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A kernel test for quasi-independence
Tamara Fernandez · Wenkai Xu · Marc Ditzhaus · Arthur Gretton

Wed Dec 09 07:10 AM -- 07:20 AM (PST) @ Orals & Spotlights: Kernel Methods/Optimization
in Orals & Spotlights Track 17: Kernel Methods/Optimization »

We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the entry and survival times of patients in a clinical trial. In these settings, the two times are not independent (the second occurs after the first), yet it is still of interest to determine whether there exists significant dependence "beyond" their ordering in time. We refer to this notion as "quasi-(in)dependence." For instance, in a clinical trial, to avoid biased selection, we might wish to verify that recruitment times are quasi-independent of survival times, where dependencies might arise due to seasonal effects. In this paper, we propose a nonparametric statistical test of quasi-independence. Our test considers a potentially infinite space of alternatives, making it suitable for complex data where the nature of the possible quasi-dependence is not known in advance. Standard parametric approaches are recovered as special cases, such as the classical conditional Kendall's tau, and log-rank tests. The tests apply in the right-censored setting: an essential feature in clinical trials, where patients can withdraw from the study. We provide an asymptotic analysis of our test-statistic, and demonstrate in experiments that our test obtains better power than existing approaches, while being more computationally efficient.

Author Information

Tamara Fernandez (University College London)
Wenkai Xu (Gatsby Unit, UCL)
Marc Ditzhaus (TU Dortmund University)
Arthur Gretton (Gatsby Unit, UCL)

Arthur Gretton is a Professor with the Gatsby Computational Neuroscience Unit at UCL. He received degrees in Physics and Systems Engineering from the Australian National University, and a PhD with Microsoft Research and the Signal Processing and Communications Laboratory at the University of Cambridge. He previously worked at the MPI for Biological Cybernetics, and at the Machine Learning Department, Carnegie Mellon University. Arthur's recent research interests in machine learning include the design and training of generative models, both implicit (e.g. GANs) and explicit (high/infinite dimensional exponential family models), nonparametric hypothesis testing, and kernel methods. He has been an associate editor at IEEE Transactions on Pattern Analysis and Machine Intelligence from 2009 to 2013, an Action Editor for JMLR since April 2013, an Area Chair for NeurIPS in 2008 and 2009, a Senior Area Chair for NeurIPS in 2018, an Area Chair for ICML in 2011 and 2012, and a member of the COLT Program Committee in 2013. Arthur was program chair for AISTATS in 2016 (with Christian Robert), tutorials chair for ICML 2018 (with Ruslan Salakhutdinov), workshops chair for ICML 2019 (with Honglak Lee), program chair for the Dali workshop in 2019 (with Krikamol Muandet and Shakir Mohammed), and co-organsier of the Machine Learning Summer School 2019 in London (with Marc Deisenroth).

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