  Blind source separation algorithms such as independent component analysis
(ICA) are widely used in the analysis of neuroimaging data. In order to
leverage larger sample sizes, different data holders/sites may wish to
collaboratively learn feature representations. However, such datasets are often
privacy-sensitive, precluding centralized analyses that pool the data at a
single site. In this work, we propose a differentially private algorithm for
performing ICA in a decentralized data setting. Conventional approaches to
decentralized differentially private algorithms may introduce too much noise
due to the typically small sample sizes at each site. We propose a novel
protocol that uses correlated noise to remedy this problem. We show that our
algorithm outperforms existing approaches on synthetic and real neuroimaging
datasets and demonstrate that it can sometimes reach the same level of utility
as the corresponding non-private algorithm. This indicates that it is possible
to have meaningful utility while preserving privacy.

Machine Learning;Machine Learning;Signal Processing