Detection of cheating by decimation algorithm

Abstract

We expand the item response theory to study the case of "cheating students" for a set of exams, trying to detect them by applying a greedy algorithm of inference. This extended model is closely related to the Boltzmann machine learning. In this paper we aim to infer the correct biases and interactions of our model by considering a relatively small number of sets of training data. Nevertheless, the greedy algorithm that we employed in the present study exhibits good performance with a few number of training data. The key point is the sparseness of the interactions in our problem in the context of the Boltzmann machine learning: the existence of cheating students is expected to be very rare (possibly even in real world). We compare a standard approach to infer the sparse interactions in the Boltzmann machine learning to our greedy algorithm and we find the latter to be superior in several aspects.

15 pages, 7 figures

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• Statistical-mechanical analysis of compressed sensing for Hamiltonian estimation of Ising spin glass
• Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models
• Statistical-mechanical analysis of pre-training and fine tuning in deep learning
• L_1-regularized Boltzmann machine learning using majorizer minimization
• Stochastic gradient method with accelerated stochastic dynamics
• Phase transition in binary compressed sensing based on $L_1$-norm minimization