Machine intelligence plays a fundamental role in contemporary human society. Early milestones include the advent of search engines, applications in online marketing/advertising, and the integration in industrial logistics; but now machine intelligence is appearing in high-stakes domains such as medicine, autonomous transportation technologies, forensic science, etc. It is widely accepted that machine intelligence technologies are effective, but it is largely undetermined how to quantify uncertainty in their performance guarantees. Moreover, there is no generally accepted standard of accountability of stated uncertainties. I argue that applying the generalized fiducial (GF) inference framework to a rank-based data association leads to a model-free approach to constructing GF predictions. The resulting GF predictions lead to imprecise probabilities, and from this distribution it is shown that a conformal predictor arises. The connection to conformal predictors is important for notions of validity relating to controlling type 1 errors for finite sample sizes. Theory and simulation results are provided to demonstrate the robustness of the GF predictors when the data model is misspecified in traditional GF and Bayesian approaches. Furthermore, an extension from the imprecise GF prediction probabilities to a proper prediction probability distribution is worked out for the case of univariate data.
Jonathan Williams is Assistant Professor (tenure-track) in the Depart- ment of Statistics at North Carolina State University. Jon holds a PhD in Statistics from UNC at Chapel Hill. He was advised by Jan Hannig at UNC, and Curt Storlie at the Mayo Clinic