Reinhard Heckel (Berkeley)
Feb 13, 2017.
Title and Abstract
Active ranking from pairwise comparisons and when parametric assumptions don’t help
We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of pre-specified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-k items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point. We prove that this algorithm succeeds in recovering the ranking using a number of comparisons that is optimal up to logarithmic factors. This guarantee does not require any structural properties of the underlying pairwise probability matrix, unlike a signifi- cant body of past work on pairwise ranking based on parametric models such as the Thurstone or Bradley-Terry-Luce models. It has been a long-standing open question as to whether or not imposing these parametric assumptions allows for improved ranking algorithms. For stochastic comparison models, in which the pairwise probabilities are bounded away from zero, our second contribution is to resolve this issue by proving a lower bound for parametric models. This shows, perhaps surprisingly, that these popular parametric modeling choices offer at most logarithmic gains for stochastic comparisons.
Reinhard Heckel is a Postdoctoral researcher in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. Before that, he spent a year in the Cognitive Computing & Computational Sciences Department at IBM Research, Zurich. He completed his Ph.D. in August 2014 at ETH Zurich, Department of Information Technology and Electrical Engineering, advised by Helmut Bölcskei. In Fall 2013, he was a visiting Ph.D. student in the Statistics Department of Stanford University. Reinhard is interested in mathematical signal processing, sparse signal recovery, machine learning, and computational biology