Learning Mixed Membership Mallows Models from Pairwise Comparisons
This addresses the challenge of noisy and inconsistent user preferences in ranking tasks, though it is incremental as it builds on existing topic model insights.
The authors tackled the problem of modeling heterogeneous user preferences from pairwise comparisons by proposing a Mixed Membership Mallows Model (M4), which uses a mixture of latent Mallows components and a separable structure for efficient estimation, achieving empirical competitiveness with state-of-the-art methods.
We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our key algorithmic insight for estimation is to establish a statistical connection between M4 and topic models by viewing pairwise comparisons as words, and users as documents. This key insight leads us to explore Mallows components with a separable structure and leverage recent advances in separable topic discovery. While separability appears to be overly restrictive, we nevertheless show that it is an inevitable outcome of a relatively small number of latent Mallows components in a world of large number of items. We then develop an algorithm based on robust extreme-point identification of convex polygons to learn the reference rankings, and is provably consistent with polynomial sample complexity guarantees. We demonstrate that our new model is empirically competitive with the current state-of-the-art approaches in predicting real-world preferences.