Crowdsourced Nonparametric Density Estimation Using Relative Distances

In this paper we address the following density estimation problem: given a number of relative similarity judgements over a set of items D, assign a density value p(x) to each item x in D. Our work is motivated by human computing applications where density can be interpreted e.g. as a measure of the rarity of an item. While humans are excellent at solving a range of different visual tasks, assessing absolute similarity (or distance) of two items (e.g. photographs) is difficult. Relative judgements of similarity, such as A is more similar to B than to C, on the other hand, are substantially easier to elicit from people. We provide two novel methods for density estimation that only use relative expressions of similarity. We give both theoretical justifications, as well as empirical evidence that the proposed methods produce good estimates.