Active Mini-Batch Sampling using Repulsive Point Processes
arXiv:1804.02772
Abstract
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient estimator. This generalizes recent work on using Determinantal Point Processes (DPPs) for mini-batch diversification (Zhang et al., 2017) to the broader class of repulsive point processes. We first show that the phenomenon of variance reduction by diversified sampling generalizes in particular to non-stationary point processes. We then show that other point processes may be computationally much more efficient than DPPs. In particular, we propose and investigate Poisson Disk sampling---frequently encountered in the computer graphics community---for this task. We show empirically that our approach improves over standard SGD both in terms of convergence speed as well as final model performance.
References in corpus (9)
- Efficient Estimation of Word Representations in Vector Space
- Determinantal point processes for machine learning
- Active Bias: Training More Accurate Neural Networks by Emphasizing High Variance Samples
- Variance Reduction in SGD by Distributed Importance Sampling
- Accelerating Minibatch Stochastic Gradient Descent using Stratified Sampling
- Webly Supervised Learning of Convolutional Networks
- Efficient Sampling for k-Determinantal Point Processes
- Advances in Variational Inference
- Gradient Diversity: a Key Ingredient for Scalable Distributed Learning