Groups Don't Move as One: A Bregman Clustering View of Linearized Group Influence

arXiv:2610.14809v1 Announce Type: new Abstract: Influence functions provide an efficient alternative to retraining for assessing the effects of removing or reweighting training data. For groups, however, the standard first-order estimate reduces individual contributions to a sum that can conceal substantial differences among members, including opposing effects that cancel. We establish a Bregman centroid formulation of the linearized group influence objective, interpreting this aggregate as a single representative and using Bregman information (BI) to quantify the variation it omits. Extending this formulation to multiple clusters reveals distinct contributions whose sum recovers the original estimate. We further propose an estimator that jointly optimizes the weights of these cluster contributions, rather than simply summing them. Experiments uncover cluster-specific influence patterns and a positive association between target-specific BI and approximation error. The proposed estimator achieves higher $R^2$ than standard group influence in predicting target changes under the nonlinear proximal Bregman response function. Simplified clustering and correction variants reduce computational cost. The centroid view thus explains what additive group influence leaves out and provides a basis for using that information to improve estimation.

Abstract:Influence functions provide an efficient alternative to retraining for assessing the effects of removing or reweighting training data. For groups, however, the standard first-order estimate reduces individual contributions to a sum that can conceal substantial differences among members, including opposing effects that cancel. We establish a Bregman centroid formulation of the linearized group influence objective, interpreting this aggregate as a single representative and using Bregman information (BI) to quantify the variation it omits. Extending this formulation to multiple clusters reveals distinct contributions whose sum recovers the original estimate. We further propose an estimator that jointly optimizes the weights of these cluster contributions, rather than simply summing them. Experiments uncover cluster-specific influence patterns and a positive association between target-specific BI and approximation error. The proposed estimator achieves higher $R^2$ than standard group influence in predicting target changes under the nonlinear proximal Bregman response function. Simplified clustering and correction variants reduce computational cost. The centroid view thus explains what additive group influence leaves out and provides a basis for using that information to improve estimation.

Machine Learning (cs.LG)

arXiv:2610.14809 [cs.LG]

(or arXiv:2610.14809v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.14809 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

Groups Don't Move as One: A Bregman Clustering View of Linearized Group Influence

Subiecte conexe