提出BAND方法，用稀疏贝叶斯网络提升高维混合数据分布估计效率。
Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions
- 基于稀疏贝叶斯网络，结合条件均值的稀疏感知估计
- 高维时间序列下实现多项式总变差收敛率，维度可随样本量多项式增长
- 相比传统直方图密度估计，收敛速度显著更快，适合高维数据建模
高维多变量分布估计的极小极大最优率受维数诅咒影响。本文提出一种稀疏贝叶斯网络方法，其中每个条件概率通过稀疏感知的条件均值法估计。所得估计器——贝叶斯网络分布回归（BAND）——能处理高维时间序列中的混合数据类型，实现多项式总变差收敛率，且特征维度可随样本量多项式增长。该速率远快于缺乏稀疏性的经典多变量直方图密度估计器的最优率。实证评估显示，BAND在数据采样和置信区域预测方面表现优于多种前沿基准。
原文摘要 · Abstract (English)
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.
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