  A generative model may generate utter nonsense when it is fit to maximize the
likelihood of observed data. This happens due to "model error," i.e., when the
true data generating distribution does not fit within the class of generative
models being learned. To address this, we propose a model of active
distribution learning using a binary invalidity oracle that identifies some
examples as clearly invalid, together with random positive examples sampled
from the true distribution. The goal is to maximize the likelihood of the
positive examples subject to the constraint of (almost) never generating
examples labeled invalid by the oracle. Guarantees are agnostic compared to a
class of probability distributions. We show that, while proper learning often
requires exponentially many queries to the invalidity oracle, improper
distribution learning can be done using polynomially many queries.
