Near Neighbor: Who is the Fairest of Them All?
This addresses fairness concerns in near neighbor search for applications like recommendation systems, though it is incremental as it adapts existing LSH methods.
The paper tackles the problem of ensuring fairness in near neighbor search by making any point in the query's r-neighborhood equally likely to be reported, and shows that LSH-based algorithms can achieve this with minimal efficiency loss, as demonstrated by experiments on real data.
$\newcommand{\ball}{\mathbb{B}}\newcommand{\dsQ}{\mathcal{Q}}\newcommand{\dsS}{\mathcal{S}}$In this work we study a fair variant of the near neighbor problem. Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to preprocess the points, such that given a query point $q$, any point in the $r$-neighborhood of the query, i.e., $\ball(q,r)$, have the same probability of being reported as the near neighbor. We show that LSH based algorithms can be made fair, without a significant loss in efficiency. Specifically, we show an algorithm that reports a point in the $r$-neighborhood of a query $q$ with almost uniform probability. The query time is proportional to $O\bigl( \mathrm{dns}(q.r) \dsQ(n,c) \bigr)$, and its space is $O(\dsS(n,c))$, where $\dsQ(n,c)$ and $\dsS(n,c)$ are the query time and space of an LSH algorithm for $c$-approximate near neighbor, and $\mathrm{dns}(q,r)$ is a function of the local density around $q$. Our approach works more generally for sampling uniformly from a sub-collection of sets of a given collection and can be used in a few other applications. Finally, we run experiments to show performance of our approach on real data.