Tossing coins under monotonicity

Matey Neykov*

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

Abstract

This paper considers the following problem: we are given n coin tosses of coins with monotone increasing probability of getting heads (success). We study the performance of the monotone constrained likelihood estimate, which is equivalent to the estimate produced by isotonic regression. We derive adaptive and non-adaptive bounds on the performance of the isotonic estimate, i.e., we demonstrate that for some probability vectors the isotonic estimate converges much faster than in general. As an application of this framework we propose a two step procedure for the binary monotone single index model, which consists of running LASSO and consequently running an isotonic regression. We provide thorough numerical studies in support of our claims.

Original languageEnglish (US)
StatePublished - 2020
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
Country/TerritoryJapan
CityNaha
Period4/16/194/18/19

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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