MULTIDIMENSIONAL DENSITY SHAPING BY SIGMOIDS

An estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights, Classification prob lems can be solved by selecting the class associated with the maximal estimated density, Newton's optimization method, applied to the estima ted density, yields a recursive estimator for a random variable or a r andom sequence, A constrained connectivity structure yields a linear e stimator, which is particularly suitable for ''real time'' prediction, A Gaussian nonlinearity yields a closed-form solution for the network 's parameters, which may also be used for initializing the optimizatio n algorithm when other nonlinearities are employed. A triangular conne ctivity between the neurons and the input, which is naturally suggeste d by the statistical setting, reduces the number of parameters, Applic ations to classification and forecasting problems are demonstrated.