PAC-learning with approximate predictors

Abstract Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and quest to explain guarantee good generalisation abilities for such methods has just begun. In this paper, we study role approximability learning, both full precision approximated settings. We do through a notion sensitivity predictors action approximation operator at hand. prove upper bounds on yielding following main findings, any PAC-learnable class given operator: (1) show that under mild conditions, approximable target concepts are learnable from smaller labelled sample, provided sufficient unlabelled data; (2) give algorithms predictor whose also enjoys same guarantees; (3) highlight natural examples structure sensitivities, which reduce, possibly even eliminate abundant requirement additional data, henceforth shed new light onto what makes one problem instance easier learn than another. These results embed scope modern model-compression approaches into general goal statistical theory, return suggests appropriate minimising uniform bounds.