A plausible neural network (PLANN) is an artificial neural network with weight connection given by mutual information, which has the capability of inference and learning, and yet retains many characteristics of a biological neural network. The learning algorithm is based on statistical estimation, which is faster than the gradient decent approach currently used. The network after training becomes a fuzzy/belief network; the inference and weight are exchangeable, and as a result, knowledge extraction becomes simple. PLANN performs associative memory, supervised, semi-supervised, unsupervised learning and function/relation approximation in a single network architecture. This network architecture can easily be implemented by analog VLSI circuit design.