Continuous Indeterminate Probability Neural Network

Tao Yang

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Keywords: Indeterminate Probability Theory, Continuous Random Variable, Analytical Solution, DLVMs, Auto-Encoder

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TL;DR: Indeterminate Probability Theory is the analytical solution for a general posterior, and based on it, we propose an analytical probability neural network with continuous latent random variables.

Abstract:

Currently, there is no mathematical analytical form for a general posterior, however, Indeterminate Probability Theory has now discovered a way to address this issue. This is a big discovery in the field of probability and it is applicable in various fields.
This paper introduces a general model called CIPNN - Continuous Indeterminate Probability Neural Network, which is an analytical probability neural network with continuous latent random variables.
Our contributions are Four-fold. First, we apply the analytical form of the posterior for 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, instead of using a neural network as the decoder component, we first employ a probabilistic equation. 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.

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Submission Number: 1578