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.

Nearly optimal solutions to many combinatorial problems can be found using stochastic simulated annealing. This paper extends the concept of simulated annealing from its original formulation as a Markov process to a new formulation based on mean field theory. Mean field annealing essentially replaces the discrete degrees of freedom in simulated annealing with their average values as computed by the mean field approximation. The net result is that equilibrium at a given temperature is achieved 1-2 orders of magnitude faster than with simulated annealing. A general framework for the mean field annealing algorithm is derived, and its relationship to Hopfield networks is shown. The behavior of MFA is examined both analytically and experimentally for a generic combinatorial optimization problem: graph bipartitioning. This analysis indicates the presence of critical temperatures which could be important in improving the performance of neural networks.

The Boltzmann Machine has been introduced as a means to perform global optimization for multimodal objective functions using the principles of simulated annealing. In this paper we consider its utility as a spurious-free content-addressable memory, and provide bounds on its performance in this context. We show how to exploit the machine's ability to escape local minima, in order to use it, at a constant temperature, for unambiguous associative pattern-retrieval in noisy environments. An association rule, which creates a sphere of influence around each stored pattern, is used along with the Machine's dynamics to match the machine's noisy input with one of the pre-stored patterns. Spurious fIxed points, whose regions of attraction are not recognized by the rule, are skipped, due to the Machine's fInite probability to escape from any state. The results apply to the Boltzmann machine and to the asynchronous net of binary threshold elements (Hopfield model'). They provide the network designer with worst-case and best-case bounds for the network's performance, and allow polynomial-time tradeoff studies of design parameters.

Howard and M. A. Huckvale, "Acoustic-phonetic attribute determination using multi-layer perceptrons", IEEE Colloquium Digest 1988/11.

The use of a one-stage dynamic programming algorithm for connected word recognition.

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 BMinto 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.

Nearly optimal solutions to many combinatorial problems can be found using stochastic simulated annealing. This paper extends the concept of simulated annealing from its original formulation as a Markov process to a new formulation based on mean field theory. Mean field annealing essentially replaces the discrete degrees offreedom in simulated annealing with their average values as computed by the mean field approximation. The net result is that equilibrium at a given temperature is achieved 1-2 orders of magnitude faster than with simulated annealing. A general framework forthe mean field annealing algorithm is derived, and its relationship toHopfield networks is shown. The behavior of MFA is examined both analytically and experimentally for a generic combinatorial optimizationproblem: graph bipartitioning. This analysis indicates the presence of critical temperatures which could be important inimproving the performance of neural networks.

Causal probabilistic networks have proved to be a useful knowledge representation tool for modelling domains where causal relations in a broad sense are a natural way of relating domain objects and where uncertainty is inherited in these relations. This paper outlines an implementation the HUGIN shell--for handling a domain model expressed by a causal probabilistic network. The only topological restriction imposed on the network is that, it must not contain any directed loops. The approach is illustrated step by step by solving a. genetic breeding problem. A graph representation of the domain model is interactively created by using instances of the basic network components—nodes and arcs—as building blocks. This structure, together with the quantitative relations between nodes and their immediate causes expressed as conditional probabilities, are automatically transformed into a tree structure, a junction tree. Here a computationally efficient and conceptually simple algebra of Bayesian belief universes supports incorporation of new evidence, propagation of information, and calculation of revised beliefs in the states of the nodes in the network. Finally, as an example of a real world application, MUN1N an expert system for electromyography is discussed.IJCAI-89, Vol. 2, pp. 1080–1085

Management Science, 35 (5), 527-50.

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