VERTIcal Grid lOgistic regression with Confidence Intervals (VERTIGO-CI).

Federated learning of data from multiple participating parties is getting more attention and has many healthcare applications. We have previously developed VERTIGO, a distributed logistic regression model for vertically partitioned data. The model takes advantage of the linear separation property of kernel matrices of a dual space model to harmonize information in a privacy-preserving manner. However, this method does not handle the variance estimation and only provides point estimates: it cannot report test statistics and associated P-values. In this work, we extend VERTIGO by introducing a novel ring-structure protocol to pass on intermediary statistics among clients and successfully reconstructed the covariance matrix in the dual space. This extension, VERTIGO-CI, is a complete protocol to construct a logistic regression model from vertically partitioned datasets as if it is trained on combined data in a centralized setting. We evaluated our results on synthetic and real data, showing the equivalent accuracy and tolerable performance overhead compared to the centralized version. This novel extension can be applied to other types of generalized linear models that have dual objectives.