arXiv subjects

Kyurae Kim

Publications and source records attributed to Kyurae Kim.

21 records · Page 2Linked to original sources

arXiv2023

Practical and Matching Gradient Variance Bounds for Black-Box Variational Bayesian Inference

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the $ABC$ condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

cs.LG↗

arXiv2022

Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradients

Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov chain gradient descent framework. Furthermore, by leveraging this new understanding, we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter bound on the gradient variance. We demonstrate that this improved theoretical result translates to superior empirical performance.

cs.LG↗

arXiv2022

A Probabilistic Machine Learning Approach to Scheduling Parallel Loops with Bayesian Optimization

This paper proposes Bayesian optimization augmented factoring self-scheduling (BO FSS), a new parallel loop scheduling strategy. BO FSS is an automatic tuning variant of the factoring self-scheduling (FSS) algorithm and is based on Bayesian optimization (BO), a black-box optimization algorithm. Its core idea is to automatically tune the internal parameter of FSS by solving an optimization problem using BO. The tuning procedure only requires online execution time measurement of the target loop. In order to apply BO, we model the execution time using two Gaussian process (GP) probabilistic machine learning models. Notably, we propose a locality-aware GP model, which assumes that the temporal locality effect resembles an exponentially decreasing function. By accurately modeling the temporal locality effect, our locality-aware GP model accelerates the convergence of BO. We implemented BO FSS on the GCC implementation of the OpenMP standard and evaluated its performance against other scheduling algorithms. Also, to quantify our method's performance variation on different workloads, or workload-robustness in our terms, we measure the minimax regret. According to the minimax regret, BO FSS shows more consistent performance than other algorithms. Within the considered workloads, BO FSS improves the execution time of FSS by as much as 22% and 5% on average.

cs.DC↗