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.

Many real-world systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inference, i.e., infer the hidden state of the system given some noisy observations. For example, we can ask what is the probability that a certain word was pronounced given the readings of our microphone, what is the probability that a submarine is trying to surface given our sonar data, and what is the probability of a valve being open given our pressure and flow readings. Bayesian networks are

Markov logic networks (MLNs) combine first-order logic and Markov networks, allowing us to handle the complexity and uncertainty of real-world problems in a single consistent framework. However, in MLNs all variables and features are discrete, while most real-world applications also contain continuous ones. In this paper we introduce hybrid MLNs, in which continuous properties (e.g., the distance between two objects) and functions over them can appear as features. Hybrid MLNs have all distributions in the exponential family as special cases (e.g., multivariate Gaussians), and allow much more compact modeling of non-i.i.d. data than propositional representations like hybrid Bayesian networks. We also introduce inference algorithms for hybrid MLNs, by extending the MaxWalkSAT and MC-SAT algorithms to continuous domains. Experiments in a mobile robot mapping domain—involving joint classification, clustering and regression—illustrate the power of hybrid MLNs as a modeling language, and the accuracy and efficiency of the inference algorithms.

The development of user interfaces based on vision and speech requires the solution of a challenging statistical inference problem: The intentions and actions of multiple individuals must be inferred from noisy and ambiguous data. We argue that Bayesian network models are an attractive statistical framework for cue fusion in these applications. Bayes nets combine a natural mechanism for expressing contextual information with efficient algorithms for learning and inference. We illustrate these points through the development of a Bayes net model for detecting when a user is speaking. The model combines four simple vision sensors: face detection, skin color, skin texture, and mouth motion. We present some promising experimental results. 1

for explicitly modeling components and their relationships of Korean Hangul characters. A Hangul character is modeled with hierarchical components: a syllable model, grapheme models, stroke models and point models. Each model is constructed with subcomponents and their relationships except a point model, the primitive one, which is represented by a 2-D Gaussian for X-Y coordinates of point instances. Relationships between components are modeled with their positional dependencies. For on-line handwritten Hangul characters, the proposed system shows higher recognition rates than the HMM system with chain code features: 95.7% vs 92.9% on average.

Introduction We consider the problem of nding the Maximum Likelihood (ML) estimates of the parameters of a conditional Gaussian node Y with continuous parent X and discrete parent Q, i.e., p(yjx; Q = i) = cj i j 1 2 exp 1 2 (y B i x) 0 1 i (y B i x) where c = (2) d=2 is a constant and jyj = d. The j'th row of B i is the regression vector for the j component of y given that Q = i. To allo

This paper shows how non-linear functions can be approximated by hybrid Bayesian networks. The basic idea is to make a piecewise linear approximation with several base points. This approach is applied to an engineering domain and the accuracy is compared to Gibbs sampling. Great accuracy is shown even at noncontinuous functions. Due to the general underlying principle, it is possible to adapt this type of network to other domains.

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Bayesian networks for the static as well as for the dynamic case have gained an enormous interest in the research community of artificial intelligence, machine learning and pattern recognition. Although the parallels between dynamic Bayesian networks and Kalman filters are well known since many years, Bayesian networks have not been applied to problems in the area of adaptive control of dynamic systems.