Related papers: The Group R2D2 Shrinkage Prior for Sparse Linear M…
This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…
We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case…
Bayesian methods constitute a popular approach for estimating the conditional independence structure in Gaussian graphical models, since they can quantify the uncertainty through the posterior distribution. Inference in this framework is…
Statistical inference for sparse covariance matrices is crucial to reveal dependence structure of large multivariate data sets, but lacks scalable and theoretically supported Bayesian methods. In this paper, we propose beta-mixture…
In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…
Shrinkage for time-varying parameter (TVP) models is investigated within a Bayesian framework, with the aim to automatically reduce time-varying parameters to static ones, if the model is overfitting. This is achieved through placing the…
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…
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable"…
Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…
We introduce a novel prior distribution for modelling the weights in mixture models based on a generalisation of the Dirichlet distribution, the Selberg Dirichlet distribution. This distribution contains a repulsive term, which naturally…
We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
Time-varying parameter (TVP) models have the potential to be over-parameterized, particularly when the number of variables in the model is large. Global-local priors are increasingly used to induce shrinkage in such models. But the…
Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…
Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non-zero, which…
This paper proposes Dirichlet Variational Autoencoder (DirVAE) using a Dirichlet prior for a continuous latent variable that exhibits the characteristic of the categorical probabilities. To infer the parameters of DirVAE, we utilize the…
Machine learning-aided clinical decision support has the potential to significantly improve patient care. However, existing efforts in this domain for principled quantification of uncertainty have largely been limited to applications of…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…