Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions
Shuo-Chieh Huang, Chien-Ming Chi, Jau-er Chen
stat.ML, cs.LG, stat.ME
Submitted: 2026-07-29
Comments: 24 pages, 2 figures, 5 tables
Code: https://github.com/no-name213/band
License: http://creativecommons.org/licenses/by/4.0/
The gist: Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality.
Terminology
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 sparsity-aware conditional mean methods. The resulting estimator, 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.
Sources
- Generating Long Sequences with Sparse Transformers
- Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization
- Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity
- Kernel Density Estimators in Large Dimensions
- Temporal Wasserstein Imputation: A Versatile Method for Time Series Imputation
- Score-Based Generative Modeling through Stochastic Differential Equations
- Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions
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