Estimate of a Probability Density Function through Neural Networks

A correct estimate of the probability density function of an unknown stochatic process is a preliminary step of utmost importance for any subsequent elaboration stages, such as modelling and classification. Traditional approaches are based on the preliminary choice of a mathematical model of the function and subsequent fitting on its parameters. Therefore some a-priori knowledge and/or assumptions on the phenomenon under consideration are required. Here an alternative approach is presented, which does not require any assumption on the available data, but extracts the probability density function from the output of a neural network, that is trained with a suitable database including the original data and some ad hoc created data with known distribution. This approach has been tested on a synthetic and on an industrial dataset and the obtained results are presented and discussed.