You Only Accept Samples Once: Fast, Self-Correcting Stochastic Variational Inference

We introduce YOASOVI, an algorithm for performing fast, self-correcting stochastic optimization for Variational Inference (VI) on large Bayesian heirarchical models. To accomplish this, we take advantage of available information on the objective function used for stochastic VI at each iteration and replace regular Monte Carlo sampling with acceptance sampling. Rather than spend computational resources drawing and evaluating over a large sample for the gradient, we draw only one sample and accept it with probability proportional to the expected improvement in the objective. The following paper develops two versions of the algorithm: the first one based on a naive intuition, and another building up the algorithm as a Metropolis-type scheme. Empirical results based on simulations and benchmark datasets for multivariate Gaussian mixture models show that YOASOVI consistently converges faster (in clock time) and within better optimal neighborhoods than both regularized Monte Carlo and Quasi-Monte Carlo VI algorithms.

Variance Control for Black Box Variational Inference Using The James-Stein Estimator

Black Box Variational Inference is a promising framework in a succession of recent efforts to make Variational Inference more ``black box". However, in basic version it either fails to converge due to instability or requires some fine-tuning of the update steps prior to execution that hinder it from being completely general purpose. We propose a method for regulating its parameter updates by reframing stochastic gradient ascent as a multivariate estimation problem. We examine the properties of the James-Stein estimator as a replacement for the arithmetic mean of Monte Carlo estimates of the gradient of the evidence lower bound. The proposed method provides relatively weaker variance reduction than Rao-Blackwellization, but offers a tradeoff of being simpler and requiring no fine tuning on the part of the analyst. Performance on benchmark datasets also demonstrate a consistent performance at par or better than the Rao-Blackwellized approach in terms of model fit and time to convergence.

Semiparametric Latent Topic Modeling on Consumer-Generated Corpora

Legacy procedures for topic modelling have generally suffered problems of overfitting and a weakness towards reconstructing sparse topic structures. With motivation from a consumer-generated corpora, this paper proposes semiparametric topic model, a two-step approach utilizing nonnegative matrix factorization and semiparametric regression in topic modeling. The model enables the reconstruction of sparse topic structures in the corpus and provides a generative model for predicting topics in new documents entering the corpus. Assuming the presence of auxiliary information related to the topics, this approach exhibits better performance in discovering underlying topic structures in cases where the corpora are small and limited in vocabulary. In an actual consumer feedback corpus, the model also demonstrably provides interpretable and useful topic definitions comparable with those produced by other methods.