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In counterfactual learning to rank (CLTR) user interactions are used as asource of supervision. Since user interactions come with bias, an importantfocus of research in this field lies in developing methods to correct for thebias of interactions. Inverse propensity scoring (IPS) is a popular methodsuitable for correcting position bias. Affine correction (AC) is ageneralization of IPS that corrects for position bias and trust bias. IPS andAC provably remove bias, conditioned on an accurate estimation of the biasparameters. Estimating the bias parameters, in turn, requires an accurateestimation of the relevance probabilities. This cyclic dependency introducespractical limitations in terms of sensitivity, convergence and efficiency.  We propose a new correction method for position and trust bias in CLTR inwhich, unlike the existing methods, the correction does not rely on relevanceestimation. Our proposed method, mixture-based correction (MBC), is based onthe assumption that the distribution of the CTRs over the items being ranked isa mixture of two distributions: the distribution of CTRs for relevant items andthe distribution of CTRs for non-relevant items. We prove that our method isunbiased. The validity of our proof is not conditioned on accurate biasparameter estimation. Our experiments show that MBC, when used in differentbias settings and accompanied by different LTR algorithms, outperforms AC, thestate-of-the-art method for correcting position and trust bias, in somesettings, while performing on par in other settings. Furthermore, MBC is ordersof magnitude more efficient than AC in terms of the training time.

Mixture-Based Correction for Position and Trust Bias in Counterfactual Learning to Rank