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Stability Theory of Game-Theoretic Explanations for Machine Learning Models


Core Concepts
The core message of this article is to establish a rigorous stability theory for game-theoretic feature attributions, such as conditional and marginal explanations, and to design group explainers that unify these two approaches while alleviating the instability issues associated with marginal explanations.
Abstract
The article studies feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the conditional and marginal expectations. The first part of the work formulates a stability theory for these explanation operators by establishing certain bounds for both marginal and conditional explanations. It is shown that the marginal explanations can become discontinuous on some naturally-designed domains, while the conditional explanations remain stable. In the second part, group explanation methodologies are devised based on game values with coalition structure, where the features are grouped based on dependencies. It is analytically shown that grouping features this way has a stabilizing effect on the marginal operator on both group and individual levels, and allows for the unification of marginal and conditional explanations. The results are verified in numerical experiments where an information-theoretic measure of dependence is used for grouping.
Stats
The article does not contain any explicit numerical data or statistics. It focuses on theoretical analysis and properties of game-theoretic feature attribution methods.
Quotes
"Stability theory of game-theoretic group feature explanations for machine learning models" "The main focus is on random games based on the conditional and marginal expectations." "We show analytically that grouping features this way has a stabilizing effect on the marginal operator on both group and individual levels, and allows for the unification of marginal and conditional explanations."

Deeper Inquiries

How can the proposed group explainers be extended to handle more complex feature dependencies, such as nonlinear or higher-order interactions

The proposed group explainers can be extended to handle more complex feature dependencies, such as nonlinear or higher-order interactions, by incorporating advanced techniques from machine learning and statistics. One approach could involve using non-linear models or kernel methods to capture complex relationships between features. For example, kernel-based methods like the kernel SHAP algorithm can handle non-linear interactions by mapping the features into a higher-dimensional space where the relationships are more easily captured. Additionally, ensemble methods like random forests or gradient boosting can naturally capture non-linear interactions between features. By incorporating these advanced modeling techniques into the group explainers, it would be possible to handle more complex feature dependencies effectively.

What are the potential limitations or drawbacks of the information-theoretic approach used for feature grouping, and how could it be further improved

While the information-theoretic approach used for feature grouping has its advantages, such as providing a principled way to group features based on their dependencies, there are also potential limitations and drawbacks. One limitation is that the method may struggle with capturing non-linear dependencies or interactions between features. In cases where the relationships between features are complex and non-linear, the information-theoretic approach may not be able to fully capture these dependencies. Additionally, the method may be sensitive to the choice of the information-theoretic measure used for grouping, as different measures may lead to different groupings of features. To improve the information-theoretic approach for feature grouping, one could explore the use of more advanced dependency measures that can capture non-linear relationships, such as mutual information estimators that are robust to non-linear dependencies. Additionally, incorporating domain knowledge or expert input into the grouping process could help refine the feature groupings and make them more interpretable.

Can the stability analysis and unification of marginal and conditional explanations be applied to other game-theoretic feature attribution methods beyond the ones considered in this work

The stability analysis and unification of marginal and conditional explanations can be applied to other game-theoretic feature attribution methods beyond the ones considered in this work. By extending the analysis to different game values and operators, researchers can assess the stability and consistency of explanations provided by various feature attribution methods. This analysis can help identify which methods are more robust and reliable in different scenarios and provide insights into when to use certain methods based on the nature of the data and the model being analyzed. Additionally, the unification of marginal and conditional explanations can help streamline the interpretation process and provide a more cohesive understanding of feature contributions in machine learning models.
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