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Efficient Inference and Learning in Decimatable Boltzmann Machines
, 1997
"... Inference and learning in general Boltzmann machines are NPhard problems. Several restricted Boltzmann machines can be handled efficiently with the decimation technique known from statistical mechanics. A set of thus decimatable Boltzmann machines is defined. We show that the FourierStieltjes tran ..."
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Inference and learning in general Boltzmann machines are NPhard problems. Several restricted Boltzmann machines can be handled efficiently with the decimation technique known from statistical mechanics. A set of thus decimatable Boltzmann machines is defined. We show that the FourierStieltjes transformation of the probability distribution given by a Boltzmann machine is closely related to its partition sum. Decimation allows for the efficient calculation of the partition sum with the help of an adjoint deterministic feedforward network. We exploit this structure in order to specify powerful algorithms for exact inference and learning. The original stochastic Boltzmann machine may be disregarded, since all relevant probability computations can be performed exactly in the corresponding adjoint networks. 1 Introduction Boltzmann machines (Hinton and Sejnowski 1983) were the first explicitly stochastic networks for which a learning rule (Ackley, Hinton, and Sejnowski 1985) was developed...
Making Stochastic Networks Deterministic
, 1997
"... . Graphical models are considered more and more as a key technique for describing the dependency relations of random variables. Various learning and inference algorithms have been described and analysed. This article demonstrates how an important subclass of graphical models can be treated by transf ..."
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. Graphical models are considered more and more as a key technique for describing the dependency relations of random variables. Various learning and inference algorithms have been described and analysed. This article demonstrates how an important subclass of graphical models can be treated by transforming the underlying model into a regular feedforward network with special, yet deterministic, activation functions. Inference and the relevant quantities for learning can be calculated exactly in these networks. Moreover, all the known techniques for feedforward networks can be exploited and applied here. 1 Introduction Graphical models [9] aim at describing conditional independence relations of random variables. Given a specific graphical model, inference is the task of calculating the joint posterior probability of a set of variables, given the observations for some other variables, while the value of still other variables may be unknown. Learning means the computing of the parameters ...