Related papers: Bayesian Multivariate Density-Density Regression
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
We propose a Bayesian distributionally robust variational inequality (DRVI) framework that models the data-generating distribution through a finite mixture family, which allows us to study the DRVI on a tractable finite-dimensional…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a…
We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities, e.g., for applications…
We propose a robust and scalable framework for variational Bayes (VB) that effectively handles outliers and contamination of arbitrary nature in large datasets. Our approach divides the dataset into disjoint subsets, computes the posterior…
Background: Mendelian randomization (MR) is a useful approach to causal inference from observational studies when randomised controlled trials are not feasible. However, study heterogeneity of two association studies required in MR is often…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…
This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…
In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…
Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…
Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction tool that allows one to model and visualize data consisting of dissimilarities between pairs of objects. Although BMDS has proven useful within, e.g., Bayesian…
In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…
In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…
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…