When: Sunday, March 14, 10am
Where: Schreiber 309
Speaker: Chaim Even-Zohar, Alan Turing Institute, London
Title:
Rank-Based Independence Testing in Near Linear Time
In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on
the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time.
Hoeffding's test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate
distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum,
Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have
required quadratic time.
We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for
counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.
Joint work with Calvin Leng