Bayesian Experimental Design with Mutual Information and Learned Errors for Human-Computer Interaction
Résumé
This work provides a Bayesian framework for handling user errors in interactive systems, with applications in human-computer interaction (HCI) and user modeling. The Bayesian Information Gain (BIG) algorithm [1, 2, 3, 4] is an iterative variant of Bayesian experimental design with mutual information as a cost function, used in HCI. It is a principled approach that maximizes expected information gained from each interaction. More precisely, let Θ be the potential target in the user’s mind with prior distribution p(θ), X be the system feedback, and Y be the corresponding user’s input. In each interaction loop, BIG selects feedback x that maximizes mutual information I(Θ; Y|X= x), assuming a known user model (likelihood) p(y|x,θ), and then updates the posterior distribution p(θ|x,y). This work extends the BIG algorithm to learn from user errors while preserving its mathematical foundations. We incorporate an error rate parameter ϵinto the likelihood function p(y|x,θ,ϵ) and develop an adaptive algorithm that jointly infers both θ and ϵ by updating the posterior p(θ,ϵ|x,y) at each interaction step. We also discuss three simplifying hypotheses for the prior expression p(θ,ϵ) and three user models: (i) zero error; (ii) fixed error rate; (iii) arbitrary random error rate. We prove mathematical continuity between these three models, showing that our adaptive approach naturally extends BIG. We also investigate model mismatch on the overall performance and degradation properties with respect to the standard BIG algorithm. While standard BIG converges quickly with perfect responses, it degrades with even small error rates. The fixed-error model depends critically on correctly estimating the error parameter, while our adaptive model achieves the highest accuracy under varying error conditions, at the expense of additional interactions.