Water from Two Rocks: Maximizing the Mutual Information
This provides a unified theoretical framework for multi-view learning and peer-prediction mechanisms, but it is incremental as it builds on existing information-theoretic approaches.
The paper tackles the problem of optimally combining two views of data in co-training and designing mechanisms for forecast elicitation without ground truth verification, showing that truth-telling can be a strict equilibrium with better payoffs under mild conditions.
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.