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Explore a generalized framework for ranking problems that learns distance metrics directly from data in this 47-minute probability and statistics seminar. Discover how probabilistic ranking models like the Mallows model capture uncertainty and infer consensus order from noisy observations, while addressing the key challenge of choosing appropriate distance functions for measuring ranking differences. Learn about the exponential-family distribution on permutations and understand how model parameters including central ranking, dispersion, and learned distance can be estimated consistently via maximum likelihood with asymptotic normality guarantees. Examine the polynomial-time approximation scheme (PTAS) for efficient sampling and partition-function estimation, and see how this approach applies to real-world domains from consumer preferences and product recommendations to sports performance and hiring decisions. Gain insights into empirical validation results showing improved prediction accuracy and interpretable insights about ranking behavior when distance metrics are learned from data rather than predetermined.
