论文标题
精确学习树结构图形模型的精确渐近学，带有附带信息：嘈杂和嘈杂的样本
Exact Asymptotics for Learning Tree-Structured Graphical Models with Side Information: Noiseless and Noisy Samples
论文作者
论文摘要
给定的侧面信息表明，伊斯丁树结构的图形模型是同质的，没有外部场，我们从独立绘制的样本中得出了学习其结构的确切渐近学。我们的结果利用了从强大的大偏差理论中利用概率工具的使用，可以完善棕褐色，Anandkumar，Tong和Willsky [IEEE Trans的大偏差（错误指数）结果。通知。 Th。，57（3）：1714--1735，2011]，严格改善了Bresler和Karzand [Ann。统计学家，2020年]。此外，我们将结果扩展到在随机噪声中观察到样品的情况。在这种情况下，我们表明它们严格改善了Nikolakakis，Kalogerias和Sarwate的最新结果[Proc。 Aistats，1771--1782，2019]。我们的理论结果表明，与数百个样本量相当小的样本量的实验结果敏锐的一致性。
Given side information that an Ising tree-structured graphical model is homogeneous and has no external field, we derive the exact asymptotics of learning its structure from independently drawn samples. Our results, which leverage the use of probabilistic tools from the theory of strong large deviations, refine the large deviation (error exponents) results of Tan, Anandkumar, Tong, and Willsky [IEEE Trans. on Inform. Th., 57(3):1714--1735, 2011] and strictly improve those of Bresler and Karzand [Ann. Statist., 2020]. In addition, we extend our results to the scenario in which the samples are observed in random noise. In this case, we show that they strictly improve on the recent results of Nikolakakis, Kalogerias, and Sarwate [Proc. AISTATS, 1771--1782, 2019]. Our theoretical results demonstrate keen agreement with experimental results for sample sizes as small as that in the hundreds.
