Tuning-free coreset Markov chain Monte Carlo

A Bayesian coreset is a small, weighted subset of a data set that replaces the full data during inference to reduce computational cost. The state-of-the-art coreset construction algorithm, Coreset Markov chain Monte Carlo (Coreset MCMC), uses draws from an adaptive Markov chain targeting the coreset posterior to train the coreset weights via stochastic gradient optimization. However, the quality of the constructed coreset, and thus the quality of its posterior approximation, is sensitive to the stochastic optimization learning rate. In this work, we propose a learning-rate-free stochastic gradient optimization procedure, Hot-start Distance over Gradient (Hot DoG), Figure 1: Relative Coreset MCMC posterior approximation for training coreset weights in Coreset MCMC error (average squared coordinate-wise z-score) without user tuning effort. Empirical results using ADAM with different learning rates versus the demonstrate that Hot DoG provides higher proposed Hot DoG method (with fixed r = 0.001). Median quality posterior approximations than other values after 200,000 optimization iterations across learning-rate-free stochastic gradient methods, 10 trials are used for the relative comparison for a variety and performs competitively to optimallytuned of datasets, models, and coreset sizes.