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...

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...

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...