Abstract
This paper treats the following problem: consider an ergodic signal source S. Suppose that each time the source transmitts a multidimensional signal x according to an unknown ergodic probability distribution with density p(x). Then the problem is to estimate the unknown density p(x). The problem is solved via a Reccurent High-Order Neural Network (RHONN) and is based on the Energy Coordinates Equivalence (ECE) principle proposed by the authors. In the proposed method the signals are considered to be the states of a stochastic gradient dynamical system (Langevin s.d.e.) after it converges (in a stochastic manner). Then the (unknown) system is identified using ECE neural networks. After the learning procedure converges, the energy function of the ECE neural network is the estimate of the unknown probability distribution.
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