Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling

26th Conference on Learning Theory

Stanislav Minsker [e-mail]

PID  :  121274

来源: CEUR

【 摘 要 】

We propose a new method for estimating the locations and the value of an absolute maxi mum (minimum) of a function from the observations contaminated by random noise. Our goal is to solve the problem under minimal regularity and shape constraints. In particular, we do not assume differentiability of a function nor that its maximum is attained at a single point. We provide tight upper and lower bounds for the performance of proposed estima tors. Our method is adaptive with respect to the unknown parameters of the problem over a large class of underlying distributions.