1. A neural network learning system for inferring an input-output relationship from a set of given input and output samples, comprising: a) probability density means for determining a probability density on a sum space of an input space and an output space from the set of given input and output samples by learning a value of a parameter through a prescribed maximum likelihood method; b) inference means for determining a probability density function based on the probability density from said probability density means, to infer the input-output relationship of the samples from the probability density function; wherein the learning a value of the parameter is repeated by said inference means until a value of a predefined parameter differential function using the prescribed maximum likelihood method is smaller than a prescribed value, thereby determining said parameter value; c) conditional probability distribution means for computing a conditional probability distribution from either the given input samples or the given output samples in accordance with the probability density function determined by said inference means; and d) output means for obtaining an inference value based on the conditional probability distribution from said conditional probability distribution means and for outputting said inference value.