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This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense image prediction tasks. This is achieved through a convolutional neural…

Computer Vision and Pattern Recognition · Computer Science 2022-03-30 Ivor J. A. Simpson , Sara Vicente , Neill D. F. Campbell

Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse Cholesky factor of the precision matrix. We propose a…

Computation · Statistics 2021-09-27 Marcin Jurek , Matthias Katzfuss

In this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression,…

Numerical Analysis · Mathematics 2021-11-17 Helmut Harbrecht , Michael Multerer

We construct a new distribution for the simplex using the Kumaraswamy distribution and an ordered stick-breaking process. We explore and develop the theoretical properties of this new distribution and prove that it exhibits symmetry under…

Machine Learning · Computer Science 2019-12-17 Andrew Stirn , Tony Jebara , David A Knowles

The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…

Methodology · Statistics 2025-01-10 Vahe Avagyan

Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…

Computation · Statistics 2023-04-05 Willem van den Boom , Alexandros Beskos , Maria De Iorio

A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…

Machine Learning · Statistics 2017-12-07 Victor Veitch , Ekansh Sharma , Zacharie Naulet , Daniel M. Roy

Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over…

Machine Learning · Statistics 2023-05-25 Sebastian Ober , Ben Anson , Edward Milsom , Laurence Aitchison

We consider the problem of estimating a time-varying sparse precision matrix, which is assumed to evolve in a piece-wise constant manner. Building upon the Group Fused LASSO and LASSO penalty functions, we estimate both the network…

Statistics Theory · Mathematics 2024-10-08 Ying Lin , Benjamin Poignard , Ting Kei Pong , Akiko Takeda

Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient…

Numerical Analysis · Computer Science 2015-07-21 Jeffrey N. Chadwick , David S. Bindel

In this paper, we study weakly-supervised laparoscopic image segmentation with sparse annotations. We introduce a novel Bayesian deep learning approach designed to enhance both the accuracy and interpretability of the model's segmentation,…

Computer Vision and Pattern Recognition · Computer Science 2024-10-14 Zhou Zheng , Yuichiro Hayashi , Masahiro Oda , Takayuki Kitasaka , Kensaku Mori

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

Machine Learning · Statistics 2017-11-15 Arthur Mensch , Julien Mairal , Bertrand Thirion , Gaël Varoquaux

We show variants of spectral sparsification routines can preserve the total spanning tree counts of graphs, which by Kirchhoff's matrix-tree theorem, is equivalent to determinant of a graph Laplacian minor, or equivalently, of any SDDM…

Data Structures and Algorithms · Computer Science 2017-05-03 David Durfee , John Peebles , Richard Peng , Anup B. Rao

We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…

Disordered Systems and Neural Networks · Physics 2009-11-13 Reimer Kuehn

This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…

Methodology · Statistics 2008-05-27 Clifford Lam

Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…

Methodology · Statistics 2019-02-20 Mitchell Krock , William Kleiber , Stephen Becker

Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on the autoregressive coefficients. Introducing shrinkage on the error covariance matrix is sometimes done but, in the vast majority of cases, without considering the…

Econometrics · Economics 2024-07-24 Florian Huber , Gary Koop , Massimiliano Marcellino , Tobias Scheckel

Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…

Numerical Analysis · Mathematics 2023-03-31 Daniela Calvetti , Erkki Somersalo

We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…

Methodology · Statistics 2020-06-19 Youngseok Kim , Chao Gao

Natural gradients can improve convergence in stochastic variational inference significantly but inverting the Fisher information matrix is daunting in high dimensions. Moreover, in Gaussian variational approximation, natural gradient…

Computation · Statistics 2025-02-05 Linda S. L. Tan