  In this position paper, we study interactive learning for structured output
spaces, with a focus on active learning, in which labels are unknown and must
be acquired, and on skeptical learning, in which the labels are noisy and may
need relabeling. These scenarios require expressive models that guarantee
reliable and efficient computation of probabilistic quantities to measure
uncertainty. We identify conditions under which a class of probabilistic models
-- which we denote CRISPs -- meet all of these conditions, thus delivering
tractable computation of the above quantities while preserving expressiveness.
Building on prior work on tractable probabilistic circuits, we illustrate how
CRISPs enable robust and efficient active and skeptical learning in large
structured output spaces.
