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Activity Number: 426 - Computing in Large and Complex Data Analysis
Type: Contributed
Date/Time: Wednesday, August 10, 2022 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract #322588
Title: Generalized Kernel Thinning
Author(s): Raaz Dwivedi*
Companies: MIT
Keywords: coresets; better than Monte Carlo rates; kernel maximum mean discrepancy; reproducing kernel Hilbert space; MCMC; thinning

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed-function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Matern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. We demonstrate the power of KT+ in numerous experiments even in 100 dimensions

Authors who are presenting talks have a * after their name.

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