Statistical Gains from Looped Estimation under Parameter Budgets
Read the original on arXiv Machine Learning →The paper investigates whether a looped estimator—one that repeatedly applies a single fitted operator with shared parameters—can enhance statistical accuracy while staying within a fixed parameter budget. It establishes upper and lower bounds on squared Hellinger risk for looped sieve maximum likelihood and compares them to the untied counterpart, revealing a tradeoff between parameter sharing, iteration count, and accuracy. For models with known H"older smoothness, looped residual feedforward networks and a post‑layer‑normalized Transformer achieve minimax polynomial rates with a fixed number of bounded real parameters, and under certain conditions the looped estimator’s worst‑case risk vanishes as sample size grows, outperforming the untied approach.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.