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BSTabDiff addresses the ill-conditioned density learning problem in High-Dimensional Low-Sample Size (HDLSS) domains by partitioning features into latent blocks to concentrate global dependence learning. This approach enables stable synthesis of realistic synthetic data for complex tabular structures like omics datasets, outperforming unstructured generators in the $n \ll m$ regime. The method's integration of diffusion priors with explicit missingness mechanisms offers a robust framework for generating controllable benchmarks in high-dimensional feature spaces.
BSTabDiff: Block-Subunit Diffusion Priors for High-Dimensional Tabular Data Generation
arXiv:2606.09257v1 Announce Type: new Abstract: High-Dimensional Low-Sample Size (HDLSS) tabular domains (e.g., omics) are characterized by $n \ll m$, where $n$ = number of samples, and $m$ = number of features. Such domains often exhibit strong local correlation groups, sparse cross-group dependencies, heavy-tailed non-Gaussian marginals, heteroscedastic noise, and structured missingness, making direct density learning in $\mathbb{R}^m$ ill-conditioned since $n \ll m$. We propose BSTabDiff, a block-subunit generative framework that partitions the $m$ observed features into $M$ latent blocks ($M \ll m$) and generates each block via a shared low-dimensional subunit variable, concentrating global dependence learning in the compact block-latent space $\mathbb{R}^M$ while decoding to the full feature space with copula-driven dependence, flexible per-feature marginals, and explicit missingness mechanisms. BSTabDiff supports modern deep priors on block latents, including diffusion and normalizing flows, enabling stable synthesis and controllable benchmark generation in the HDLSS regime. Empirically, BSTabDiff produces more realistic and stable high-dimensional synthetic data when compared with unstructured tabular generators on HDLSS data.
Abstract:High-Dimensional Low-Sample Size (HDLSS) tabular domains (e.g., omics) are characterized by $n \ll m$, where $n$ = number of samples, and $m$ = number of features. Such domains often exhibit strong local correlation groups, sparse cross-group dependencies, heavy-tailed non-Gaussian marginals, heteroscedastic noise, and structured missingness, making direct density learning in $\mathbb{R}^m$ ill-conditioned since $n \ll m$. We propose BSTabDiff, a block-subunit generative framework that partitions the $m$ observed features into $M$ latent blocks ($M \ll m$) and generates each block via a shared low-dimensional subunit variable, concentrating global dependence learning in the compact block-latent space $\mathbb{R}^M$ while decoding to the full feature space with copula-driven dependence, flexible per-feature marginals, and explicit missingness mechanisms. BSTabDiff supports modern deep priors on block latents, including diffusion and normalizing flows, enabling stable synthesis and controllable benchmark generation in the HDLSS regime. Empirically, BSTabDiff produces more realistic and stable high-dimensional synthetic data when compared with unstructured tabular generators on HDLSS data.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
arXiv:2606.09257 [cs.LG]
(or arXiv:2606.09257v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.09257 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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