  Collaborative machine learning involves training models on data from multiple
parties but must incentivize their participation. Existing data valuation
methods fairly value and reward each party based on shared data or model
parameters but neglect the privacy risks involved. To address this, we
introduce differential privacy (DP) as an incentive. Each party can select its
required DP guarantee and perturb its sufficient statistic (SS) accordingly.
The mediator values the perturbed SS by the Bayesian surprise it elicits about
the model parameters. As our valuation function enforces a privacy-valuation
trade-off, parties are deterred from selecting excessive DP guarantees that
reduce the utility of the grand coalition's model. Finally, the mediator
rewards each party with different posterior samples of the model parameters.
Such rewards still satisfy existing incentives like fairness but additionally
preserve DP and a high similarity to the grand coalition's posterior. We
empirically demonstrate the effectiveness and practicality of our approach on
synthetic and real-world datasets.
