Model-free generalized fiducial inference for empirical risk minimizers

Oregon Convention Center 

Model-free generalized fiducial (MFGF) inference was previously introduced to facilitate the development of safe and reliable methods for uncertainty quantification in machine learning. Ideas were proposed and developed for a model-free statistical framework for imprecise probabilistic prediction inference, and provided finite sample control of frequentist type 1 errors. It was found that approximating a belief/plausibility measure pair by an [optimal in some sense] probability measure in the credal set is a critical resolution needed for the broader adoption of imprecise probabilistic approaches to inference in statistical and machine learning communities. In this new work, we develop ideas for how to transform the MFGF predictive inference framework to provide safe and reliable uncertainty quantification for empirical risk minimizers. Important special cases include parameters of a specified likelihood function, tuning parameters in regularized regression, and uncertainty quantification for model selection.