Neural Information Processing Systems http://nips.cc/

We consider a Bayesian forecast aggregation model where n experts, after observing private signals about an unknown binary event, report th eir posterior beliefs about the event to a principal, who then aggregates the repor ts into a single prediction for the event. The signals of the experts and the outcome of the event follow a joint distribution that is unknown to the principal, but th e principal has access to i.i.d. "samples" from the distribution, where each sampl e is a tuple of the experts' reports (not signals) and the realization of the even t. Using these samples, the principal aims to find an ε -approximately optimal aggregator, where optimal-ity is measured in terms of the expected squared distance bet ween the aggregated prediction and the realization of the event.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

A fundamental result in differential privacy states that the privacy guarantees of a mechanism are preserved by any post-processing of its output. In this paper we investigate under what conditions stochastic post-processing can amplify the privacy of a mechanism. By interpreting post-processing as the application of a Markov operator, we first give a series of amplification results in terms of uniform mixing properties of the Markov process defined by said operator. Next we provide amplification bounds in terms of coupling arguments which can be applied in cases where uniform mixing is not available. Finally, we introduce a new family of mechanisms based on diffusion processes which are closed under post-processing, and analyze their privacy via a novel heat flow argument. On the applied side, we generalize the analysis of "privacy amplification by iteration" in Noisy SGD and show it admits an exponential improvement in the strongly convex case, and study a mechanism based on the Ornstein-Uhlenbeck diffusion process which contains the Gaussian mechanism with optimal post-processing on bounded inputs as a special case.

Asynchronous Gibbs sampling has been recently shown to be fast-mixing and an accurate method for estimating probabilities of events on a small number of variables of a graphical model satisfying Dobrushin's condition [DSOR16].