Residual-Information Generalization Bounds Under Selective Privacy: Extended Version

Information-theoretic generalization bounds usually control dependence on the task sample, whereas selective privacy may constrain only a different, private coordinate. We study i.i.d. pairs $(X,Y)$, where a learner observes $(X^n,Y^n)$, leaks at most $ε_n$ nats about $X^n$, and incurs loss on $Y$.