Related papers: Testing-driven Variable Selection in Bayesian Moda…
Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during…
In computational biology, gene expression datasets are characterized by very few individual samples compared to a large number of measurements per sample. Thus, it is appealing to merge these datasets in order to increase the number of…
We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…
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…
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…
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
Many papers on high-dimensional statistics have proposed methods for variable selection and inference in linear regression models by relying explicitly or implicitly on the assumption that all regressors are exogenous. However, applications…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
The selection of essential variables in logistic regression is vital because of its extensive use in medical studies, finance, economics and related fields. In this paper, we explore four main typologies (test-based, penalty-based,…
We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the…
We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…
Given the cost and duration of phase III and phase IV clinical trials, the development of statistical methods for go/no-go decisions is vital. In this paper, we introduce a Bayesian methodology to compute the probability of success based on…