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Research questionHow many linear samples are needed to approximate Lipschitz operators under Gaussian measures, and how fast can errors decay?Approximating mappings between infinite-dimensional function spaces from finitely many observations can remain difficult even when the operators are Lipschitz. The attainable error depends on the number of linear samples and the regularity induced by the Gaussian measure.
Machine Learning
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Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian MeasuresThe paper establishes Sobolev regularity and Hermite approximation bounds, then characterizes the sample complexity for reconstruction from m linear samples. It shows that algebraic convergence in m is impossible in general, while sufficiently fast covariance decay allows rates arbitrarily close to algebraic.research paper · Sep 4, 2026
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