Bayesian Multiple Multivariate Density-Density Regression

• URL: http://arxiv.org/abs/2601.02640v1
• Date: Tue, 06 Jan 2026 01:21:20 GMT
• Title: Bayesian Multiple Multivariate Density-Density Regression
• Authors: Khai Nguyen, Yang Ni, Peter Mueller,
• Abstract summary: We propose the first approach for multiple multivariate density-density regression (MDDR)<n>We define a fitted distribution using a sliced Wasserstein barycenter (SWB) of push-forwards of the predictors.<n> Regression functions, which map predictors' supports to the response support, and barycenter weights are inferred within a generalized Bayes framework.<n>We demonstrate MDDR in an application to inference for population-scale single-cell data.
• Score: 25.35298354797079
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose the first approach for multiple multivariate density-density regression (MDDR), making it possible to consider the regression of a multivariate density-valued response on multiple multivariate density-valued predictors. The core idea is to define a fitted distribution using a sliced Wasserstein barycenter (SWB) of push-forwards of the predictors and to quantify deviations from the observed response using the sliced Wasserstein (SW) distance. Regression functions, which map predictors' supports to the response support, and barycenter weights are inferred within a generalized Bayes framework, enabling principled uncertainty quantification without requiring a fully specified likelihood. The inference process can be seen as an instance of an inverse SWB problem. We establish theoretical guarantees, including the stability of the SWB under perturbations of marginals and barycenter weights, sample complexity of the generalized likelihood, and posterior consistency. For practical inference, we introduce a differentiable approximation of the SWB and a smooth reparameterization to handle the simplex constraint on barycenter weights, allowing efficient gradient-based MCMC sampling. We demonstrate MDDR in an application to inference for population-scale single-cell data. Posterior analysis under the MDDR model in this example includes inference on communication between multiple source/sender cell types and a target/receiver cell type. The proposed approach provides accurate fits, reliable predictions, and interpretable posterior estimates of barycenter weights, which can be used to construct sparse cell-cell communication networks.

Related papers

• Mean-field Variational Bayes for Sparse Probit Regression [0.9023847175654603]
  We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior to the regression coefficients.<n>Motivated by the computational challenges encountered by Markov chain Monte Carlo samplers in high-dimensional regimes, we develop a mean-field variational Bayes approximation.
  arXiv  Detail & Related papers  (2026-01-29T14:16:31Z)
• Robust Variational Bayes by Min-Max Median Aggregation [13.102667562202386]
  We propose a robust variational Bayes framework to handle contamination and outliers in dataset.<n>Our approach partitions the data into $m$ disjoint subsets and formulates a joint optimization problem based on robust aggregation principles.<n>Our findings indicate that the two-stage approach yields a smaller approximation error compared to directly aggregating the $m$-powered local posteriors.
  arXiv  Detail & Related papers  (2025-12-14T13:02:00Z)
• Likelihood-Free Adaptive Bayesian Inference via Nonparametric Distribution Matching [2.0319002824093015]
  We propose Adaptive Bayesian Inference (ABI), a framework that bypasses traditional data-space discrepancies.<n>ABI transforms the problem of measuring divergence between posterior distributions into a tractable sequence of conditional quantile regression tasks.<n>We demonstrate that ABI significantly outperforms data-based Wasserstein, summary-based ABC, and state-of-the-art likelihood-free simulators.
  arXiv  Detail & Related papers  (2025-05-07T17:50:14Z)
• Bayesian Multivariate Density-Density Regression [25.35298354797079]
  We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR)<n>Our approach addresses the critical issue of distributions residing in spaces of differing dimensions.<n>We show that Bayesian DDR provides robust fits, superior predictive performance compared to traditional methods, and valuable insights into complex biological interactions.
  arXiv  Detail & Related papers  (2025-04-17T03:46:03Z)
• Robust and Scalable Variational Bayes [2.014089835498735]
  We propose a robust framework for variational Bayes (VB) that effectively handles outliers and contamination of arbitrary nature in large datasets.<n>Our approach divides the dataset into disjoint subsets, computes the posterior for each subset, and applies VB approximation independently to these posteriors.<n>This novel aggregation method yields the Variational Median Posterior (VM-Posterior) distribution.
  arXiv  Detail & Related papers  (2025-04-16T23:20:43Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate.<n>We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• An Optimal Transport Approach for Network Regression [0.6238182916866519]
  We build upon recent developments in generalized regression models on metric spaces based on Fr'echet means. We propose a network regression method using the Wasserstein metric.
  arXiv  Detail & Related papers  (2024-06-18T02:03:07Z)
• Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise [51.87307904567702]
  Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the distribution of outputs.<n>We propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint.<n>We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities.
  arXiv  Detail & Related papers  (2024-06-05T13:36:38Z)
• Mutual Wasserstein Discrepancy Minimization for Sequential Recommendation [82.0801585843835]
  We propose a novel self-supervised learning framework based on Mutual WasserStein discrepancy minimization MStein for the sequential recommendation. We also propose a novel contrastive learning loss based on Wasserstein Discrepancy Measurement.
  arXiv  Detail & Related papers  (2023-01-28T13:38:48Z)
• Random Forest Weighted Local Fréchet Regression with Random Objects [18.128663071848923]
  We propose a novel random forest weighted local Fr'echet regression paradigm.<n>Our first method uses these weights as the local average to solve the conditional Fr'echet mean.<n>Second method performs local linear Fr'echet regression, both significantly improving existing Fr'echet regression methods.
  arXiv  Detail & Related papers  (2022-02-10T09:10:59Z)
• Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence [77.06203118175335]
  Variational Inference (VI) is a popular alternative to exact sampling in Bayesian inference. Importance sampling (IS) is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. We propose a novel combination of optimization and sampling techniques for approximate Bayesian inference.
  arXiv  Detail & Related papers  (2021-06-30T11:00:24Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Sampling-free Variational Inference for Neural Networks with Multiplicative Activation Noise [51.080620762639434]
  We propose a more efficient parameterization of the posterior approximation for sampling-free variational inference. Our approach yields competitive results for standard regression problems and scales well to large-scale image classification tasks.
  arXiv  Detail & Related papers  (2021-03-15T16:16:18Z)

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.