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Research questionHow can noisy Lipschitz regression recover an unknown function uniformly on a general metric space?Recovering an unknown Lipschitz function from noisy observations on a general metric space requires controlling errors uniformly rather than only at observed points. The estimator must also avoid introducing additional error through approximate optimization.
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Machine Learning
Neural and Evolutionary Computing
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Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network RealizationsThe setting is real-valued regression from N i.i.d. noisy observations on a metric space. The source gives high-probability L∞ recovery guarantees and, for Ahlfors-regular spaces, optimal fat-shattering behavior and parameter stability; on [0,1]^d with the ℓ∞ metric, it specifies sparse ReLU-MLP and exact ReLU multi-head transformer realizations with depth O(log N) and O(N) nonzero parameters.research paper · Sep 2, 2026
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