Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On the duality between belief networks and feedforward neural networks
 IEEE transactions on neural networks and learning systems 30 (2019), Nr.1, S.190200 ISSN: 2162237X 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer FKIE () 
Abstract
This paper addresses the duality between the deterministic feedforward neural networks (FFNNs) and linear Bayesian networks (LBNs), which are the generative stochastic models representing probability distributions over the visible data based on a linear function of a set of latent (hidden) variables. The maximum entropy principle is used to define a unique generative model corresponding to each FFNN, called projected belief network (PBN). The FFNN exactly recovers the hidden variables of the dual PBN. The largeN asymptotic approximation to the PBN has the familiar structure of an LBN, with the addition of an invertible nonlinear transformation operating on the latent variables. It is shown that the exact nature of the PBN depends on the range of the input (visible) data details for the three cases of input data range are provided. The likelihood function of the PBN is straightforward to calculate, allowing it to be used as a generative classifier. An example is provided in which a generative classifier based on the PBN has comparable performance to a deep belief network in classifying handwritten characters. In addition, several examples are provided that demonstrate the duality relationship, for example, by training networks from either side of the duality.