Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions
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 ...
| Authors | Shuo-Chieh Huang, Chien-Ming Chi, Jau-er Chen |
|---|---|
| Primary category | stat.ML |
| Published | 29 July 2026 |
| Last updated at source | 29 July 2026 |
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