A Tale of Three Probabilistic Families: Discriminative, Descriptive and Generative Models

TL;DR

This paper reviews three probabilistic model families—discriminative, descriptive, and generative—within the pattern theory framework, highlighting their connections and recent advances with deep neural networks.

Contribution

It provides a unified review of these three probabilistic families and discusses recent developments leveraging deep neural networks' approximation capabilities.

Findings

Unified framework for discriminative, descriptive, and generative models

Connections between different probabilistic model families

Recent advances using deep neural networks

Abstract

The pattern theory of Grenander is a mathematical framework where patterns are represented by probability models on random variables of algebraic structures. In this paper, we review three families of probability models, namely, the discriminative models, the descriptive models, and the generative models. A discriminative model is in the form of a classifier. It specifies the conditional probability of the class label given the input signal. A descriptive model specifies the probability distribution of the signal, based on an energy function defined on the signal. A generative model assumes that the signal is generated by some latent variables via a transformation. We shall review these models within a common framework and explore their connections. We shall also review the recent developments that take advantage of the high approximation capacities of deep neural networks.