تقرير
Optimal estimation of Gaussian (poly)trees
| العنوان: | Optimal estimation of Gaussian (poly)trees |
|---|---|
| المؤلفون: | Wang, Yuhao, Gao, Ming, Tai, Wai Ming, Aragam, Bryon, Bhattacharyya, Arnab |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Statistics - Machine Learning |
| الوصف: | We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first approach is based on the Chow-Liu algorithm, and learns an optimal tree-structured distribution efficiently. The second approach is a modification of the PC algorithm for polytrees that uses partial correlation as a conditional independence tester for constraint-based structure learning. We derive explicit finite-sample guarantees for both approaches, and show that both approaches are optimal by deriving matching lower bounds. Additionally, we conduct numerical experiments to compare the performance of various algorithms, providing further insights and empirical evidence. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.06380 |
| رقم الأكسشن: | edsarx.2402.06380 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |