Tag: minimax
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The Minimax Lower Bound of Kernel Stein Discrepancy Estimation
The Minimax Lower Bound of Kernel Stein Discrepancy Estimation arXiv:2510.15058v1 Announce Type: new Abstract: Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $sqrt n$-convergence. In this work, we…
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Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds arXiv:2506.00171v1 Announce Type: new Abstract: We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution $rho$ supported on a manifold $M$. The operators discussed in the paper are relevant in unsupervised learning and in particular are…
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Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces
Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces arXiv:2412.20556v1 Announce Type: new Abstract: We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem. Recent research has explored learning the worst-case distribution using…