Stochastic Descent Analysis of Representation Learning Algorithms
This work addresses a theoretical bottleneck for researchers in machine learning, providing a tool to formally analyze and design deep learning algorithms, though it appears incremental as it builds on existing stochastic approximation methods.
The paper tackles the challenge of applying stochastic approximation theorems to analyze deep learning algorithms by introducing a new theorem with easily verifiable assumptions, applicable to algorithms like adaptive learning and contrastive divergence.
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic approximation theorems typically possess assumptions which are difficult to communicate and verify. This paper presents a new stochastic approximation theorem for state-dependent noise with easily verifiable assumptions applicable to the analysis and design of important deep learning algorithms including: adaptive learning, contrastive divergence learning, stochastic descent expectation maximization, and active learning.