Kernelized Complete Conditional Stein Discrepancy

Abstract

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepancies (KSDs). While kernels make Stein discrepancies tractable, they pose several challenges in high dimensions. We introduce kernelized complete conditional Stein discrepancies (KCC-SDs). Complete conditionals turn a multivariate distribution into multiple univariate distributions. We show that KCC-SDs distinguish distributions. To show the efficacy of KCC-SDs in distinguishing distributions, we introduce a goodness-of-fit test using KCC-SDs. We empirically show that KCC-SDs have higher power over baselines and use KCC-SDs to assess sample quality in Markov chain Monte Carlo.

References in corpus (10)

• Measuring Sample Quality with Stein's Method
• A Kernel Test of Goodness of Fit
• Measuring Sample Quality with Kernels
• Operator Variational Inference
• Message Passing Stein Variational Gradient Descent
• A Linear-Time Kernel Goodness-of-Fit Test
• A Wild Bootstrap for Degenerate Kernel Tests
• Random Feature Stein Discrepancies
• Sliced Kernelized Stein Discrepancy
• Kernel Stein Tests for Multiple Model Comparison

Cited by in corpus (3)

• Sliced Kernelized Stein Discrepancy
• The reproducing Stein kernel approach for post-hoc corrected sampling
• Active Slices for Sliced Stein Discrepancy