Variance Reduction in Stochastic Gradient Langevin Dynamics.

Area of Science:

• Machine Learning
• Computational Statistics
• Optimization

Background:

• Stochastic gradient-based Monte Carlo methods, like stochastic gradient Langevin dynamics, are vital for large-scale machine learning posterior inference.
• These methods utilize mini-batches, but the inherent gradient variance slows convergence and degrades performance.
• Efficient posterior inference on large datasets remains a significant challenge in machine learning.

Purpose of the Study:

• To develop novel stochastic Monte Carlo methods by reducing variance in stochastic gradients.
• To improve the performance and mixing of stochastic gradient Langevin dynamics.
• To provide theoretical guarantees and empirical validation for the proposed variance reduction techniques.

Main Methods:

• Introducing techniques to reduce variance in stochastic gradients within Langevin dynamics.
• Developing novel stochastic Monte Carlo algorithms based on variance reduction.
• Analyzing theoretical convergence rates and conducting empirical evaluations.

Main Results:

• Proposed methods demonstrate improved theoretical convergence rates compared to standard stochastic Langevin dynamics.
• Significant empirical performance gains observed across diverse real-world datasets.
• Successful application demonstrated on regression, classification, independent component analysis, and mixture modeling tasks.

Conclusions:

• Variance reduction is a crucial component for enhancing stochastic Monte Carlo methods.
• The proposed techniques offer a compelling improvement for large-scale posterior inference in machine learning.
• These advancements facilitate more efficient and accurate analysis of complex datasets.