Bernstein polynomials and learning theory

By Dietrich Braess, Tomas Sauer. 2004

66 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Learning discrete distributions: user vs item-level privacy (2020, methodology): “The min-max rate of learning discrete distributions for item-level privacy, which corresponds to m = 1, was studied by Diakonikolas et al. [2015] and Acharya et al.”
Learning Discrete Distributions from Untrusted Batches (2017, neutral): “r distributions supported on n elements, given access to k i.i.d. samples, minimax optimal loss rates as a function of n and k have been considered for various loss functions, including KL-divergence [BS04], ℓ 2 [KOPS15], χ2 loss [KOPS15]. For ℓ 1 error (equivalently, “total variation distance” or “”
Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication (2018, background): “| In non-private setting, the sample complexity of distribution estimation under these distances is known even including precise constants [10, 34].”
Joint additive Kullback–Leibler residual minimization and regularization for linear inverse problems (2007, background): “Two recent papers [18, 19] derived estimates for the approximation of the entropy function x ln x and examined the minimization of the KL-functional for unknown finite distributions, respectively.”
On Learning Distributions from their Samples (2015, background): “(2002); Paninski (2004), just eleven years ago, Braess and Sauer (2004) showed that for fixed k, as n increases,”
Competitive Distribution Estimation: Why is Good-Turing Good (2015, background): “[10] showed that as for every k, as n→∞, an estimator related to add-3/4 is near optimal and achieves”
ON THE DEGREE OF APPROXIMATION IN VORONOVSKAJA'S THEOREM (2007, background): “In [2] several interesting phenomena concerning the approximation of the entropy function f by Bnf are discussed.”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, background): “D. Lower bounds for estimation of H(P ) Braess and Sauer [69] derived the following lower bound for the approximation error of Bernstein polynomials for the function g(x) = −x lnx: Lemma 21.”