The Knowledge Gradient with Logistic Belief Models for Binary Classification

TL;DR

This paper introduces a sequential decision-making approach using Bayesian logistic regression and a knowledge-gradient policy to efficiently identify the best binary classification alternative with limited, costly samples.

Contribution

It develops a novel knowledge-gradient policy tailored for logistic belief models in binary classification, with finite-time error analysis and empirical validation.

Findings

Effective in small-sample, costly observation scenarios

Outperforms baseline methods on UCI datasets

Provides finite-time error bounds for the proposed policy

Abstract

We consider sequential decision making problems for binary classification scenario in which the learner takes an active role in repeatedly selecting samples from the action pool and receives the binary label of the selected alternatives. Our problem is motivated by applications where observations are time consuming and/or expensive, resulting in small samples. The goal is to identify the best alternative with the highest response. We use Bayesian logistic regression to predict the response of each alternative. By formulating the problem as a Markov decision process, we develop a knowledge-gradient type policy to guide the experiment by maximizing the expected value of information of labeling each alternative and provide a finite-time analysis on the estimated error. Experiments on benchmark UCI datasets demonstrate the effectiveness of the proposed method.