# On kernel methods for covariates that are rankings

@article{Mania2016OnKM, title={On kernel methods for covariates that are rankings}, author={Horia Mania and Aaditya Ramdas and Martin J. Wainwright and Michael I. Jordan and Benjamin Recht}, journal={arXiv: Machine Learning}, year={2016} }

Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has been relatively limited study of regression, classification, and testing problems based on permutation-valued features, as opposed to permutation-valued responses. This paper studies the use of reproducing kernel Hilbert space methods for learning from…

## 18 Citations

Sampling Permutations for Shapley Value Estimation

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This paper proposes and studies an harmonic analysis of the covariance operators that allows to put into action the full machinery of Gaussian processes learning in the less classical case where X is the non commutative finite group of permutations.

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This paper designs two-sample tests for pairwise comparison data and ranking data, establishes an upper bound on the sample complexity required to correctly distinguish between the distributions of the two sets of samples, and investigates the role of modeling assumptions by proving lower bounds for a range of pairwise comparisons models.

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This paper proposes and study an harmonic analysis of the covariance operators that enables to consider Gaussian processes models and forecasting issues and is motivated by statistical ranking problems.

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Two algorithms for BO over Permutation Spaces (BOPS) are proposed and evaluated, showing that both BOPS-T and Bops-H perform better than the state-of-the-art BO algorithm for combinatorial spaces.

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The work carried out in this thesis aims at proposing new statistical methods based on dependence measures for GSA of numerical simulators, particularly interested in HSIC-type dependence measures (Hilbert-Schmidt Independence Criterion).

Bandwidth-Optimal Random Shuffling for GPUs

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Experimental results show that the bijective shuffle algorithm outperforms competing algorithms on GPUs, showing improvements of between one and two orders of magnitude and approaching peak device bandwidth.

Catch Me if I Can: Detecting Strategic Behaviour in Peer Assessment

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This paper designs a principled test for detecting strategic behaviour, designs an experiment that elicits strategic behaviour from subjects and releases a dataset of patterns of strategic behaviour that may be of independent interest, and proves that the test has strong false alarm guarantees.

Fourier Bases for Solving Permutation Puzzles

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The effectiveness of learning a value function in the Fourier basis for solving various permutation puzzles is demonstrated and it is shown that it outperforms standard deep learning methods.

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