Data valuation is a core function in data markets and cooperative data sharing.Shapley valueis a widely used approach to fairly measure the contribution of data points towards a collective utility (e.g., a machine learning model trained from the data). However, computing Shapley values is known to be in general #P-hard due to the exponential utility evaluation. Furthermore, the presence of dynamic data poses additional challenges due to the prohibitively expensive cost of recomputing from scratch. In this paper, we study the problem ofDynamic Shapley Value Computation, which focuses on updating Shapley values when dynamically adding or deleting data points. For adding, to prune redundant computation of overlapping model utilities, we propose the pivot-based algorithm that can reduce half the computation time in expectation. We also propose delta-based algorithms to capture Shapley value changes, which require only a smaller sample size to converge. For deleting, we present the YN-NN algorithm that derives the new Shapley values from precomputed utilities efficiently. Based on Shapley value changes, we give another version of the delta-based algorithm for deleting data points. Besides, we propose heuristic algorithms that draw on experimental observations for addition, deletion, and hybrid scenarios. Extensive experimental results demonstrate the efficiency and effectiveness of our proposed algorithms.

Shapley value provides a unique way to fairly assess each player's contribution in a coalition and has enjoyed many applications. However, the exact computation of Shapley value is #P-hard due to the combinatoric nature of Shapley value. Many existing applications of Shapley value are based on Monte-Carlo approximation, which requires a large number of samples and the assessment of utility on many coalitions to reach high-quality approximation, and thus is still far from being efficient. Can we achieve an efficient approximation of Shapley value by smartly obtaining samples? In this paper, we treat the sampling approach to Shapley value approximation as a stratified sampling problem. Our main technical contributions are a novel stratification design and a sampling method based on Neyman allocation. Moreover, computing the Shapley value in a dynamic setting, where new players may join the game and others may leave it poses an additional challenge due to the considerable cost of recomputing from scratch. To tackle this issue, we propose to capture changes in Shapley value, making our approaches applicable to scenarios with dynamic players. Experimental results on several real data sets and synthetic data sets demonstrate the effectiveness and efficiency of our approaches.

With the prevalence of data-driven research, data valuation has attracted attention from the computer science field. How to appraise a single datum becomes an imperative problem, especially in the context of machine learning. Shapley value is widely used to fairly measure the contribution of data points in machine learning since it is the unique definition that satisfies all four desired properties: balance, symmetry, additivity, and zero element. However, computing Shapley value is known to be a #P-hard problem. As data is subject to changes, dynamic data exists pervasively in real-world scenarios. Pricing such dynamic data is more challenging due to the prohibitively expensive cost of recalculation from scratch. In this paper, we study the problem of Dynamic Shapley Value Computation, which updates Shapley value when dynamically adding/deleting data points. For adding data points, to prune unnecessary computation of overlapping model utilities, we propose the pivot-based algorithm that can reduce half computation time in general. We also propose the delta-based algorithm to capture Shapley value changes, which requires a smaller sample size to converge. For deleting data points, we present the YN-NN algorithm that derives the new Shapley value from the data structure of precomputed model utilities in an efficient way. Based on Shapley value changes, we give another version of the delta-based algorithm for deleting data points. Besides, we propose heuristic algorithms to draw on experimental observations for both adding and deleting data points. Extensive experimental results demonstrate the efficiency and effectiveness of our proposed algorithms.

Federated Learning (FL) allows clients to form a consortium to train a global model under the orchestration of a central server while keeping data on the local client without sharing it, thus mitigating data privacy issues. However, training a robust global model is challenging since the local data is invisible to the server. The local data of clients are naturally heterogeneous, while some clients can use corrupted data or send malicious updates to interfere with the training process artificially. Meanwhile, communication and computation costs are inevitable challenges in designing a practical FL algorithm. In this paper, to improve the robustness of FL, we propose a Shapley value-inspired adaptive weighting mechanism, which regards the FL training as sequential cooperative games and adjusts clients' weights according to their contributions. We also develop a client sampling strategy based on importance sampling, which can reduce the communication cost by optimizing the variance of the global updates according to the weights of clients. Furthermore, to diminish the computation cost of the server, we propose a weight calculation method by estimating differences between the Shapley value of clients. Our experimental results on several real data sets demonstrate the effectiveness of our approaches.

Shapley value provides a unique way to fairly assess each player's contribution in a coalition and has enjoyed many applications. However, the exact computation of Shapley value is #P-hard due to the combinatoric nature of Shapley value. Many existing applications of Shapley value are based on Monte-Carlo approximation, which requires a large number of samples and the assessment of utility on many coalitions to reach high quality approximation, and thus is still far from being efficient. Can we achieve an efficient approximation of Shapley value by smartly obtaining samples? In this paper, we treat the sampling approach to Shapley value approximation as a stratified sampling problem. Our main technical contributions are a novel stratification design and two sample allocation methods based on Neyman allocation and empirical Bernstein bound, respectively. Experimental results on several real data sets and synthetic data sets demonstrate the effectiveness and efficiency of our novel stratification design and sampling approaches.

Geometric computation can be heavy duty for spatial queries, in particular for complex geometries such as polygons with many edges based on a vector-based representation. While many techniques have been provided for spatial partitioning and indexing, they are mainly built on minimal bounding boxes or other approximation methods, which will not mitigate the high cost of geometric computation. In this paper, we propose a novel vector-raster hybrid approach through rasterization, where pixel-centric rich information is preserved to help not only filtering out more candidates but also reducing geometry computation load. Based on the hybrid model, we develop an efficient rasterization based ray casting method for point-in-polygon queries and a circle buffering method for point-to-polygon distance calculation, which is a common operation for distance based queries. Our experiments demonstrate that the hybrid model can boost the performance of spatial queries on complex polygons by up to one order of magnitude.