#approximationtheory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #approximationtheory, aggregated by home.social.
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I recently read two interesting survey articles by my academic brother Ben Adcock at Simon Fraser University about theoretical aspect of sampling: how to approximate a function 𝑓 given random point samples 𝑓(𝑥ᵢ) with noise. This is a fundamental problem in Machine Learning.
The first paper, "Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks" (by Ben and co-authors), is about how fast the approximation error may decrease as you take more samples. We can overcome the curse of dimensionality if the function gets increasingly smooth in higher dimensions. URL: https://arxiv.org/abs/2404.03761
The second paper, "Optimal sampling for least-squares approximation", is about choosing where to sample in order to get as close to the unknown function (in least-square sense) as possible. https://arxiv.org/abs/2409.02342
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This chocolate reminded me of Bernstein ellipses, which govern how fast the Chebyshev approximation converges to a function.
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This chocolate reminded me of Bernstein ellipses, which govern how fast the Chebyshev approximation converges to a function.
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This chocolate reminded me of Bernstein ellipses, which govern how fast the Chebyshev approximation converges to a function.
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This chocolate reminded me of Bernstein ellipses, which govern how fast the Chebyshev approximation converges to a function.
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This chocolate reminded me of Bernstein ellipses, which govern how fast the Chebyshev approximation converges to a function.