Related papers: Tree-guided group lasso for multi-response regress…
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…
Nowadays, several data analysis problems require for complexity reduction, mainly meaning that they target at removing the non-influential covariates from the model and at delivering a sparse model. When categorical covariates are present,…
We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large…
In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…
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…
We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an…
Sparse mapping has been a key methodology in many high-dimensional scientific problems. When multiple tasks share the set of relevant features, learning them jointly in a group drastically improves the quality of relevant feature selection.…
Multi-task learning (MTL) is a methodology that aims to improve the general performance of estimation and prediction by sharing common information among related tasks. In the MTL, there are several assumptions for the relationships and…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
The elastic net combines lasso and ridge regression to fuse the sparsity property of lasso with the grouping property of ridge regression. The connections between ridge regression and gradient descent and between lasso and forward stagewise…
Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…
In multi-label learning, each sample is associated with several labels. Existing works indicate that exploring correlations between labels improve the prediction performance. However, embedding the label correlations into the training…
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…
Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…
Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…
This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…
The analysis of case-control studies with several subtypes of cases is increasingly common, e.g. in cancer epidemiology. For matched designs, we show that a natural strategy is based on a stratified conditional logistic regression model.…