Research map / Learning theory and algorithms / Prediction and decision losses
Bootstrap in High Dimension with Low Computation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use cheap bootstrap (t-interval with fixed small B) instead of basic/percentile/standard-error bootstrap | high-dimensional regression and simulation examples · Table 1 across six examples | coverage probability: e.g. ellipsoidal B=10: 97.5% vs 82.1% basic, 20.8% percentile, 73.6% SEB | Helped |
| Increase number of resamples B from 1 to 10 for cheap bootstrap (ablation) | Cheap bootstrap · Interval width across examples | interval width: widths decrease roughly 2/3 from B=1 to B=2 and about 4/5 from B=1 to B=10 | Helped |
| Increase dimension p from 18000 to 21000 in logistic regression (n=1e5) (ablation) | Cheap bootstrap · Logistic regression varying p | interval width: B=1 width 11.473 at p=18000 vs 1272.497 at p=21000 | Hurt |
| Increase dimension p to 15000-18000 in logistic regression with n=1e5 (cheap bootstrap over-covers) (ablation) | Cheap bootstrap · Logistic regression varying p | coverage probability: coverage near 100% vs nominal 95% | Hurt |
| Add l2 regularization to logistic regression (ablation) | Cheap bootstrap · Regularized logistic regression varying p | coverage probability: validity boundary of p extends to about 12000-15000 vs about 9000 unregularized | Helped |
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