Related papers: B-CONCORD -- A scalable Bayesian high-dimensional …

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

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…

In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…

Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture epistemic uncertainty, which can lead to overconfident predictions in data-sparse regions. Although recent conformal scores…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge,…

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…