Closed-form expressions are derived for the expected hyperbolic volume of the convex hull of n beta-distributed random points in the d-dimensional unit ball under the Klein model.
Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro
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GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
Witness motifs in constrained geometric graphs saturate Weyl bounds on Laplacian perturbations under heavy-tailed noise, with new metrics SC and S3I to distinguish noise-driven spectral effects.
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GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression
GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.