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369
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 564 (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.
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 414 (12 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the “Bethe method, ” the “junction graph method, ” the “cluster variation method, ” and the “region graph method.” Finally, we explain how to tell whether a regionbased approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.
Generalized Belief Propagation
 IN NIPS 13
, 2000
"... Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs ..."
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Cited by 400 (9 self)
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Belief propagation (BP) was only supposed to work for treelike networks but works surprisingly well in many applications involving networks with loops, including turbo codes. However, there has been little understanding of the algorithm or the nature of the solutions it finds for general graphs. We show that
Discriminative probabilistic models for relational data
, 2002
"... In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, igno ..."
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Cited by 348 (11 self)
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In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, ignoring the correlations between them. Recently, Probabilistic Relational Models, a relational version of Bayesian networks, were used to define a joint probabilistic model for a collection of related entities. In this paper, we present an alternative framework that builds on (conditional) Markov networks and addresses two limitations of the previous approach. First, undirected models do not impose the acyclicity constraint that hinders representation of many important relational dependencies in directed models. Second, undirected models are well suited for discriminative training, where we optimize the conditional likelihood of the labels given the features, which generally improves classification accuracy. We show how to train these models effectively, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities. We provide experimental results on a webpage classification task, showing that accuracy can be significantly improved by modeling relational dependencies. 1
On the Optimality of Solutions of the MaxProduct Belief Propagation Algorithm in Arbitrary Graphs
, 2001
"... Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The maxproduct "belief propagation" algorithm is a localmessage passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tr ..."
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Cited by 185 (15 self)
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Graphical models, suchasBayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. The maxproduct "belief propagation" algorithm is a localmessage passing algorithm on this graph that is known to converge to a unique fixed point when the graph is a tree. Furthermore, when the graph is a tree, the assignment based on the fixedpoint yields the most probable a posteriori (MAP) values of the unobserved variables given the observed ones. Recently, good
Dynamic Conditional Random Fields: Factorized Probabilistic Models for Labeling and Segmenting Sequence Data
 IN ICML
, 2004
"... In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linearchain cond ..."
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Cited by 122 (11 self)
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In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linearchain conditional random fields (CRFs) in which each time slice contains a set of state variables and edgesa distributed state representation as in dynamic Bayesian networks (DBNs)and parameters are tied across slices. Since exact
Towards highly reliable enterprise network services via inference of multilevel dependencies
 IN SIGCOMM
, 2007
"... Localizing the sources of performance problems in large enterprise networks is extremely challenging. Dependencies are numerous, complex and inherently multilevel, spanning hardware and software components across the network and the computing infrastructure. To exploit these dependencies for fast, ..."
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Cited by 112 (10 self)
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Localizing the sources of performance problems in large enterprise networks is extremely challenging. Dependencies are numerous, complex and inherently multilevel, spanning hardware and software components across the network and the computing infrastructure. To exploit these dependencies for fast, accurate problem localization, we introduce an Inference Graph model, which is welladapted to userperceptible problems rooted in conditions giving rise to both partial service degradation and hard faults. Further, we introduce the Sherlock system to discover Inference Graphs in the operational enterprise, infer critical attributes, and then leverage the result to automatically detect and localize problems. To illuminate strengths and limitations of the approach, we provide results from a prototype deployment in a large enterprise network, as well as from testbed emulations and simulations. In particular, we find that taking into account multilevel structure leads to a 30 % improvement in fault localization, as compared to twolevel approaches.
A DoubleLoop Algorithm to Minimize the Bethe and Kikuchi Free Energies
 NEURAL COMPUTATION
, 2001
"... Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail t ..."
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Cited by 108 (4 self)
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Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail to work [4], [5], [10] [11]. In this paper we rst obtain the dual energy of the Bethe free energy which throws light on the BP algorithm. Next we introduce a discrete iterative algorithm which we prove is guaranteed to converge to a minimum of the Bethe free energy. We call this the doubleloop algorithm because it contains an inner and an outer loop. It extends a class of mean eld theory algorithms developed by [7],[8] and, in particular, [13]. Moreover, the doubleloop algorithm is formally very similar to BP which may help understand when BP converges. Finally, we extend all our results to the Kikuchi approximation which includes the Bethe free energy as a special case [3]. (Yedidia et al [22] showed that a \generalized belief propagation" algorithm also has its xed points at extrema of the Kikuchi free energy). We are able both to obtain a dual formulation for Kikuchi but also obtain a doubleloop discrete iterative algorithm that is guaranteed to converge to a minimum of the Kikuchi free energy. It is anticipated that these doubleloop algorithms will be useful for solving optimization problems in computer vision and other applications.
Efficient structure learning of Markov networks using L1regularization
 In NIPS
, 2006
"... Markov networks are widely used in a wide variety of applications, in problems ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to ..."
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Cited by 107 (2 self)
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Markov networks are widely used in a wide variety of applications, in problems ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to the lack of effective algorithms for learning Markov network structure from data. In this paper, we provide a computationally effective method for learning Markov network structure from data. Our method is based on the use of L1 regularization on the weights of the loglinear model, which has the effect of biasing the model towards solutions where many of the parameters are zero. This formulation converts the Markov network learning problem into a convex optimization problem in a continuous space, which can be solved using efficient gradient methods. A key issue in this setting is the (unavoidable) use of approximate inference, which can lead to errors in the gradient computation when the network structure is dense. Thus, we explore the use of different feature introduction schemes and compare their performance. We provide results for our method on synthetic data, and on two real world data sets: modeling the joint distribution of pixel values in the MNIST data, and modeling the joint distribution of genetic sequence variations in the human HapMap data. We show that our L1based method achieves considerably higher generalization performance than the more standard L2based method (a Gaussian parameter prior) or pure maximumlikelihood learning. We also show that we can learn MRF network structure at a computational cost that is not much greater than learning parameters alone, demonstrating the existence of a feasible method for this important problem. 1
A statistical model for general contextual object recog. ECCV
, 2004
"... Abstract. We consider object recognition as the process of attaching meaningful labels to specific regions of an image, and propose a model that learns spatial relationships between objects. Given a set of images and their associated text (e.g. keywords, captions, descriptions), the objective is to ..."
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Cited by 105 (7 self)
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Abstract. We consider object recognition as the process of attaching meaningful labels to specific regions of an image, and propose a model that learns spatial relationships between objects. Given a set of images and their associated text (e.g. keywords, captions, descriptions), the objective is to segment an image, in either a crude or sophisticated fashion, then to find the proper associations between words and regions. Previous models are limited by the scope of the representation. In particular, they fail to exploit spatial context in the images and words. We develop a more expressive model that takes this into account. We formulate a spatially consistent probabilistic mapping between continuous image feature vectors and the supplied word tokens. By learning both wordtoregion associations and object relations, the proposed model augments scene segmentations due to smoothing implicit in spatial consistency. Context introduces cycles to the undirected graph, so we cannot rely on a straightforward implementation of the EM algorithm for estimating the model parameters and densities of the unknown alignment variables. Instead, we develop an approximate EM algorithm that uses loopy belief propagation in the inference step and iterative scaling on the pseudolikelihood approximation in the parameter update step. The experiments indicate that our approximate inference and learning algorithm converges to good local solutions. Experiments on a diverse array of images show that spatial context considerably improves the accuracy of object recognition. Most significantly, spatial context combined with a nonlinear discrete object representation allows our models to cope well with oversegmented scenes. 2 Peter Carbonetto et al. 1