Estimating Unbiased Averages of Sensitive Attributes without Handshakes among Agents
Abstract: We consider the problem of distributed averaging of sensitive attributes in a network of agents without central coordinators, where the graph of the network has an arbitrary degree sequence (degrees refer to numbers of neighbors of vertices). Usually, existing works solve this problem by assuming that either (i) the agents reveal their degrees to their neighbors or (ii) every two neighboring agents can perform handshakes (requests that rely on replies) in every exchange of information. However, the degrees suggest the profiles of the agents and the handshakes are impractical upon inactive agents. We propose an approach which solves the problem with privatized degrees and without handshakes upon a stronger self-organization. In particular, we propose a simple gossip algorithm that computes averages that are biased by the variance of the degrees and a mechanism that corrects that bias. We will suggest a use case of the proposed approach that allows for fitting a linear regression model in a distributed manner, while privatizing the target values, the features and the degrees. We will provide theoretical guarantees that the mean squared error between an estimated regression parameter and a true regression parameter is $\mathcal{O}(\frac{1}{n})$, where $n$ is the number of agents. We will show on synthetic graph datasets that the theoretical error is close to its empirical counterpart. Also, we will show on synthetic graph datasets and real graph datasets that the regression model fitted by our approach is close to the solution when locally privatized values are averaged by central coordinators.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Varun_Kanade1
Submission Number: 31
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