Abstract:
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We present the Landmark-GMM (L-GMM), a statistical model for preference data expressed either as rankings or ratings. These two modalities of eliciting preferences carry complementary information, and the L-GMM is designed to seamlessly and naturally integrate this information.
L-GMM also inherits the computational elegance, interpretability and flexibility that characterize the GMM family and models based on counting inversions. In particular, when complete rankings + ratings are available, the L-GMM is an exponential family model with a permutation as "location parameter"; the normalization constant can be computed in closed form; sufficient statistics are available. When only the rating information is complete, the L-GMM can be used to estimate a consensus rating AND ranking, with minor algorithmic changes w.r.t. the complete data
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