Table 1 Average \(\ell _2\)-estimation errors (standard errors) for logistic regression under Pareto noise with regularization.
From: Robust learning for ridge-penalized quasi-GLMs under non-identical distributions
\(\tau\) | \(\beta\) | Truncation | Non-truncation | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
(100, 50) | (200, 100) | (500, 200) | (700, 300) | (1000, 1000) | (100, 50) | (200, 100) | (500, 200) | (700, 300) | (1000, 1000) | ||
1.60 | 1.5 | 0.369 (0.190) | 0.366 (0.157) | 0.362 (0.137) | 0.362 (0.125) | 0.360 (0.115) | 0.500 (0.350) | 0.475 (0.313) | 0.450 (0.275) | 0.425 (0.238) | 0.400 (0.200) |
1.80 | 1.5 | 0.358 (0.144) | 0.349 (0.116) | 0.343 (0.101) | 0.347 (0.091) | 0.347 (0.090) | 0.480 (0.325) | 0.460 (0.294) | 0.440 (0.263) | 0.420 (0.231) | 0.400 (0.200) |
2.01 | 2.0 | 0.351 (0.106) | 0.343 (0.087) | 0.336 (0.077) | 0.342 (0.069) | 0.340 (0.067) | 0.503 (0.300) | 0.421 (0.263) | 0.394 (0.225) | 0.387 (0.188) | 0.380 (0.150) |
4.01 | 2.0 | 0.208 (0.155) | 0.201 (0.235) | 0.188 (0.253) | 0.193 (0.262) | 0.215 (0.235) | 0.220 (0.246) | 0.301 (0.311) | 0.306 (0.360) | 0.299 (0.363) | 0.297 (0.349) |
6.01 | 2.0 | 0.202 (0.135) | 0.184 (0.193) | 0.166 (0.207) | 0.169 (0.215) | 0.185 (0.231) | 0.210 (0.202) | 0.309 (0.311) | 0.369 (0.345) | 0.327 (0.310) | 0.315 (0.288) |
