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About this paper
Mélissa Tamine, Benjamin Heymann, Maxime Vono, Patrick Loiseau
A geometric framework and a quantitative metric, R_p, were developed to assess the stability of data point rankings generated by semivalue-based data valuation when the underlying utility function changes. Empirical findings demonstrate that the Data Banzhaf semivalue consistently exhibits higher R_p scores, indicating greater ranking stability, compared to Shapley and Beta Shapley across various datasets and utility configurations.
Key insights
- Data point ranking by a utility function is geometrically equivalent to sorting their projections onto a utility direction vector in a K-dimensional embedded space.
- The Data Banzhaf semivalue consistently induces a more 'collinear' spatial signature for data points, which geometrically explains its superior ranking robustness.
- The robustness of a semivalue is analytically linked to the correlation of marginal contributions at different coalition sizes, with Banzhaf's weight distribution favoring higher alignment.
Summary by alphaXiv.
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