Importance Sampling for Minibatches

TL;DR

This paper introduces the first importance sampling method designed specifically for minibatches in supervised learning, demonstrating significant potential for accelerating training times through theoretical analysis and empirical validation.

Contribution

It presents a novel importance sampling technique tailored for minibatches, with rigorous complexity analysis and practical experiments showing substantial speedups.

Findings

Potential for several orders of magnitude speedup on synthetic data

Achieves up to an order of magnitude improvement on real datasets

Provides theoretical guarantees for the proposed method

Abstract

Minibatching is a very well studied and highly popular technique in supervised learning, used by practitioners due to its ability to accelerate training through better utilization of parallel processing power and reduction of stochastic variance. Another popular technique is importance sampling -- a strategy for preferential sampling of more important examples also capable of accelerating the training process. However, despite considerable effort by the community in these areas, and due to the inherent technical difficulty of the problem, there is no existing work combining the power of importance sampling with the strength of minibatching. In this paper we propose the first {\em importance sampling for minibatches} and give simple and rigorous complexity analysis of its performance. We illustrate on synthetic problems that for training data of certain properties, our sampling can lead to several orders of magnitude improvement in training time. We then test the new sampling on several popular datasets, and show that the improvement can reach an order of magnitude.