Inference on covariance structure in high-dimensional multi-view data

• URL: http://arxiv.org/abs/2509.02772v1
• Date: Tue, 02 Sep 2025 19:20:42 GMT
• Title: Inference on covariance structure in high-dimensional multi-view data
• Authors: Lorenzo Mauri, David B. Dunson,
• Abstract summary: Posterior computation is conducted via expensive and brittle Markov chain Monte Carlo sampling or variational approximations.<n>Our proposed methodology employs spectral decompositions to estimate and align latent factors that are active in at least one view.<n>We show excellent performance in simulations, including accurate uncertainty, and apply the methodology to integrate four high-dimensional views from a multi-omics dataset of cancer cell samples.
• Score: 8.549941732144035
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle Markov chain Monte Carlo (MCMC) sampling or variational approximations that underestimate uncertainty and lack theoretical guarantees. Our proposed methodology employs spectral decompositions to estimate and align latent factors that are active in at least one view. Conditionally on these factors, we choose jointly conjugate prior distributions for factor loadings and residual variances. The resulting posterior is a simple product of normal-inverse gamma distributions for each variable, bypassing MCMC and facilitating posterior computation. We prove favorable increasing-dimension asymptotic properties, including posterior contraction and central limit theorems for point estimators. We show excellent performance in simulations, including accurate uncertainty quantification, and apply the methodology to integrate four high-dimensional views from a multi-omics dataset of cancer cell samples.

Related papers

• Bias-Reduced Estimation of Finite Mixtures: An Application to Latent Group Structures in Panel Data [0.0]
  This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias.<n>The bias arises from the influence of outliers in component densities with unbounded or large support.<n>I show that maximizing the classification-mixture likelihood function yields parameter estimates that are less biased than those obtained by standard maximum likelihood estimation.
  arXiv  Detail & Related papers  (2026-01-28T02:48:28Z)
• An Elementary Approach to Scheduling in Generative Diffusion Models [55.171367482496755]
  An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed.<n> Experiments across different datasets and pretrained models demonstrate that the time discretization strategy selected by our approach consistently outperforms baseline and search-based strategies.
  arXiv  Detail & Related papers  (2026-01-20T05:06:26Z)
• Efficient Covariance Estimation for Sparsified Functional Data [51.69796254617083]
  proposed Random-knots (Random-knots-Spatial) and B-spline (Bspline-Spatial) estimators of the covariance function are computationally efficient.<n>Asymptotic pointwise of the covariance are obtained for sparsified individual trajectories under some regularity conditions.
  arXiv  Detail & Related papers  (2025-11-23T00:50:33Z)
• Spectral decomposition-assisted multi-study factor analysis [7.925272817108244]
  Methods are applied to integrate three studies on gene associations among immune cells.<n> Conditional distribution of factor loadings has a simple product form across outcomes.
  arXiv  Detail & Related papers  (2025-02-20T14:33:40Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• Variance-Reducing Couplings for Random Features [57.73648780299374]
  Random features (RFs) are a popular technique to scale up kernel methods in machine learning. We find couplings to improve RFs defined on both Euclidean and discrete input spaces. We reach surprising conclusions about the benefits and limitations of variance reduction as a paradigm.
  arXiv  Detail & Related papers  (2024-05-26T12:25:09Z)
• Reverse Diffusion Monte Carlo [19.35592726471155]
  We propose a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC) rdMC is distinct from the Markov chain Monte Carlo (MCMC) methods.
  arXiv  Detail & Related papers  (2023-07-05T05:42:03Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Optimal regularizations for data generation with probabilistic graphical models [0.0]
  Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models. We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
  arXiv  Detail & Related papers  (2021-12-02T14:45:16Z)
• Trustworthy Multimodal Regression with Mixture of Normal-inverse Gamma Distributions [91.63716984911278]
  We introduce a novel Mixture of Normal-Inverse Gamma distributions (MoNIG) algorithm, which efficiently estimates uncertainty in principle for adaptive integration of different modalities and produces a trustworthy regression result. Experimental results on both synthetic and different real-world data demonstrate the effectiveness and trustworthiness of our method on various multimodal regression tasks.
  arXiv  Detail & Related papers  (2021-11-11T14:28:12Z)
• Entropy Minimizing Matrix Factorization [102.26446204624885]
  Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem. Considering that the outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization.
  arXiv  Detail & Related papers  (2021-03-24T21:08:43Z)
• Recovery of Joint Probability Distribution from one-way marginals: Low rank Tensors and Random Projections [2.9929093132587763]
  Joint probability mass function (PMF) estimation is a fundamental machine learning problem. In this work, we link random projections of data to the problem of PMF estimation using ideas from tomography. We provide a novel algorithm for recovering factors of the tensor from one-way marginals, test it across a variety of synthetic and real-world datasets, and also perform MAP inference on the estimated model for classification.
  arXiv  Detail & Related papers  (2021-03-22T14:00:57Z)
• A Class of Conjugate Priors for Multinomial Probit Models which Includes the Multivariate Normal One [0.3553493344868413]
  We show that the entire class of unified skew-normal (SUN) distributions is conjugate to several multinomial probit models. We improve upon state-of-the-art solutions for posterior inference and classification.
  arXiv  Detail & Related papers  (2020-07-14T10:08:23Z)
• Batch Stationary Distribution Estimation [98.18201132095066]
  We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. We propose a consistent estimator that is based on recovering a correction ratio function over the given data.
  arXiv  Detail & Related papers  (2020-03-02T09:10:01Z)

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.