Related papers: Bayesian Variable Selection for Linear Regression …

In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…

We propose a new approach to safe variable preselection in high-dimensional penalized regression, such as the lasso. Preselection - to start with a manageable set of covariates - has often been implemented without clear appreciation of its…

Expected-posterior priors (EPP) have been proved to be extremely useful for testing hypothesis on the regression coefficients of normal linear models. One of the advantages of using EPPs is that impropriety of baseline priors causes no…

The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…

A standard tool for model selection in a Bayesian framework is the Bayes factor which compares the marginal likelihood of the data under two given different models. In this paper, we consider the class of hierarchical loglinear models for…

Varying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it…

In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…

Gene-environment (G$\times$E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G$\times$E…

This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is…

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…

We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…

The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables…

In recent years, Ising prior with the network information for the "in" or "out" binary random variable in Bayesian variable selections has received more and more attentions. In this paper, we discover that even without the informative prior…

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Spatially dependent data arises in many applications, and Gaussian processes are a popular modelling choice for these scenarios. While Bayesian analyses of these problems have proven to be successful, selecting prior distributions for these…