  We build a natural connection between the learning problem, co-training, and
forecast elicitation without verification (related to peer-prediction) and
address them simultaneously using the same information theoretic approach.
  In co-training/multiview learning, the goal is to aggregate two views of data
into a prediction for a latent label. We show how to optimally combine two
views of data by reducing the problem to an optimization problem. Our work
gives a unified and rigorous approach to the general setting.
  In forecast elicitation without verification we seek to design a mechanism
that elicits high quality forecasts from agents in the setting where the
mechanism does not have access to the ground truth. By assuming the agents'
information is independent conditioning on the outcome, we propose mechanisms
where truth-telling is a strict equilibrium for both the single-task and
multi-task settings. Our multi-task mechanism additionally has the property
that the truth-telling equilibrium pays better than any other strategy profile
and strictly better than any other "non-permutation" strategy profile when the
prior satisfies some mild conditions.
