Continuous Indeterminate Probability Neural Network

Abstract

This paper introduces a general model called CIPNN - Continuous Indeterminate Probability Neural Network, and this model is based on IPNN, which is used for discrete latent random variables. Currently, posterior of continuous latent variables is regarded as intractable, with the new theory proposed by IPNN this problem can be solved. Our contributions are Four-fold. First, we derive the analytical solution of the posterior calculation of continuous latent random variables and propose a general classification model (CIPNN). Second, we propose a general auto-encoder called CIPAE - Continuous Indeterminate Probability Auto-Encoder, the decoder part is not a neural network and uses a fully probabilistic inference model for the first time. Third, we propose a new method to visualize the latent random variables, we use one of N dimensional latent variables as a decoder to reconstruct the input image, which can work even for classification tasks, in this way, we can see what each latent variable has learned. Fourth, IPNN has shown great classification capability, CIPNN has pushed this classification capability to infinity. Theoretical advantages are reflected in experimental results.