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Paper · 2607.26955 · 2026

Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions

Shuo-Chieh Huang, Chien-Ming Chi, Jau-Er Chen, Chien- Ming Chi

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 3 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
no-name213/band canonical 3 of 3
FunctionStatusWhere it lives
cramer_wold_distance Ran no-name213/band/simulation_experiments/nflow.py
pointer only (licence: NONE) · get_code("e85c84f432a6dd36")
ecdf_grid Ran no-name213/band/simulation_experiments/nflow.py
pointer only (licence: NONE) · get_code("a161848bfa015c0a")
evaluate_nll Ran no-name213/band/simulation_experiments/nflow.py
pointer only (licence: NONE) · get_code("2706a69a8a4623d7")

Repositories linked to this paper

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Abstract

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 sparsityaware conditional mean methods. The resulting estimator, BAyesian Network Distribution regression (BAND), handles mixed data types in highdimensional 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-theart benchmarks.

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