Fair Near Neighbor Search: Independent Range Sampling in High Dimensions
Abstract
Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. There are several variants of the similarity search problem, and one of the most relevant is the $r$near neighbor ($r$NN) problem: given a radius $r>0$ and a set of points $S$, construct a data structure that, for any given query point $q$, returns a point $p$ within distance at most $r$ from $q$. In this paper, we study the $r$NN problem in the light of fairness. We consider fairness in the sense of equal opportunity: all points that are within distance $r$ from the query should have the same probability to be returned. In the lowdimensional case, this problem was first studied by Hu, Qiao, and Tao (PODS 2014). Locality sensitive hashing (LSH), the theoretically strongest approach to similarity search in high dimensions, does not provide such a fairness guarantee. To address this, we propose efficient data structures for $r$NN where all points in $S$ that are near $q$ have the same probability to be selected and returned by the query. Specifically, we first propose a blackbox approach that, given any LSH scheme, constructs a data structure for uniformly sampling points in the neighborhood of a query. Then, we develop a data structure for fair similarity search under inner product that requires nearlylinear space and exploits locality sensitive filters. The paper concludes with an experimental evaluation that highlights (un)fairness in a recommendation setting on realworld datasets and discusses the inherent unfairness introduced by solving other variants of the problem.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.01859
 Bibcode:
 2019arXiv190601859A
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Geometry;
 Computer Science  Information Retrieval;
 Computer Science  Machine Learning
 EPrint:
 Proceedings of the 39th ACM SIGMODSIGACTSIGAI Symposium on Principles of Database Systems (PODS), Pages 191204, June 2020