Table 1.

Private Poisson regression with a privacy factor ε = 1 using raw data, data privatized by data-flush in (2.2), and data privatized by GEM (Liu, Vietri, & Wu, 2021). Kullback-Leibler divergence (KL) and root mean square error (RMSE) for regression coefficients (with the standard error in parenthesis), together with privatization time (Time, in seconds) are presented based on 200 replications. Here σ is the standard deviation of each covariate before discretization (a step required by GEM), and NA indicates that an algorithm fails to converge within two days.

	σ = 1	σ = 10	σ = 100
KL
Raw data	0.001 (0.001)	0.001 (0.001)	0.001 (0.001)
GEM	0.140 (0.126)	NA	NA
Data-flush	0.005 (0.003)	0.005 (0.003)	0.005 (0.004)
RMSE
Raw data	0.040 (0.014)	0.005 (0.002)	0.001 (0.0002)
GEM	0.273 (0.108)	NA	NA
Data-flush	0.090 (0.033)	0.013 (0.005)	0.001 (0.0005)
Time
GEM	423.25	NA	NA
Data-flush	0.35	0.34	0.33