Papers › Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms

Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms

22 Aug 2019arXiv:1908.08619archive 2025-07-28

Ruoxi Jia, David Dao, Boxin Wang, Frances Ann Hubis, Nezihe Merve Gurel, Bo Li, Ce Zhang, Costas J. Spanos, Dawn Song

Given a data set 𝒟 containing millions of data points and a data consumer who is willing to pay for \Xto train a machine learning (ML) model over𝒟, how should we distribute thisX$ to each data point to reflect its "value"? In this paper, we define the "relative value of data" via the Shapley value, as it uniquely possesses properties with appealing real-world interpretations, such as fairness, rationality and decentralizability. For general, bounded utility functions, the Shapley value is known to be challenging to compute: to get Shapley values for all N data points, it requires O(2ᴺ) model evaluations for exact computation and O(NlogN) for (ϵ, δ)-approximation. In this paper, we focus on one popular family of ML models relying on K-nearest neighbors ($K$NN). The most surprising result is that for unweighted $K$NN classifiers and regressors, the Shapley value of all N data points can be computed, exactly, in O(NlogN) time -- an exponential improvement on computational complexity! Moreover, for (ϵ, δ)-approximation, we are able to develop an algorithm based on Locality Sensitive Hashing (LSH) with only sublinear complexity O(N^(h(ϵ,K))logN) when ϵ is not too small and K is not too large. We empirically evaluate our algorithms on up to $10$ million data points and even our exact algorithm is up to three orders of magnitude faster than the baseline approximation algorithm. The LSH-based approximation algorithm can accelerate the value calculation process even further. We then extend our algorithms to other scenarios such as (1) weighed $K$NN classifiers, (2) different data points are clustered by different data curators, and (3) there are data analysts providing computation who also requires proper valuation.

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