AI RESEARCH
GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression
arXiv CS.LG
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ArXi:2506.03074v5 Announce Type: replace-cross We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang, 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan, 2019; Kang, 2022), and reveal a novel experimental design objective, $\mathrm{GL}(\pi