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 Learning Graphical Models


Training Stochastic Model Recognition Algorithms as Networks can Lead to Maximum Mutual Information Estimation of Parameters

Neural Information Processing Systems

One of the attractions of neural network approaches to pattern recognition is the use of a discrimination-based training method. We show that once we have modified the output layer of a multilayer perceptronto provide mathematically correct probability distributions, andreplaced the usual squared error criterion with a probability-based score, the result is equivalent to Maximum Mutual Informationtraining, which has been used successfully to improve theperformance of hidden Markov models for speech recognition. Ifthe network is specially constructed to perform the recognition computations of a given kind of stochastic model based classifier then we obtain a method for discrimination-based training of the parameters of the models. Examples include an HMM-based word discriminator, which we call an'Alphanet'.




Identifying independence in Bayesian networks

Classics

An important feature of Bayesian networks is that they facilitate explicit encoding of information about independencies in the domain, information that is indispensable for efficient inferencing. This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions. The algorithm's correctness is based on the soundness of a graphical criterion, called d-separation, and its optimality stems from the completeness of d-separation. An enhanced version of d-separation, called D-separation, is defined, extending the algorithm to networks that encode functional dependencies. Finally, the algorithm is shown to work for a broad class of nonprobabilistic independencies.


Symbolic probabilistic inference in belief networks

Classics

Díez's algorithm for the noisy MAX is very efficient for polytrees, but when the network has loops, it has to be combined with local conditioning, a suboptimal propagation algorithm. Other algorithms, based on several factorizations of the conditional probability of the noisy MAX, are not as efficient for polytrees but can be combined with general propagation algorithms such as clustering or variable elimination, which are more efficient for networks with loops. In this article we propose a new factorization of the noisy MAX that amounts to Díez's algorithm in the case of polytrees and at the same time is more efficient than previous factorizations when combined with either variable elimination or clustering.


The computational complexity of probabilistic inference using Bayesian belief networks

Classics

Bayesian belief networks provide a natural, efficient method for representing probabilistic dependencies among a set of variables. For these reasons, numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence. Algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks. More general classes of belief networks, however, have eluded efforts to develop efficient inference algorithms. We show that probabilistic inference using belief networks is NP-hard.


Coping with uncertainty in a control system for navigation and exploration

Classics

A significant problem in designing mobile robot control systems involves coping with the uncertainty that arises in moving about in an unknown or partially unknown environment and relying on noisy or ambiguous sensor data to acquire knowledge about that environment. We describe a control system that chooses what activity to engage in next on the basis of expectations about how the information returned as a result of a given activity will improve its knowledge about the spatial layout of its environment. Certain of the higher-level components of the control system are specified in terms of probabilistic decision models whose output is used to mediate the behavior of lower-level control components responsible for movement and sensing. The control system is capable of directing the behavior of the robot in the exploration and mapping of its environment, while attending to the real-time requirements of navigation and obstacle avoidance.



Influence Diagrams, Belief Nets and Decision Analysis

Classics

Based on the proceedings of a conference on Influence Diagrams for Decision Analysis, Inference and Prediction held at the University of California at Berkeley in May of 1988, this is the first book devoted to the subject. The editors have brought together recent results from researchers actively investigating influence diagrams and also from practitioners who have used influence diagrams in developing models for problem-solving in a wide range of fields.


The Boltzmann Perceptron Network: A Multi-Layered Feed-Forward Network Equivalent to the Boltzmann Machine

Neural Information Processing Systems

The concept of the stochastic Boltzmann machine (BM) is auractive for decision making and pattern classification purposes since the probability of attaining the network states is a function of the network energy. Hence, the probability of attaining particular energy minima may be associated with the probabilities of making certain decisions (or classifications). However, because of its stochastic nature, the complexity of the BM is fairly high and therefore such networks are not very likely to be used in practice. In this paper we suggest a way to alleviate this drawback by converting the stochastic BM into a deterministic network which we call the Boltzmann Perceptron Network (BPN). The BPN is functionally equivalent to the BM but has a feed-forward structure and low complexity.