Related papers: Bayesian $l_0$-regularized Least Squares

High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare…

We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…

Bayesian synthetic likelihood (BSL) is now a well established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable…

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

Biclustering is a powerful unsupervised learning technique for simultaneously identifying coherent subsets of rows and columns in a data matrix, thus revealing local patterns that may not be apparent in global analyses. However, most…

This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem, i.e., $\mathbf{x}^\star=\arg\min_\mathbf{x} \lbrace \|…

Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a…

Bayesian deep learning (BDL) has emerged as a principled approach to produce reliable uncertainty estimates by integrating deep neural networks with Bayesian inference, and the selection of informative prior distributions remains a…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

In this manuscript, a new high-dimensional approach for simultaneous variable and group selection is proposed, called sparse-group SLOPE (SGS). SGS achieves false discovery rate control at both variable and group levels by incorporating the…

In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…

Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations…

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…

In this work, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our method uses a hierarchical Bayesian structure and latent variables to enable an adaptive covariate selection process for…