Nonparametric maximum likelihood estimation using neural networks

•Estimating probability density functions based on neural network.•Nonparametric and maximum likelihood estimation of probability density functions.•The result model in compact form.•Do not require keeping training patterns for evaluating new patterns. Estimation of probability density functions is an essential component of various applications. Nonparametric techniques have been widely used for this task owing to the difficulty in parameterization of data. In particular, certain kernel density estimation methods have been developed. However, they are either incapable of maximum likelihood estimation or require the maintenance of a training set to process new patterns. In this study, a new approach, called the nonparametric maximum likelihood neural network (MLNN), is proposed. This is a nonparametric method, relying on maximum likelihood and neural network. It is compact in form and does not require the maintenance of training patterns. Theoretical and experimental analyses demonstrate the efficacy of the proposed approach.