Learning Permutations with Exponential Weights
The Journal of Machine Learning Research
A Fourier space algorithm for solving quadratic assignment problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Learning probability distributions over permutations by means of fourier coefficients
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
Clustering rankings in the fourier domain
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part I
Fourier-information duality in the identity management problem
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Riffled independence for efficient inference with partial rankings
Journal of Artificial Intelligence Research
ACM Transactions on Intelligent Systems and Technology (TIST) - Special section on twitter and microblogging services, social recommender systems, and CAMRa2010: Movie recommendation in context
Property management in wireless sensor networks with overcomplete radon bases
ACM Transactions on Sensor Networks (TOSN)
A Fourier-theoretic approach for inferring symmetries
Computational Geometry: Theory and Applications
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Permutations are ubiquitous in many real-world problems, such as voting, ranking, and data association. Representing uncertainty over permutations is challenging, since there are n! possibilities, and typical compact and factorized probability distribution representations, such as graphical models, cannot capture the mutual exclusivity constraints associated with permutations. In this paper, we use the "low-frequency" terms of a Fourier decomposition to represent distributions over permutations compactly. We present Kronecker conditioning, a novel approach for maintaining and updating these distributions directly in the Fourier domain, allowing for polynomial time bandlimited approximations. Low order Fourier-based approximations, however, may lead to functions that do not correspond to valid distributions. To address this problem, we present a quadratic program defined directly in the Fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions. We demonstrate the effectiveness of our approach on a real camera-based multi-person tracking scenario.