Table 1.
Coefficients of GMMAT and FedGMMAT in experiment 1.
Fig 1.
Scatter plot on -log10 scale of P-values of Synthetic data in FedGMMAT and GMMAT (Experimental Setup 3).
Table 2.
P-values estimation accuracy of FedGMMAT.
Fig 2.
Scatter plot on -log10 scale of P-values in FedGMMAT and GMMAT.
(A) Heterogeneity; (B) Homogeneity.
Table 3.
Coefficients of GMMAT and FedGMMAT in experiment 2.
Fig 3.
Scatter plot on -log10 scale of P-values in FedGMMAT and GMMAT on real data.
Table 4.
Coefficients of GMMAT and FedGMMAT in experiment 3.
Fig 4.
The comparison of computation time with different numbers of SNPs per batch in minutes between HE and Non-HE protection of FedGMMAT.
Fig 5.
The total run-time per site (y-axis) in second with respect to the number of subjects on each site (x-axis).
Table 5.
Network traffic from each client to the server.
Table 6.
Network traffic from server directly to the clients.
Table 7.
Nomenclature table.
Fig 6.
Matrix Splitting at the Central Server and aggregation among local data repositories.
In the FedGMMAT framework, each local data repository will maintain its unique dataset locally and gather intermediate model information from Global updates. The vertical splitting of Σ−1 among local repositories is illustrated in the figure as an example. Each site receives nj × n sized covariate matrices (Xj), which are multiplied locally with nj × p sized matrices. The resulting n × p matrices are encrypted and aggregated among sites via round-robin schedule and sent to the server. Splitting and aggregation of other matrices is accomplished with similar protocol.
Fig 7.
Key setup and aggregation via round-robin schedule.
The central server initiates the public/private key pair at the initialization and broadcasts the public key to all sites. Aggregation of split matrices are performed among sites by taking turns in aggregation. Each site encrypts their matrix “share” before aggregation. Symmetric keys (secret seeds) for OTP-like encryption is sent to all sites at the scoring stage whenever an aggregation is performed (S2 and S3 Figs).
Table 8.
Communication information.