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This document is additional material to our previous study comparing several strategies for variable subset selection. Our recommended approach was to fit the full model with all the candidate variables and best possible prior information,…

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 and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…

Multi-vector dense retrieval methods like ColBERT systematically use a single-layer linear projection to reduce the dimensionality of individual vectors. In this study, we explore the implications of the MaxSim operator on the gradient…

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…

Continuous prompt search offers a computationally efficient alternative to conventional parameter tuning in natural language processing tasks. Nevertheless, its practical effectiveness can be significantly hindered by the black-box nature…

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

In the Naive Bayes classification model the class conditional densities are estimated as the products of their marginal densities along the cardinal basis directions. We study the problem of obtaining an alternative basis for this…

We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

Predicting future frames for a video sequence is a challenging generative modeling task. Promising approaches include probabilistic latent variable models such as the Variational Auto-Encoder. While VAEs can handle uncertainty and model…

Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…

Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we…

The concepts of Bayesian prediction, model comparison, and model selection have developed significantly over the last decade. As a result, the Bayesian community has witnessed a rapid growth in theoretical and applied contributions to…

We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…