Asymmetric Data Shapley: A New Framework for Data Valuation in Machine Learning

Core Concepts

Traditional data valuation methods, like data Shapley, fail to account for inherent structures within datasets, leading to potentially unfair valuations. This paper introduces asymmetric data Shapley, a novel framework that incorporates these structures to provide a more accurate and equitable assessment of data value in machine learning.

Abstract

Bibliographic Information:

Zheng, X., Chang, X., Jia, R., & Tan, Y. (2024). Towards Data Valuation via Asymmetric Data Shapley. arXiv preprint arXiv:2411.00388.

Research Objective:

This paper addresses the limitations of traditional data Shapley in capturing the value of data points within structured datasets. The authors propose a novel framework called "asymmetric data Shapley" to provide a more accurate and fair data valuation method for machine learning applications.

Methodology:

The authors leverage the concept of asymmetric Shapley value from cooperative game theory and adapt it for data valuation in supervised machine learning. They introduce the concept of "weight systems" to incorporate inherent structures within datasets, allowing for differential weighting of data points based on their relationships. The paper presents a mathematical formulation for asymmetric data Shapley under general weight systems and proposes a specific type - "intra-class uniform weight system" (ICU-WS) - tailored for data valuation tasks. Furthermore, the authors develop two efficient algorithms for approximating and accurately computing asymmetric data Shapley: a Monte Carlo approach and a KNN surrogate method.

Key Findings:

• Asymmetric data Shapley, using ICU-WS, effectively captures the incremental value of augmented data points added to an original training set.
• The framework accurately quantifies the value of data points arriving sequentially in a data stream, considering their contribution relative to previously observed data.
• In simulated data markets, asymmetric data Shapley enables fairer allocation of profits among data creators and data packagers, preventing exploitation via simple data replication.

Main Conclusions:

Asymmetric data Shapley offers a more accurate and equitable approach to data valuation in machine learning compared to traditional data Shapley. By incorporating inherent data structures, the framework allows for a nuanced understanding of individual data point contributions, leading to fairer compensation in data markets and improved data augmentation strategies.

Significance:

This research significantly contributes to the field of data valuation by addressing the limitations of existing methods in capturing the value of structured data. The proposed asymmetric data Shapley framework has the potential to improve fairness and transparency in data-driven applications, particularly in data markets and algorithmic decision-making.

Limitations and Future Research:

The current work primarily focuses on ICU-WS, leaving room for exploring the application and computational efficiency of asymmetric data Shapley under general weight systems. Further research could investigate the statistical properties of asymmetric data Shapley and its robustness to different data distributions.

Stats

Removing low-value augmented data points, as identified by asymmetric data Shapley, resulted in the greatest performance gain in the augmented training set.
Adding high-value augmented data points to the original training dataset yielded the most significant performance gain.
In the sequential data experiment, adding the top 10% high-value data points from August to the July training set resulted in peak performance.

Quotes

"Data Shapley has recently gained widespread recognition for quantifying the contribution of individual data points to ML models."
"However, its symmetry axiom evaluates all data points equally, based solely on their content and influence on model performance, overlooking any inherent structures that exist in real-world datasets."
"Addressing these questions necessitates incorporating inherent structures among data points into their valuation."

Key Insights Distilled From

Towards Data Valuation via Asymmetric Data Shapley

by Xi Zheng, Xi... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2411.00388.pdf

Deeper Inquiries

How can the concept of asymmetric data Shapley be extended to unsupervised learning tasks where the value of data points is not directly tied to a supervised learning objective?

Extending asymmetric data Shapley to unsupervised learning tasks presents a unique challenge because we lack a readily available supervised learning objective like accuracy or loss to quantify data value. However, several promising avenues can be explored:
1. Leveraging Objective Functions from Unsupervised Learning:

Clustering: For clustering algorithms like k-means, we can define the score function (v(S)) based on metrics like cluster cohesion (e.g., within-cluster sum of squares) or separation (e.g., between-cluster sum of squares). The intuition is that data points contributing to well-defined and separated clusters are more valuable.
Dimensionality Reduction: In techniques like Principal Component Analysis (PCA), the score function can be based on the amount of variance explained by a subset of principal components. Data points contributing more to the explained variance are considered more valuable.
Generative Models: For models like Variational Autoencoders (VAEs) or Generative Adversarial Networks (GANs), the score function can be based on the quality of generated samples (e.g., using metrics like Inception Score or Fréchet Inception Distance). Data points leading to more realistic and diverse generated samples are deemed more valuable.
2. Introducing Proxy Tasks:

Reconstruction Error: Train an autoencoder on the dataset and use the reconstruction error on a held-out set as a proxy for data value. Data points with lower reconstruction errors are considered more valuable as they contain more information captured by the model.
Pseudo-Labeling and Downstream Tasks: Use unsupervised methods to generate pseudo-labels for the data and then define a score function based on the performance of a simple classifier trained on these pseudo-labels. This approach indirectly links data value to a downstream task.
3. Adapting the Weight System:

Structure-Based Weights: In unsupervised settings, the weight system (ω = (Λ, σ)) in asymmetric data Shapley can be designed to reflect inherent data structures. For example, in a density-based clustering scenario, data points in denser regions could be assigned higher weights, reflecting their greater influence on cluster formation.
Challenges and Considerations:

Defining Meaningful Score Functions: The key challenge lies in defining score functions that truly capture the value of data in the context of the specific unsupervised task.
Computational Complexity: Evaluating the score function for numerous data subsets can be computationally expensive, especially for large datasets. Efficient approximation methods will be crucial.

Could the emphasis on data structure in asymmetric data Shapley inadvertently lead to biases against certain types of data or reinforce existing inequalities within datasets?

Yes, the emphasis on data structure in asymmetric data Shapley could potentially lead to biases and exacerbate existing inequalities, warranting careful consideration:
1. Amplifying Existing Biases:

Over-representation and Under-representation: If a dataset already contains an over-representation of a particular group or class, and the weight system in asymmetric data Shapley prioritizes data points from this dominant group (e.g., based on density or similarity), it could further amplify their importance and marginalize under-represented groups.
Propagating Historical Biases: If the inherent structure of the data reflects historical biases or discrimination (e.g., in loan applications or facial recognition datasets), using this structure to assign data values could perpetuate and even worsen these biases.
2. Creating New Biases:

Sensitivity to Data Representation: The choice of distance metric or similarity measure used to define data structure can introduce biases. For instance, using Euclidean distance in a high-dimensional space might not accurately capture the true relationships between data points, potentially disadvantaging certain data types.
Ignoring Contextual Information: Relying solely on data structure might overlook crucial contextual information relevant to fairness. For example, in a healthcare dataset, simply considering the proximity of patients based on symptoms might not be sufficient; factors like socioeconomic status and access to healthcare should also be considered.
Mitigating Potential Biases:

Careful Weight System Design: Critically assess the weight system to ensure it does not disproportionately favor certain data types or reinforce existing biases. Explore alternative weight systems that promote fairness.
Incorporating Fairness Constraints: Integrate fairness constraints directly into the asymmetric data Shapley framework. For example, impose constraints that ensure data points from different demographic groups receive comparable values when their contributions to the learning task are similar.
Data Preprocessing and Augmentation: Address biases in the data itself through preprocessing techniques like re-sampling, re-weighting, or adversarial debiasing. Augmenting the dataset with data from under-represented groups can also help mitigate bias.

How might the principles of asymmetric data Shapley be applied to other fields beyond machine learning, such as economics or social science, where valuing contributions within complex systems is crucial?

The principles of asymmetric data Shapley hold significant promise for applications beyond machine learning, particularly in fields grappling with valuing contributions within complex systems:
1. Economics:

Supply Chain Management: Quantify the value contributions of different entities (suppliers, manufacturers, distributors) in a supply chain, considering factors like production capacity, lead times, and reliability. This can inform fair pricing models and incentivize efficient collaboration.
Team Production and Collaboration: Assess the individual contributions of team members in collaborative projects, accounting for factors like expertise, workload, and communication patterns. This can facilitate fair compensation and performance evaluations.
Market Design and Auctions: Design mechanisms for allocating resources or goods in markets with interdependent participants, where the value of an item to a bidder depends on the bids of others. Asymmetric Shapley can help determine fair market prices and allocations.
2. Social Science:

Social Network Analysis: Measure the influence or importance of individuals within social networks, considering factors like connections, information flow, and group dynamics. This can inform targeted interventions or marketing strategies.
Political Science and Voting Systems: Analyze the power dynamics in voting systems and assess the influence of different voters or groups, taking into account factors like voting rules, coalitions, and strategic behavior.
Public Policy and Resource Allocation: Evaluate the impact of different policies or interventions on various stakeholders, considering the complex interplay of social, economic, and environmental factors.
3. Other Potential Applications:

Environmental Science: Quantify the contributions of different factors (land use, emissions, climate change) to environmental outcomes, aiding in the development of effective conservation strategies.
Healthcare: Assess the relative importance of different risk factors or treatments in patient outcomes, considering the complex interactions within the human body.
Key Advantages of Asymmetric Data Shapley:

Capturing Interdependencies: Effectively accounts for the interdependencies between entities or factors within a system, moving beyond simplistic, independent valuations.
Flexibility and Adaptability: The framework is flexible and can be adapted to various domains by defining appropriate score functions and weight systems that reflect the specific context.
Promoting Fairness and Transparency: Provides a principled and transparent approach to valuing contributions, potentially fostering greater fairness and cooperation within complex systems.