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Complexity of approximating Hoelder classes from information with varying Gaussian noise

机译：从不同高斯噪声的信息近似声音课程的复杂性

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摘要

We consider information epsilon-complexity of L-p-approximation (1 = p infinity) of functions f epsilon C-r ([0,1](d)) for which all the partial derivatives of order r are Holder continuous with exponent rho is an element of (0, 1]. Allowable approximations use nonadaptive or adaptive observations of f at finitely many points, and these observations are additionally contaminated by Gaussian noise. The cost of a single observation depends on the variance of the noise and equals c(sigma) where c is a nonincreasing cost function. We find quite general formulas for information epsilon-complexity of our problem depending on the cost function. In particular, we show that adaptive observations do not offer essentially better approximations compared to nonadaptive observations. Order optimal approximations use the regular grid and piecewise polynomial interpolation applied to exact or smoothed data. (C) 2020 Elsevier Inc. All rights reserved.
机译：我们考虑函数的信息epsilon - 复杂性的LP近似（1 <= P

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