Yeganeh Alimohammadi, USC

Title: How to Measure Differences in Rankings: A Data-Driven Extension of the Mallows Model

Abstract: Ranking problems appear across domains, from consumer preferences and product recommendations to sports performance and hiring decisions. Probabilistic ranking models such as the Mallows model provide a principled way to capture uncertainty and infer a consensus order, assuming that observed rankings are noisy versions of an underlying truth. A key modeling challenge, however, lies in choosing the distance function that measures how “far apart” two rankings are, since different distances imply different ways of penalizing ranking swaps.

In this talk, I introduce a generalized framework based on Mallows model that learns this distance metric directly from data. I will show that the model forms an exponential-family distribution on permutations, and that its parameters (the central ranking, dispersion, and learned distance) can be estimated consistently via maximum likelihood with asymptotic normality guarantees. On the algorithmic side, I present a polynomial-time approximation scheme (PTAS) for efficient sampling and partition-function estimation.

Finally, I will discuss empirical validation on real datasets, demonstrating how learning the distance metric leads to more accurate predictions and interpretable insights about ranking behavior.