发表机构
Rutgers University; Academia Sinica; National Taiwan University（罗格斯大学; 中央研究院; 台湾大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对多元分布估计的维数诅咒问题，提出稀疏贝叶斯网络方法BAND，可处理高维混合数据，达到多项式级收敛率，在数据采样和置信区域预测任务中表现优于经典方法，与现有基准相当。
AI 中文摘要
已知多元分布估计的极小极大最优率会受维数诅咒影响。我们提出一种稀疏贝叶斯网络方法，其中每个条件概率采用感知稀疏的条件均值方法估计。所得估计器BAND（贝叶斯网络分布回归）可处理高维时间序列中的混合数据类型，在特征维度随样本量多项式增长时，能达到多项式级总变差收敛率，该速率远快于缺乏稀疏性的多元直方图密度估计器的经典最优率。实证评估显示，在数据采样和置信区域预测任务中，BAND与一系列最先进基准的表现相当。
英文摘要
Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality. We propose a sparse Bayesian network approach in which each conditional probability is estimated using sparsity-aware conditional mean methods. The resulting estimator, \textit{BAyesian Network Distribution regression} (BAND), handles mixed data types in high-dimensional time series and achieves polynomial total variation convergence rates while allowing the feature dimension to grow polynomially with the sample size. These rates are substantially faster than the classical optimal rates for multivariate histogram density estimators that lack sparsity. Empirical evaluations show that BAND performs competitively for data sampling and confidence region forecasting against a range of state-of-the-art benchmarks.
Comments24 pages, 2 figures, 5 tables
