The Convergence Rate of Majority Vote under Exchangeability
Year: 2013
Type: preprint
Abstract: Majority vote plays a fundamental role in many applications of statistics, such as ensemble classifiers, crowdsourcing, and elections. When using majority vote as a prediction rule, it is of basic interest to ask How many votes are needed to obtain a reliable prediction? In the context of binary classification with Random Forests or Bagging, we give a precise answer: If err_t denotes the test error achieved by the majority vote of t \geq 1 classifiers, and err* denotes its nominal limiting value, then under basic regularity conditions, err_t = err* + c/t + o(1/t), where c is a constant given by a simple formula. More generally, we show that if V_1,V_2,... is an exchangeable Bernoulli sequence with mixture distribution F, and the majority vote is written as M_t=median(V_1,...,V_t), then 1-\E[M_t] = F(1/2)+ (F(1/2)/8)(1/t)+o(1/t) when F is sufficiently smooth.
Source: arXiv (Cornell University)
Author: Miles E. Lopes
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1906343640