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We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

Numerical Analysis · Mathematics 2013-08-07 Tan Bui-Thanh , Omar Ghattas , James Martin , Georg Stadler

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…

Methodology · Statistics 2025-03-04 Lorenzo Cappello , Oscar Hernan Madrid Padilla

In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a…

Methodology · Statistics 2024-04-22 Bohao Tang , Sandipan Pramanik , Yi Zhao , Brian Caffo , Abhirup Datta

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

Computation · Statistics 2019-11-26 Linda S. L. Tan , Nial Friel

In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph $G$. Working with the $W_{P_G}$ family defined by Letac and Massam [Ann. Statist. 35…

Statistics Theory · Mathematics 2009-01-22 Bala Rajaratnam , Hélène Massam , Carlos M. Carvalho

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Machine Learning · Statistics 2025-02-06 Yazid Janati , Badr Moufad , Mehdi Abou El Qassime , Alain Durmus , Eric Moulines , Jimmy Olsson

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…

Computation · Statistics 2016-07-25 Isabell M. Franck , P. S. Koutsourelakis

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

Statistics Theory · Mathematics 2014-04-08 Sayantan Banerjee , Subhashis Ghosal

We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…

Statistics Theory · Mathematics 2023-12-27 Alen Alexanderian

Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…

Machine Learning · Statistics 2013-06-06 Mohammad Emtiyaz Khan , Aleksandr Y. Aravkin , Michael P. Friedlander , Matthias Seeger

We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…

Numerical Analysis · Mathematics 2026-05-19 Hojjat Kaveh , Ricardo Baptista , Andrew M. Stuart

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

Machine Learning · Statistics 2020-04-22 Tianxi Li , Cheng Qian , Elizaveta Levina , Ji Zhu

Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even…

Computation · Statistics 2014-05-15 Onkar Dalal , Bala Rajaratnam

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Numerical Analysis · Mathematics 2023-01-18 Mengwu Guo , Shane A. McQuarrie , Karen E. Willcox

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

In this paper, we aim to design robust estimation techniques based on the compound-Gaussian (CG) process and adapted for calibration of radio interferometers. The motivation beyond this is due to the presence of outliers leading to an…

Applications · Statistics 2018-07-31 Virginie Ollier , Mohammed Nabil El Korso , André Ferrari , Rémy Boyer , Pascal Larzabal

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…

Computer Vision and Pattern Recognition · Computer Science 2024-06-04 Xinyu Peng , Ziyang Zheng , Wenrui Dai , Nuoqian Xiao , Chenglin Li , Junni Zou , Hongkai Xiong

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

Statistics Theory · Mathematics 2018-10-31 Shota Gugushvili , Aad van der Vaart , Dong Yan

In this paper we present Poisson mixture approaches for origin-destination (OD) modeling in transportation analysis. We introduce covariate-based models which incorporate different transport modeling phases and also allow for direct…

Methodology · Statistics 2020-11-13 Konstantinos Perrakis , Dimitris Karlis , Mario Cools , Davy Janssens

We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian…

Methodology · Statistics 2010-01-18 Philipp Rütimann , Peter Bühlmann