Multivariate Varying-Coefficient BART with Graphical Horseshoe Priors

• URL: http://arxiv.org/abs/2606.29114v1
• Date: Sat, 27 Jun 2026 23:42:08 GMT
• Title: Multivariate Varying-Coefficient BART with Graphical Horseshoe Priors
• Abstract summary: MultiVCBART is a varying-coefficient Bayesian additive regression tree framework.<n>It jointly models outcome-specific coefficient surfaces and a sparse residual precision matrix.<n>In a re-analysis of the Genomics of Drug Sensitivity in Cancer dataset, our method identifies distinct biomarker signals and recovers a coherent residual pharmacologic network.
• Score: 1.9571018958232795
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Modern multivariate regression problems involve several related outcomes whose regression effects are not only nonlinear, heterogeneous, and outcome-specific, but also where the residual dependence among outcomes is scientifically meaningful. Existing multivariate Bayesian tree-based methods typically address only part of this problem: some impose substantial sharing of tree architecture across outcomes, which is overly restrictive when responses depend on distinct predictors or effect modifiers, while others accommodate residual dependence but retain simpler mean structures. This paper develops multiVCBART, a multivariate varying-coefficient Bayesian additive regression tree framework that jointly models flexible outcome-specific coefficient surfaces and a sparse residual precision matrix. Each entry of the coefficient matrix $B(x)$ is represented by an independent BART ensemble, allowing predictor effects to vary nonlinearly with modifiers $x$ across outcomes, while a Graphical Horseshoe prior on the precision matrix $Ω$ captures parsimonious residual conditional dependence. To permit efficient computation, we introduce a sampler that reduces the multivariate Gaussian likelihood to a sequence of scalar pseudo-response updates, decoupling the tree backfitting from the Graphical Horseshoe step. Theoretically, we establish the first posterior contraction rates for a multivariate BART model with jointly estimated residual dependence, proving near-minimax adaptation to underlying smoothness and structural sparsity. Empirically, multiVCBART outperforms existing multivariate tree models and Bayesian SUR competitors on sparse, high-dimensional datasets. Finally, in a re-analysis of the Genomics of Drug Sensitivity in Cancer dataset, our method identifies distinct biomarker signals and recovers a coherent residual pharmacologic network.

Related papers

• Denoised Variance-Based Pruning with Optimal Brain Bias Compensation [45.88028371034407]
  Variance-Based Pruning (VBP) introduced a promising paradigm by selecting neurons based on activation variance.<n>We introduce Denoised Variance-Based Pruning with Optimal Brain Bias Compensation (DVBP + OB$2$C)<n>It achieves state-of-the-art training-free performance; at 50% pruning, it retains over 90% of the original Top-1 accuracy.
  arXiv  Detail & Related papers  (2026-08-18T11:23:49Z)
• Semi-Parametric Bayesian Additive Regression Trees for Risk Prediction with High-Dimensional Epigenetic Signatures and Low-Dimensional Covariates [3.3590614024901195]
  Genome-wide epigenetic modifications offer rich data that could inform risk prediction.<n>These data are high-dimensional and exhibit complex dependence structures.<n>We propose a semi-parametric BART model (spBART) that addresses this limitation.
  arXiv  Detail & Related papers  (2026-05-19T17:31:20Z)
• Bayesian Additive Distribution Regression [0.0]
  We introduce DistBART, a nonparametric approach to distribution regression that models the regression function as a linear functional.<n>We show this empirically on synthetic and real data and theoretically through an adaptive posterior concentration result.<n>We also establish connections to kernel methods, and use this connection to motivate variants of DistBART that can learn nonlinear functionals.
  arXiv  Detail & Related papers  (2026-03-06T16:49:38Z)
• DOGMA: Weaving Structural Information into Data-centric Single-cell Transcriptomics Analysis [43.565183518761984]
  We propose DOGMA, a data-centric framework designed for the structural reshaping and semantic enhancement of raw data.<n>In complex multi-species and multi-organ benchmarks, DOGMA SOTA performance, exhibiting superior zero-shot robustness and sample efficiency.
  arXiv  Detail & Related papers  (2026-02-02T09:10:09Z)
• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Back to Square Roots: An Optimal Bound on the Matrix Factorization Error for Multi-Epoch Differentially Private SGD [28.66960497912785]
  We introduce a new explicit factorization method, Banded Inverse Square Root (BISR), which imposes a banded structure on the inverse correlation matrix.<n>BISR achieves anally optimal error by matching the upper and lower bounds.
  arXiv  Detail & Related papers  (2025-05-17T19:41:44Z)
• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression [47.1405366895538]
  Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization algorithm.
  arXiv  Detail & Related papers  (2023-09-15T22:06:29Z)
• Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction [51.82628081279621]
  Multi-modal regression is important in forecasting nonstationary processes or with a complex mixture of distributions. A Structured Radial Basis Function Network is presented as an ensemble of multiple hypotheses predictors for regression problems. It is proved that this structured model can efficiently interpolate this tessellation and approximate the multiple hypotheses target distribution.
  arXiv  Detail & Related papers  (2023-09-02T01:27:53Z)
• Multiple Augmented Reduced Rank Regression for Pan-Cancer Analysis [0.0]
  We propose multiple augmented reduced rank regression (maRRR), a flexible matrix regression and factorization method. We consider a structured nuclear norm objective that is motivated by random matrix theory. We apply maRRR to gene expression data from multiple cancer types (i.e., pan-cancer) from TCGA.
  arXiv  Detail & Related papers  (2023-08-30T21:40:58Z)
• Bayesian predictive modeling of multi-source multi-way data [0.0]
  We consider molecular data from multiple 'omics sources as predictors of early-life iron deficiency (ID) in a rhesus monkey model. We use a linear model with a low-rank structure on the coefficients to capture multi-way dependence. We show that our model performs as expected in terms of misclassification rates and correlation of estimated coefficients with true coefficients.
  arXiv  Detail & Related papers  (2022-08-05T21:58:23Z)
• Machine Learning for Multi-Output Regression: When should a holistic multivariate approach be preferred over separate univariate ones? [62.997667081978825]
  Tree-based ensembles such as the Random Forest are modern classics among statistical learning methods. We compare these methods in extensive simulations to help in answering the primary question when to use multivariate ensemble techniques.
  arXiv  Detail & Related papers  (2022-01-14T08:44:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.