arXiv Statistics ML By Karl B. Gregory, Daniel J. Nordman

New explanations and inference for least angle regression

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The paper introduces a new inference framework for least angle regression (LAR), clarifying its behavior and providing a formal stopping rule. It shows that LAR estimates non‑zero population correlations as independent normal variables, while zero correlations follow a non‑normal joint distribution, enabling variable importance interpretation. A modified bootstrap method is proposed to quantify uncertainty and assess variable entry, with results validated by simulation and data examples.

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arXiv Machine Learning
5d ago

Pro-Active Inference

The paper introduces Pro-Active Inference (PAI), a method for efficiently estimating a population mean when only a subset of outcomes can be observed. PAI proactively selects which observation to label next from a covariate pool, updating machine‑learning predictions online, and provides finite‑sample unbiasedness, asymptotic validity, and an improved variance estimator. Experiments on eight datasets show that PAI outperforms Sequential Active Inference in most settings, while diagnostics reveal when additional adaptivity is beneficial or detrimental.

By Skyler Wu, Yash Nair, Antoine Maechler, Emmanuel J. Cand\`es