Asymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
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The paper investigates weighted empirical risk minimization under nonstationary data, decomposing the excess risk into a learning component and a drift component. It establishes oracle inequalities for the learning error under mixing conditions, uniformly over arbitrary weight classes, and derives explicit bounds for drift errors in square loss settings, covering structural‑break and smoothly drifting processes. The analysis is extended to auto‑regression problems with linear models, basis approximations, and neural networks, revealing that optimal weights balance learning and drift via a bias–variance trade‑off and recover minimax‑optimal rates in unweighted, stationary cases.