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Evaluating the RBM without integration using PDF projection

: Baggenstoss, Paul

Fulltext (PDF; )

European Association for Signal Processing -EURASIP-:
25th European Signal Processing Conference, EUSIPCO 2017 : 27 August - 2 September 2017, Kos Island, Greece
Kos, 2017
ISBN: 978-0-9928626-7-1
European Signal Processing Conference (EUSIPCO) <25, 2017, Kos>
Conference Paper, Electronic Publication
Fraunhofer FKIE ()

In this paper, we apply probability density function (PDF) projection to arrive at an exact closed-form expression for the marginal distribution of the visible data of a restricted Boltzmann machine (RBM) without requiring integrating over the distribution of the hidden variables or needing to know the partition function. We express the visible data marginal as a projected PDF based on a set of sufficient statistics. When a Gaussian mixture model (GMM) is used to estimate the PDF of the sufficient statistics, then we arrive at a combined RBM/GMM model that serves as a general-purpose PDF estimator and Bayesian classifier. The approach extends recusively to compute the input distribution of a multi-layer network. We demonstrate the method using a reduced subset of the MNIST handwritten character data set.