Towards Efficient Data Valuation Based on the Shapley Value (1902.10275v4)

Abstract: "How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining prospective compensation when data breaches happen. In this paper, we study the problem of data valuation by utilizing the Shapley value, a popular notion of value which originated in cooperative game theory. The Shapley value defines a unique payoff scheme that satisfies many desiderata for the notion of data value. However, the Shapley value often requires exponential time to compute. To meet this challenge, we propose a repertoire of efficient algorithms for approximating the Shapley value. We also demonstrate the value of each training instance for various benchmark datasets.

• The paper develops efficient algorithms to compute or approximate Shapley values for data valuation, addressing the challenge of the method's inherent exponential complexity.
• Several techniques are introduced to improve computational efficiency, including group testing, exploiting sparsity via compressive sensing, and using influence functions for heuristic estimates.
• The research has significant implications for practical machine learning applications like data marketplaces and federated learning, enabling fair and computationally viable data valuation.

Data Valuation via Shapley Value: Computational Advancements and Practical Implications

This paper presents a rigorous paper on data valuation utilizing the Shapley value (SV) from cooperative game theory. The research focuses on the computational aspects of applying the Shapley value to data contributions, a challenge primarily due to its inherent computational complexity, which is exponential with the number of contributors. The paper's primary contribution lies in the development of efficient algorithms to approximate the Shapley value, particularly in the context of training ML models.

Overview of Contributions

The research tackles a pressing question in the field of machine learning—determining the value of individual data contributions when multiple entities collectively contribute data to train ML models. By adopting the Shapley value, the authors ensure that the data value satisfies properties such as fairness and rationality, which are critical in scenarios like profit distribution among data contributors. Recognizing the computational burden of exact SV calculation, the paper introduces a series of approximation strategies, each with varying assumptions and computational efficiencies.

1. Permutation Sampling Baseline: The authors review a permutation sampling method as a baseline, which, although effective, involves intensive computations that grow quadratically with the dataset size.
2. Group Testing-Based Approach: Innovatively leveraging principles from group testing, this method reduces the necessary computations significantly, demonstrating a complexity that scales more gracefully—roughly proportional to $N(\log N)^2$.
3. Exploiting Sparsity: The paper introduces the concept of compressive sensing to leverage the sparsity observed in data valuation applications, achieving further computational efficiency by reducing the required model evaluations logarithmically.
4. Consideration of Stable Algorithms: For ML algorithms characterized by incremental stability, such as those with Tikhonov regularization, the authors demonstrate how uniform data valuation becomes plausible, exploiting theoretical bounds on SV differences.
5. Influence Functions: By utilizing influence functions, traditionally used for model interpretation, the authors present heuristic methods that estimate data contributions without repeated model retraining, thus achieving practical efficiency in large-scale ML tasks.

Implications and Future Directions

The implications of this work are significant for the field of machine learning, particularly in scenarios involving data marketplaces or federated learning systems where fair distribution of rewards or costs among data contributors is paramount. By making Shapley value calculations computationally viable, this research paves the way for its integration into real-world ML applications.

Theoretical advancements in approximation algorithms open the door for more decentralized and transparent data valuation systems, potentially transforming data policy formulation in business and healthcare sectors. Additionally, these methods accommodate the dynamic nature of real-world data, where contributors may possess diverse data qualities and confidentiality concerns, as evidenced by experiments showing privacy and adversarial data trade-offs.

Looking ahead, future work may explore the applicability of these algorithms in distributed and privacy-preserving ML landscapes. Given the complexity and interdependencies inherent in modern AI systems, further research could investigate synergizing Shapley-based approaches with other cooperative game theory concepts, enriching the robustness and flexibility of data valuation methodologies. There is also the promising avenue of extending these techniques to evaluate model components and configurations themselves, beyond raw data, thereby advancing model interpretability and accountability.

This paper aptly combines theoretical rigor with practical relevance, addressing a crucial gap in data-driven AI systems where data is a primary asset. The refined computational approaches ensure that stakeholders can derive equitable and insightful data valuations without prohibitive computational expenditures. As the volume and complexity of data continue to escalate, such innovations will be instrumental in shaping the future landscape of data-centric AI economies.