Selected Publications

We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to relabeling of items and can be computed efficiently in $O(n \ln(n))$ operations, where $n$ is the number of items in the permutation. Second, we propose a supervised approach to learn the weights by jointly optimizing them with the function estimated by a kernel machine. Third, while the Kendall kernel considers pairwise comparison between items, we extend it by considering higher-order comparisons among tuples of items and show that the supervised approach of learning the weights can be systematically generalized to higher-order permutation kernels.

We show that the widely used Kendall tau correlation coefficient, and the related Mallows kernel, are positive definite kernels for permutations. They offer computationally attractive alternatives to more complex kernels on the symmetric group to learn from rankings, or learn to rank. We show how to extend these kernels to partial rankings, multivariate rankings and uncertain rankings. Examples are presented on how to formulate typical problems of learning from rankings such that they can be solved with state-of-the-art kernel algorithms. We demonstrate promising results on clustering heterogeneous rank data and high-dimensional classification problems in biomedical applications.

Recent Publications

. Signaling Pathway Activities Improve Prognosis for Breast Cancer. bioRxiv, 2017.

Preprint Code

. Kernel Multitask Regression for Toxicogenetics. Mol Inform, 2017.

Preprint PDF Code Dataset Video HTML

. Failure State Prediction for Automated Analyzers for Analyzing a Biological Sample. Patent, 2016.

. Prediction of human population responses to toxic compounds by a collaborative competition. Nat Biotechnol, 2015.



I am (co-)author and maintainer of the following software:

  • kernrank - R package implementing kernel functions and kernel methods for analyzing rank data.

  • kmr - R implementation of a kernel multitask regression algorithm to solve simultaneously several regression problems.