Summary of Uncertainty Quantification For Iterative Algorithms in Linear Models with Application to Early Stopping, by Pierre C. Bellec and Kai Tan
Uncertainty quantification for iterative algorithms in linear models with application to early stopping
by Pierre C. Bellec, Kai Tan
First submitted to arxiv on: 27 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST); Computation (stat.CO); Methodology (stat.ME)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper investigates iterative algorithms in high-dimensional linear regression problems, where the feature dimension is comparable to the sample size. It proposes novel estimators for the generalization error of iterates along the trajectory and shows that these estimators are n-consistent under Gaussian designs. The paper also provides applications to early-stopping, allowing for selecting an iteration that achieves the smallest generalization error. Additionally, it presents a technique for developing debiasing corrections and valid confidence intervals for the true coefficient vector components from any finite iteration. The analysis is applicable to Gradient Descent, proximal GD, and their accelerated variants such as Fast Iterative Soft-Thresholding. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how iterative algorithms work in high-dimensional linear regression problems. It tries to figure out how well these algorithms will perform when they’re used with real data. The researchers come up with new ways to measure the performance of these algorithms and show that their methods are good at predicting how well they’ll do. They also show how their methods can be used to choose the best iteration for a given task, which is useful for early-stopping. Additionally, they present a way to correct for biases in the estimates and provide confidence intervals. |
Keywords
» Artificial intelligence » Early stopping » Generalization » Gradient descent » Linear regression
