In this paper, we consider the coherent theory of (epistemic) uncertainty ofWalley, in whichbeliefs are represented through sets of probability distributions, and we focus on the problemof modeling prior ignorance about a categorical random variable. In this setting, it isa known result that a...

We study the problem of learning the probability distribution of a multinomial variable from an observed sequence of signals, starting in a condition of ignorance about this distribution. We show that not all signals are suited for producing non-vacuous inferences under prior ignorance. To...

A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor () regression or the polynomial degree in regression with polynomials. We suggest a novel principle-the Loss Rank...