient. We also demonstrate the value of this representation in decision making. Finally, we describe an interactive elicitation procedure that takes advantage of the linear nature of the constraints on “tradeoff weights ” imposed by a UCPnetwork. 1
Improving the analysis of dependable systems by mapping fault trees into Bayesian networks
, 2001
"... Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of realworld tasks but they have received little attention in the area of dependability. The present paper is aimed at exploring the capabilities of the BN f ..."
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Cited by 54 (9 self)
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Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of realworld tasks but they have received little attention in the area of dependability. The present paper is aimed at exploring the capabilities of the BN formalism in the analysis of dependable systems. To this end, the paper compares BN with one of the most popular techniques for dependability analysis of large, safety critical systems, namely Fault Trees (FT). The paper shows that any FT can be directly mapped into a BN and that basic inference techniques on the latter may be used to obtain classical parameters computed from the former (i.e. reliability of the Top Event or of any subsystem, criticality of components, etc). Moreover, by using BN, some additional power can be obtained, both at the modeling and at the analysis level. At the modeling level, several restrictive assumptions implicit in the FT methodology can be removed and various kinds of dependencies among components can be accommodated. At the analysis level, a general diagnostic analysis can be performed. The comparison of the two methodologies is carried out by means of a running example, taken from the literature, that consists of a redundant multiprocessor system. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Dependable systems; Probabilistic methods; Bayesian networks; Fault tree analysis 1.
Lazy propagation: A junction tree inference algorithm based on lazy evaluation
 Artif. Intell
, 1999
"... Abstract In this paper we present a junction tree based inference architecture exploiting the structure of the original Bayesian network and independence relations induced by evidence to improve the efficiency of inference. The efficiency improvements are obtained by maintaining a multiplicative de ..."
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Cited by 54 (10 self)
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Abstract In this paper we present a junction tree based inference architecture exploiting the structure of the original Bayesian network and independence relations induced by evidence to improve the efficiency of inference. The efficiency improvements are obtained by maintaining a multiplicative decomposition of clique and separator potentials. Maintaining a multiplicative decomposition of clique and separator potentials offers a tradeoff between offline constructed junction trees and online exploitation of barren variables and independence relations induced by evidence. We consider the impact of the proposed architecture on a number of commonly performed Bayesian network tasks. The tasks we consider include cautious propagation of evidence, determining a most probable configuration, and fast retraction of evidence a long with a number of other tasks. The general impression is that the proposed architecture increases the computational efficiency of performing these tasks. The efficiency improvement offered by the proposed architecture is emphasized through empirical evaluations involving large realworld Bayesian networks. We compare the time and space performance of the proposed architecture with nonoptimized implementations of the HUGIN and ShaferShenoy inference architectures.
Compiling Bayesian Networks Using Variable Elimination
, 2007
"... Compiling Bayesian networks has proven an effective approach for inference that can utilize both global and local network structure. In this paper, we define a new method of compiling based on variable elimination (VE) and Algebraic Decision Diagrams (ADDs). The approach is important for the followi ..."
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Cited by 48 (8 self)
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Compiling Bayesian networks has proven an effective approach for inference that can utilize both global and local network structure. In this paper, we define a new method of compiling based on variable elimination (VE) and Algebraic Decision Diagrams (ADDs). The approach is important for the following reasons. First, it exploits local structure much more effectively than previous techniques based on VE. Second, the approach allows any of the many VE variants to compute answers to multiple queries simultaneously. Third, the approach makes a large body of research into more structured representations of factors relevant in many more circumstances than it has been previously. Finally, experimental results demonstrate that VE can exploit local structure as effectively as state–of–the–art algorithms based on conditioning on the networks considered, and can sometimes lead to much faster compilation times.
On probabilistic inference by weighted model counting
 Artificial Intelligence
"... A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base ..."
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Cited by 48 (5 self)
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A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base in conjunctive normal form (CNF) with weights associated to each model according to the network parameters. Given this CNF, computing the probability of some evidence becomes a matter of summing the weights of all CNF models consistent with the evidence. A number of variations on this approach have appeared in the literature recently, that vary across three orthogonal dimensions. The first dimension concerns the specific encoding used to convert a Bayesian network into a CNF. The second dimensions relates to whether weighted model counting is performed using a search algorithm on the CNF, or by compiling the CNF into a structure that renders WMC a polytime operation in the size of the compiled structure. The third dimension deals with the specific properties of network parameters (local structure) which are captured in the CNF encoding. In this paper, we discuss recent work in this area across the above three dimensions, and demonstrate empirically its practical importance in significantly expanding the reach of exact probabilistic inference. We restrict our discussion to exact inference and model counting, even though other proposals have been extended for approximate inference and approximate model counting.