Fair near neighbor search via sampling

Abstract

Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points S and a radius parameter r > 0, the rnear neighbor (r-NN) problem asks for a data structure that, given any 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 individual fairness and providing equal opportunities: all points that are within distance r from the query should have the same probability to be returned. In the low-dimensional 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.

Sampling near neighbors in search for fairness

“…A more exhaustive presentation of our results and further solutions for the Fair NN problem can be found in the full version of the paper [8]. Preliminary versions of our results were published independently in [17,9] and then jointly in [7].…”

Sampling a Near Neighbor in High Dimensions — Who is the Fairest of Them All?

“…Lastly, this paper presents a uniied experimental view on the problem of sampling a fair near neighbor. A succinct summary of the technical contributions of this paper was published in [14].…”

Tackling Provably Hard Representative Selection via Graph Neural Networks

“…Examples of such metrics use correlation, redundancy, coverage (or more general submodular functions), or distance of selected entities among each other [43,51,8,5] as well as their mutual information or correlation with the prediction label [22,50]. While these methods tackle diversity of the sample set [1,36,67,6], there has been extensive attention in the past few years on taking fairness constraints into account as well [41,54,42,58,4]. Beside random sampling, stratified and quota sampling have been other methods to match the population distribution.…”

“…Let G = (V, E) be an input to the densest k-subgraph problem. 4 For each vertex in G we define a feature and for each edge in G we construct a data point. For each data point corresponding to an edge (u, v), the value of the features corresponding to vertices u and v are 1 and the value of all other features are 0.…”

“…On the other hand, |S| ≤ k and hence |V S | ≤ 2k. One can decompose the induced subgraph of V S into 4 2 = 6 subgraphs each with k vertices, and pick the one with the maximum number of edges. This gives an Ω(α)-approximate solution to the densest k-subgraph problem.…”