Weighted Empirical Risk Minimization for Machine Learning under Long-Range Dependence: Exact Pathwise Rates and Learning-Error Geometry
We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data. The training observations are generated from a fixed finite window of a stationary Gaussian sequence, and the sample weights are regularly varying. If the loss gradient at the population minimizer has Wiener-chaos rank $m$ and a nonzero low-frequency coefficient, then, in the long-memory interior regime, the finite-lag score reduces on the iterated-logarithm scale to a single weighted Hermite chaos. This yields an almost-sure Bahadur representation, an exact limsup law for the learned parameter, and, for $m\ge2$, the functiona...
| Authors | Elina Moldavskaya |
|---|---|
| Primary category | stat.ML |
| Published | 9 September 2026 |
| Last updated at source | 9 September 2026 |
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