Related papers: Bayesian Estimation Approach for Linear Regression…

ReRecent studies in machine learning are based on models in which parameters or state variables are bounded restricted. These restrictions are from prior information to ensure the validity of scientific theories or structural consistency…

In this paper, we consider the multicollinearity problem in the gamma regression model when model parameters are linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories…

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…

Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…

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…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

The problem of estimating censored linear regression models with autocorrelated errors arises in many environmental and social studies. The present work proposes a Bayesian approach to estimate censored regression models with AR(p) errors.…

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and…

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…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…

Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing…

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability --…

This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…