Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification

• URL: http://arxiv.org/abs/2605.21033v1
• Date: Wed, 20 May 2026 11:10:15 GMT
• Title: Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification
• Abstract summary: We develop efficient algorithms specifically tailored for computing Banzhaf values in $k$-nearest neighbor ($k$NN) classifiers.<n>Our main contribution is a dynamic programming framework that achieves significant computational improvements.
• Score: 23.4280718098929
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled frameworks for fair data valuation; however, they suffer from exponential computational complexity. We address this challenge by developing efficient algorithms specifically tailored for computing Banzhaf values in $k$-nearest neighbor ($k$NN) classifiers. We first establish the theoretical hardness of the problem by proving that it is \#P-hard. Despite this intractability, we exploit the locality properties of $k$NN classifiers to develop practical exact algorithms. Our main contribution is a dynamic programming framework that achieves significant computational improvements: we present a pseudo-polynomial algorithm with $O(Wkn^2)$ time complexity for weighted $k$NN classifiers, where $W$ is the maximum sum of top-$k$ weights, and a specialized algorithm for unweighted $k$NN that achieves $O(nk^2)$ time complexity, that is, linear in the number of data points. We also offer efficient Monte Carlo estimation methods. Extensive experiments on real-world datasets demonstrate the practical efficiency of our approach and its effectiveness in data valuation applications.

Related papers

• Provably Adaptive Linear Approximation for the Shapley Value and Beyond [73.0940890296463]
  A fundamental and long-standing challenge is their efficient approximation.<n>We develop a linear-space algorithm that requires $P(|hatboldsymbol-boldsymbol|_2geq)leq $ for all commonly used semi-values.<n>Our algorithm allows explicit minimization of the mean square error for each specific utility function.
  arXiv  Detail & Related papers  (2026-04-09T16:38:14Z)
• Finding a Fair Scoring Function for Top-$k$ Selection: From Hardness to Practice [0.0]
  We address the problem of identifying a fair linear scoring function for top-$k$ selection.<n>Existing algorithms do not scale efficiently, particularly in higher dimensions.<n>We turn this potential of efficiency into an optimized algorithm delivering substantial practical performance gains.
  arXiv  Detail & Related papers  (2025-03-14T16:40:36Z)
• The Limits of Assumption-free Tests for Algorithm Performance [5.68594452139461]
  How well does an algorithm perform at a given modeling task, and which algorithm performs best?<n>We make a distinction between two questions: how good is an algorithm $A$ at the problem of learning from a training set of size $n$, versus, how good is a particular fitted model produced by running $A$ on a particular training data set of size $n$?
  arXiv  Detail & Related papers  (2024-02-12T03:19:30Z)
• Efficient Data Shapley for Weighted Nearest Neighbor Algorithms [47.62605581521535]
  WKNN-Shapley is an efficient computation of Data Shapley for weighted $K$ nearest neighbor algorithm (WKNN-Shapley) We show WKNN-Shapley's computational efficiency and its superior performance in discerning data quality compared to its unweighted counterpart.
  arXiv  Detail & Related papers  (2024-01-20T03:34:18Z)
• Provably Efficient Reinforcement Learning via Surprise Bound [66.15308700413814]
  We propose a provably efficient reinforcement learning algorithm (both computationally and statistically) with general value function approximations. Our algorithm achieves reasonable regret bounds when applied to both the linear setting and the sparse high-dimensional linear setting.
  arXiv  Detail & Related papers  (2023-02-22T20:21:25Z)
• Minimax Optimization with Smooth Algorithmic Adversaries [59.47122537182611]
  We propose a new algorithm for the min-player against smooth algorithms deployed by an adversary. Our algorithm is guaranteed to make monotonic progress having no limit cycles, and to find an appropriate number of gradient ascents.
  arXiv  Detail & Related papers  (2021-06-02T22:03:36Z)
• List-Decodable Mean Estimation in Nearly-PCA Time [50.79691056481693]
  We study the fundamental task of list-decodable mean estimation in high dimensions. Our algorithm runs in time $widetildeO(ndk)$ for all $k = O(sqrtd) cup Omega(d)$, where $n$ is the size of the dataset. A variant of our algorithm has runtime $widetildeO(ndk)$ for all $k$, at the expense of an $O(sqrtlog k)$ factor in the recovery guarantee
  arXiv  Detail & Related papers  (2020-11-19T17:21:37Z)
• On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces [208.67848059021915]
  We study the exploration-exploitation tradeoff at the core of reinforcement learning. In particular, we prove that the complexity of the function class $mathcalF$ characterizes the complexity of the function. Our regret bounds are independent of the number of episodes.
  arXiv  Detail & Related papers  (2020-11-09T18:32:22Z)
• Complete Dictionary Learning via $\ell_p$-norm Maximization [10.82081111170268]
  We investigate a family of $ell_p$-norm ($p>2,p in mathbbN$) approaches for the complete dictionary learning problem. We show that the global maximizers of these formulations are very close to the true dictionary with high probability, even when Gaussian noise is present. Experiments will demonstrate that the $ell_p$-based approaches enjoy a higher computational efficiency and better robustness than conventional approaches.
  arXiv  Detail & Related papers  (2020-02-24T02:33:01Z)
• Learning Sparse Classifiers: Continuous and Mixed Integer Optimization Perspectives [10.291482850329892]
  Mixed integer programming (MIP) can be used to solve (to optimality) $ell_0$-regularized regression problems. We propose two classes of scalable algorithms: an exact algorithm that can handlepapprox 50,000$ features in a few minutes, and approximate algorithms that can address instances with $papprox6$. In addition, we present new estimation error bounds for $ell$-regularizeds.
  arXiv  Detail & Related papers  (2020-01-17T18:47:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.