Quantifying the Value of Privileged Information Using a PAC-Bayesian Approach

Abstract:In practice, various learning scenarios provide access to auxiliary features exclusively during training. Incorporating such data to enhance model performance gave rise to a paradigm known as Learning Using Privileged Information (LUPI). While this extra information is intended to improve the resulting model, establishing a generalized, cohesive understanding of how privileged information (PI) transfers useful knowledge remains a challenge. Vapnik's original theory and subsequent works offer performance guarantees in certain cases, but these results are inherently per-algorithm and rely on setting-specific proof approaches. Consequently, a more general framework explaining how and when PI transfers useful knowledge is still missing. To bridge this gap, we introduce an algorithm-agnostic, information-theoretic approach based on the PAC-Bayes framework. Rather than asking whether a particular algorithm exploits PI, we ask how much value it could offer: comparing the tightest achievable risk bound with and without PI yields its potential - an upper limit on the extractable gain. We introduce a metric that quantifies this potential directly from empirical training risk, bypassing the need for test-time data access, and validate our findings in both supervised and unsupervised settings. The results demonstrate a robust correspondence between our training-time metric and true test-time performance gains. Ultimately, this work takes a necessary step toward an information-theoretic understanding of LUPI, and quantifying the potential of privileged features before committing to a model.

24 pages, 4 figures. Submitted to AAAI 2027

Machine Learning (cs.LG)

arXiv:2609.12891 [cs.LG]

(or arXiv:2609.12891v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.12891 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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