Related papers: Laplace Approximation in High-dimensional Bayesian…

Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…

Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). The selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting…

We examine the behaviour of the Laplace and saddlepoint approximations in the high-dimensional setting, where the dimension of the model is allowed to increase with the number of observations. Approximations to the joint density, the…

The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…

We show that a probabilistic version of the classical forward-stepwise variable inclusion procedure can serve as a general data-augmentation scheme for model space distributions in (generalized) linear models. This latent variable…

Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…