Posterior Approximation using Stochastic Gradient Ascent with Adaptive Stepsize

TL;DR

This paper introduces an adaptive stepsize stochastic gradient ascent method for efficient posterior approximation in Bayesian nonparametrics, demonstrating comparable performance to traditional methods on large-scale datasets.

Contribution

It develops an adaptive stepsize stochastic gradient ascent algorithm for posterior approximation, integrating Fisher information for improved speed and scalability.

Findings

Achieves comparable accuracy to coordinate ascent methods.

Scales effectively to large datasets like Caltech256 and SUN397.

Compatible with deep convolutional neural network features.

Abstract

Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local learning from minibatch. The main problem with stochastic variational inference is that it relies on closed form solution. Stochastic gradient ascent is a modern approach to machine learning and is widely deployed in the training of deep neural networks. In this work, we explore using stochastic gradient ascent as a fast algorithm for the posterior approximation of Dirichlet process mixture. However, stochastic gradient ascent alone is not optimal for learning. In order to achieve both speed and performance, we turn our focus to stepsize optimization in stochastic gradient ascent. As as intermediate approach, we first optimize stepsize using the momentum method. Finally, we introduce Fisher information to allow adaptive stepsize in our posterior approximation. In the experiments, we justify that our approach using stochastic gradient ascent do not sacrifice performance for speed when compared to closed form coordinate ascent learning on these datasets. Lastly, our approach is also compatible with deep ConvNet features as well as scalable to large class datasets such as Caltech256 and SUN397.