Related papers: Posterior contraction in group sparse logit models…
We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…
We develop a framework to study posterior contraction rates in sparse high dimensional generalized linear models (GLM). We introduce a new family of GLMs, denoted by clipped GLM, which subsumes many standard GLMs and makes minor…
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…
Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
We propose a unified framework for studying both latent and stochastic block models, which are used to cluster simultaneously rows and columns of a data matrix. In this new framework, we study the behaviour of the groups posterior…
In this paper, we propose a convex formulation for learning logistic regression model (logit) with latent heterogeneous effect on sub-population. In transportation, logistic regression and its variants are often interpreted as discrete…
Mixture models and topic models generate each observation from a single cluster, but standard variational posteriors for each observation assign positive probability to all possible clusters. This requires dense storage and runtime costs…
Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only small portion of groups are significant, thus consistent group selection is of significant…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the…
The estimation of categorical response models using bias-reducing adjusted score equations has seen extensive theoretical research and applied use. The resulting estimates have been found to have superior frequentist properties to what…
$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…
We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…