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.

概率密度函数的估计是各种应用程序的重要组成部分。由于数据参数化的困难，非参数技术已广泛用于此任务。特别地，已经开发了某些核密度估计方法。但是，它们要么无法进行最大似然估计，要么需要维护训练集以处理新模式。在这项研究中，提出了一种称为非参数最大似然神经网络（MLNN）的新方法。这是一种非参数方法，依赖于最大似然和神经网络。它的形式紧凑，不需要维护训练模式。理论和实验分析证明了该方法的有效性。