| |
| 95% CI | 90% CI | MSE ratio | MSE ratio |
|---|
| | | coverage | coverage | (train data) | (test data) |
|---|
Our method | 0.9073 | 0.9778 | 0.8889 | 0.2827 | 9.4630 |
Maximum likelihood | 0.1181 | 1.00 | 0.9667 | 1 | 1 |
Bayesian lasso | 0.6407 | 0.9667 | 0.9111 | 0.3727 | 8.858 |
Freq. lasso (1 SE) | 1.2020 | NA | NA | 0.0983 | 8.1163 |
Freq. lasso (min) | 0.6379 | NA | NA | 0.1851 | 8.8374 |
Freq. EN (1 SE) | 0.9278 | NA | NA | 0.1273 | 8.4439 |
Freq. EN (min) | 0.7012 | NA | NA | 0.1684 | 8.7154 |
- Freq. EN means freqentist elastic net, which was run with mixing parameter (for penalty mixture) 0.5. The estimate of σ2 is the posterior mean for our method and the Bayesian lasso. For the others, it is the mean sum of squared error. ‘CI’ is credible interval for Bayesian methods and confidence interval for frequentist methods. Note that for the frequentist lasso and elastic net, it is not possible to obtain standard errors for the coefficients set to 0, and therefore, we cannot construct the CI’s. The penalty choice of ‘1 SE’ means we used the largest parameter with error within one standard error of the minimum error, while ‘min’ means we used the parameter with minimum error (from cross validation). MSE ratio is the mean squared error from least squares divided by the MSE from the respective method. NA indicates not applicable.
