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

Area of Science:

• Computational Biology
• Machine Learning
• Health Informatics

Background:

• Federated learning enables collaborative model training on decentralized data, crucial for healthcare applications due to privacy concerns.
• Existing distributed logistic regression models like VERTIGO offer privacy-preserving point estimates but lack variance estimation capabilities.
• The absence of variance estimation prevents hypothesis testing and reporting of statistical significance (P-values).

Purpose of the Study:

• To extend the VERTIGO model for federated logistic regression with variance estimation.
• To introduce a novel protocol for reconstructing the covariance matrix in a dual space setting.
• To enable comprehensive statistical inference, including P-values, in privacy-preserving distributed machine learning.

Main Methods:

• Developed a novel ring-structure protocol for efficient communication of intermediary statistics among clients.
• Reconstructed the covariance matrix in the dual space using the gathered intermediary statistics.
• Extended the VERTIGO model to create VERTIGO-CI, a complete protocol for federated logistic regression with variance estimation.

Main Results:

• VERTIGO-CI successfully reconstructs the covariance matrix, enabling variance estimation and P-value calculation.
• Evaluations on synthetic and real datasets demonstrate accuracy equivalent to centralized logistic regression.
• The extended model, VERTIGO-CI, introduces a tolerable performance overhead compared to the original VERTIGO.

Conclusions:

• VERTIGO-CI provides a complete, privacy-preserving solution for federated logistic regression, including statistical inference.
• The developed ring-structure protocol is efficient for distributed computation of covariance matrices.
• This methodology is applicable to other generalized linear models with dual objectives in federated settings.