Distributed Differentially-private Canonical Correlation Analysis

We propose a distributed differentially-private canonical correlation analysis (CCA) algorithm to use on multi-view data. CCA finds a subspace for each view such that projecting the views onto these subspaces simultaneously reduces the dimension and maximizes correlation. In applications involving privacy-sensitive data, such as medical imaging, distributed privacy-preserving algorithms can let data holders maintain local control of their data while participating in joint computations with other data holders. Differential privacy is a framework for quantifying the privacy risk in such settings. However, conventional distributed differentially-private algorithms introduce more noise to guarantee a given level of privacy compared to their centralized counterparts. Our differentially-private CCA employs a noise-reduction strategy to achieve the same utility level as CCA on centralized data. Experiments on synthetic and real data show the benefit of our approach over conventional methods.