Misspecification uncertainties in near-deterministic regression

The expected loss is an upper bound to the model generalization error which admits robust PAC-Bayes bounds for learning. However, loss minimization is known to ignore misspecification, where models cannot exactly reproduce observations. This leads to significant underestimates of parameter uncertainties in the large data, or underparameterized, limit. We analyze the generalization error of near-deterministic, misspecified and underparametrized surrogate models, a regime of broad relevance in science and engineering. We show posterior distributions must cover every training point to avoid …

analyze bayes cs.lg data error leads loss model generalization near physics.data-an regression robust stat.ml