How To Grade a Test Without Knowing the Answers --- A Bayesian Graphical Model for Adaptive Crowdsourcing and Aptitude Testing

TL;DR

This paper introduces a Bayesian graphical model for adaptive testing that jointly estimates question difficulty, participant ability, and correct answers, enabling more efficient testing by selecting questions adaptively.

Contribution

It presents a novel probabilistic graphical model and an active learning scheme for adaptive testing that reduces the number of questions needed for accurate assessment.

Findings

The model accurately infers question difficulties and participant abilities.

Adaptive testing with the model requires fewer questions than static tests.

Experimental results validate the efficiency and accuracy of the proposed approach.

Abstract

We propose a new probabilistic graphical model that jointly models the difficulties of questions, the abilities of participants and the correct answers to questions in aptitude testing and crowdsourcing settings. We devise an active learning/adaptive testing scheme based on a greedy minimization of expected model entropy, which allows a more efficient resource allocation by dynamically choosing the next question to be asked based on the previous responses. We present experimental results that confirm the ability of our model to infer the required parameters and demonstrate that the adaptive testing scheme requires fewer questions to obtain the same accuracy as a static test scenario.