Monday, April 21, 2014
Applied Mathematics Colloquium
Statistical Learning and Optimization Based on Comparative Judgements
Robert Nowak, McFarland-Bascom Professor in Engineering, University of Wisconsin-Madison
Sequential experimental design and testing are classic examples of adaptive approaches to measurement. In this talk, I will look at two less conventional problems in sequential statistics: derivative free optimization and ranking based on pairwise comparisons. The common theme is that measurements available in both problems are comparative judgements rather than numerical evaluations. This simple sort of measurement is motivated by applications involving human subjects. I will present bounds on the number of questions needed to determine a person's preferences or ranking over a set of alternatives, including situations in which the answers may be noisy and unreliable. Notably, sequentially selected questions can be dramatically more informative than randomly chosen questions. Sequential schemes are also able to take advantage of the underlying geometrical structure of the problem.