We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges IN many practical cases, but NOT always.We derive a DOUBLE - loop algorithm, guaranteed TO converge TO a local minimum OF a Bethe free energy.Furthermore, we show that stable fixed points OF (damped) expectation propagation correspond TO local minima OF this free energy, but that the converse need NOT be the CASE .We illustrate the algorithms BY applying them TO switching linear dynamical systems AND discuss implications FOR approximate inference IN general Bayesian networks.

The Reverse Water Gas Shift system (RWGS) is a complex physical system designed to produce oxygen from the carbon dioxide atmosphere on Mars. If sent to Mars, it would operate without human supervision, thus requiring a reliable automated system for monitoring and control. The RWGS presents many challenges typical of real-world systems, including: noisy and biased sensors, nonlinear behavior, effects that are manifested over different time granularities, and unobservability of many important quantities. In this paper we model the RWGS using a hybrid (discrete/continuous) Dynamic Bayesian Network (DBN), where the state at each time slice contains 33 discrete and 184 continuous variables. We show how the system state can be tracked using probabilistic inference over the model. We discuss how to deal with the various challenges presented by the RWGS, providing a suite of techniques that are likely to be useful in a wide range of applications. In particular, we describe a general framework for dealing with nonlinear behavior using numerical integration techniques, extending the successful Unscented Filter. We also show how to use a fixed-point computation to deal with effects that develop at different time scales, specifically rapid changes occurring during slowly changing processes. We test our model using real data collected from the RWGS, demonstrating the feasibility of hybrid DBNs for monitoring complex real-world physical systems.

Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial Intelligence. Yet they have many different and often partial definitions or properties, usually restricted to one field of application and thus incompatible with other uses. This paper contributes to the design and understanding of similarity and dissimilarity measures for Artificial Intelligence. A formal dual definition for each concept is proposed, joined with a set of fundamental properties. The behavior of the properties under several transformations is studied and revealed as an important matter to bear in mind. We also develop several practical examples that work out the proposed approach.

In this paper, we derive optimality results for greedy Bayesian-network search algorithms that perform single-edge modifications at each step and use asymptotically consistent scoring criteria. Our results extend those of Meek (1997) and Chickering (2002), who demonstrate that in the limit of large datasets, if the generative distribution is perfect with respect to a DAG defined over the observable variables, such search algorithms will identify this optimal (i.e. generative) DAG model. We relax their assumption about the generative distribution, and assume only that this distribution satisfies the {em composition property} over the observable variables, which is a more realistic assumption for real domains. Under this assumption, we guarantee that the search algorithms identify an {em inclusion-optimal} model; that is, a model that (1) contains the generative distribution and (2) has no sub-model that contains this distribution. In addition, we show that the composition property is guaranteed to hold whenever the dependence relationships in the generative distribution can be characterized by paths between singleton elements in some generative graphical model (e.g. a DAG, a chain graph, or a Markov network) even when the generative model includes unobserved variables, and even when the observed data is subject to selection bias.

Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define as a wide class of discrete variable models including undirected graphical models and Bayesian networks, but also chain graphs and sigmoid belief networks. The second one is for conditional likelihood maximization in standard undirected models and Bayesian networks. In both algorithms, the iteration steps are expressed in closed form. Numerical simulations show that the algorithms are competitive with state of the art methods.

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.

We develop a closed form asymptotic formula to compute the marginal likelihood of data given a naive Bayesian network model with two hidden states and binary features. This formula deviates from the standard BIC score. Our work provides a concrete example that the BIC score is generally not valid for statistical models that belong to a stratified exponential family. This stands in contrast to linear and curved exponential families, where the BIC score has been proven to provide a correct approximation for the marginal likelihood.

Exact monitoring in dynamic Bayesian networks is intractable, so approximate algorithms are necessary. This paper presents a new family of approximate monitoring algorithms that combine the best qualities of the particle filtering and Boyen-Koller methods. Our algorithms maintain an approximate representation the belief state in the form of sets of factored particles, that correspond to samples of clusters of state variables. Empirical results show that our algorithms outperform both ordinary particle filtering and the Boyen-Koller algorithm on large systems.

In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl's causes and explanations in the structural-model approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which show that under suitable restrictions deciding causes and explanations is tractable. To our knowledge, these are the first explicit tractability results for the structural-model approach.

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider an hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of an hypothesis class in order to get good generalization. Instead, we propose a PAC-Bayesian approach that seeks for suitable weights to be given to each hypothesis in order to build a majority vote. We prove a new DA bound in the PAC-Bayesian context. This leads us to design the first DA-PAC-Bayesian algorithm based on the minimization of the proposed bound. Doing so, we seek for a \rho-weighted majority vote that takes into account a trade-off between three quantities. The first two quantities being, as usual in the PAC-Bayesian approach, (a) the complexity of the majority vote (measured by a Kullback-Leibler divergence) and (b) its empirical risk (measured by the \rho-average errors on the source sample). The third quantity is (c) the capacity of the majority vote to distinguish some structural difference between the source and target samples.