Wasserstein-p Central Limit Theorem Rates: From Local Dependence to Markov Chains
NeutralArtificial Intelligence
- A recent study has established optimal finite-time central limit theorem (CLT) rates for multivariate dependent data in Wasserstein-$p$ distance, focusing on locally dependent sequences and geometrically ergodic Markov chains. The findings reveal the first optimal $ ext{O}(n^{-1/2})$ rate in $ ext{W}_1$ and significant improvements for $ ext{W}_p$ rates under mild moment assumptions.
- This development is crucial for advancing machine learning methodologies, as it enhances the understanding of dependence structures in data, allowing for more accurate statistical inference and model performance.
- The research aligns with ongoing efforts to refine statistical methods in machine learning, particularly in addressing challenges related to data dependence and robustness, as seen in various approaches to Wasserstein metrics and statistical estimation frameworks.
— via World Pulse Now AI Editorial System
