  Eliciting labels from crowds is a potential way to obtain large labeled data.
Despite a variety of methods developed for learning from crowds, a key
challenge remains unsolved: \emph{learning from crowds without knowing the
information structure among the crowds a priori, when some people of the crowds
make highly correlated mistakes and some of them label effortlessly (e.g.
randomly)}. We propose an information theoretic approach, Max-MIG, for joint
learning from crowds, with a common assumption: the crowdsourced labels and the
data are independent conditioning on the ground truth. Max-MIG simultaneously
aggregates the crowdsourced labels and learns an accurate data classifier.
Furthermore, we devise an accurate data-crowds forecaster that employs both the
data and the crowdsourced labels to forecast the ground truth. To the best of
our knowledge, this is the first algorithm that solves the aforementioned
challenge of learning from crowds. In addition to the theoretical validation,
we also empirically show that our algorithm achieves the new state-of-the-art
results in most settings, including the real-world data, and is the first
algorithm that is robust to various information structures. Codes are available
at
\hyperlink{https://github.com/Newbeeer/Max-MIG}{https://github.com/Newbeeer/Max-MIG}
