A Probabilistic Theory of Deep Learning

TL;DR

This paper introduces a probabilistic framework called the Deep Rendering Model to explain why deep learning systems like CNNs and decision forests succeed in complex perceptual tasks involving nuisance variations.

Contribution

It develops a generative probabilistic model for deep learning that captures nuisance variations and links it to existing architectures, offering insights and avenues for improvement.

Findings

Deep Rendering Model captures nuisance variation explicitly.

Reformulating the model yields CNNs and decision forests.

Provides a theoretical basis for understanding deep learning success.

Abstract

A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves the unknown object position, orientation, and scale in object recognition while speech recognition involves the unknown voice pronunciation, pitch, and speed. Recently, a new breed of deep learning algorithms have emerged for high-nuisance inference tasks that routinely yield pattern recognition systems with near- or super-human capabilities. But a fundamental question remains: Why do they work? Intuitions abound, but a coherent framework for understanding, analyzing, and synthesizing deep learning architectures has remained elusive. We answer this question by developing a new probabilistic framework for deep learning based on the Deep Rendering Model: a generative probabilistic model that explicitly captures latent nuisance variation. By relaxing the generative model to a discriminative one, we can recover two of the current leading deep learning systems, deep convolutional neural networks and random decision forests, providing insights into their successes and shortcomings, as well as a principled route to their improvement.