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 to the nascent OpenBayes effort.

A new method is proposed for exploiting causal independencies in exact Bayesian network inference.

Recently, there has been much interest in reverse engineering genetic networks from time series data. In this paper, we show that most of the proposed discrete time models — including the boolean network model [Kau93, SS96], the linear model of D’haeseleer et al. [DWFS99], and the nonlinear model of Weaver et al. [WWS99] — are all special cases of a general class of models called Dynamic Bayesian Networks (DBNs). The advantages of DBNs include the ability to model stochasticity, to incorporate prior knowledge, and to handle hidden variables and missing data in a principled way. This paper provides a review of techniques for learning DBNs. Keywords: Genetic networks, boolean networks, Bayesian networks, neural networks, reverse engineering, machine learning. 1

Abstract. This paper describes the student modeling component of ANDES, an Intelligent Tutoring System for Newtonian physics. ANDES ’ student model uses a Bayesian network to do long-term knowledge assessment, plan recognition and prediction of students ’ actions during problem solving. The network is updated in real time, using an approximate anytime algorithm based on stochastic sampling, as a student solves problems with ANDES. The information in the student model is used by ANDES ’ Help system to tailor its support when the student reaches impasses in the problem solving process. In this paper, we describe the knowledge structures represented in the student model and discuss the implementation of the Bayesian network assessor. We also present a preliminary evaluation of the time performance of stochastic sampling algorithms to update the network. 1

Abstract. When a tutoring system aims to provide students with interactive help, it needs to know what knowledge the student has and what goals the student is currently trying to achieve. That is, it must do both assessment and plan recognition. These modeling tasks involve a high level of uncertainty when students are allowed to follow various lines of reasoning and are not required to show all their reasoning explicitly. We use Bayesian networks as a comprehensive, sound formalism to handle this uncertainty. Using Bayesian networks, we have devised the probabilistic student models forAndes, a tutoring system forNewtonian physics whose philosophy is to maximize student initiative and freedom during the pedagogical interaction. Andes’ models provide long-term knowledge assessment, plan recognition, and prediction of students’ actions during problem solving, as well as assessment of students ’ knowledge and understanding as students read and explain worked out examples. In this paper, we describe the basic mechanisms that allow Andes ’ student models to soundly perform assessment and plan recognition, as well as the Bayesian network solutions to issues that arose in scaling up the model to a full-scale, ¢eld evaluated application. We also summarize the results of several evaluations of Andes which provide evidence on the accuracy of its student models.

Despite their different perspectives, artificial intelligence (AI) and the disciplines of decision science have common roots and strive for similar goals. This paper surveys the potential for addressing problems in representation, inference, knowledge engineering, and explanation within the decision-theoretic framework. Recent analyses of the restrictions of several traditional AI reasoning techniques, coupled with the development of more tractable and expressive decisiontheoretic representation and inference strategies, have stimulated renewed interest in decision theory and decision analysis. We describe early experience with simple probabilistic schemes for automated reasoning, review the dominant expert-system paradigm, and survey some recent research at the crossroads of AI and decision science. In particular, we present the belief network and influence diagram representations. Finally, we discuss issues that have not been studied in detail within the expert-systems sett...

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in nite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from dierent stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, lik...

Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effect does not depend on what other causes have previously been applied. In this paper, we introduce an equivalent atemporal characterization of causal independence based on a functional representation of the relationship between causes and the effect. In this representation, the interaction between causes and effect can be written as a nested decomposition of functions. Causal independence can be exploited by representing this decomposition in the belief network, resulting in representations that are more efficient for inference than general causal models. We present empirical results showing the benefits of a causal-independence representation for belief-network inference. 1

ABayesian network is a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real-world problems. When there are many potential causes of a given e ect, however, both probability assessment and inference using a Bayesian network can be di cult. In this paper, we describe causal independence, a collection of conditional independence assertions and functional relationships that are often appropriate to apply to the representation of the uncertain interactions between causes and e ect. We show how the use of causal independence in a Bayesian network can greatly simplify probability assessment aswell as probabilistic inference. 1

Spiegelhalter and Lauritzen [15] studied sequential learning in Bayesian networks and proposed three models for the representation of conditional probabilities. A forth model, shown here, assumes that the parameter distribution is given by a product of Gaussian functions and updates them from the and messages of evidence propagation. We also generalize the noisy OR-gate for multivalued variables, develop the algorithm to compute probability in time proportional to the number of parents (even in networks with loops) and apply the learning model to this gate.