Related papers: The Predictive Lasso
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…
Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
Model selection based on classical information criteria, such as BIC, is generally computationally demanding, but its properties are well studied. On the other hand, model selection based on parameter shrinkage by $\ell_1$-type penalties is…
We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic…
De-biased lasso has emerged as a popular tool to draw statistical inference for high-dimensional regression models. However, simulations indicate that for generalized linear models (GLMs), de-biased lasso inadequately removes biases and…
We consider random sample splitting for estimation and inference in high dimensional generalized linear models, where we first apply the lasso to select a submodel using one subsample and then apply the debiased lasso to fit the selected…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
The Generalized Linear Model (GLM) for the Gamma distribution (glmGamma) is widely used in modeling continuous, non-negative and positive-skewed data, such as insurance claims and survival data. However, model selection for GLM depends on…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
Aims: To propose a general sample size framework for developing or updating a clinical prediction model using any statistical or machine learning method, based on drawing samples from anticipated posterior distributions and targeting…
We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
The high dimensional nature of genomics data complicates feature selection, in particular in low sample size studies - not uncommon in clinical prediction settings. It is widely recognized that complementary data on the features, `co-data',…
This paper proposes a novel method for model selection in linear regression by utilizing the solution path of $\ell_1$ regularized least-squares (LS) approach (i.e., Lasso). This method applies the complex-valued least angle regression and…