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We give oracle inequalities on procedures which combines quantization and variable selection via a weighted Lasso $k$-means type algorithm. The results are derived for a general family of weights, which can be tuned to size the influence of…

Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the…

Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…

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…

In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that…

Imbalanced regression occurs when continuous target variables have skewed distributions, creating sparse regions that are difficult for machine learning models to predict accurately. This issue particularly affects neural networks, which…

The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find…

We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…

The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

In genomic studies, identifying biomarkers associated with a variable of interest is a major concern in biomedical research. Regularized approaches are classically used to perform variable selection in high-dimensional linear models.…

We propose a new method for high-dimensional semi-supervised learning problems based on the careful aggregation of the results of a low-dimensional procedure applied to many axis-aligned random projections of the data. Our primary goal is…

With the emergence of high-throughput technologies, it is possible to measure large amounts of data relatively at low cost. Such situations arise in many fields from sciences to humanities, and variable selection may be of great help to…

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence.…

This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy.…

We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…

Variable selection in linear regression settings is a much discussed problem. Best subset selection (BSS) is often considered the intuitive 'gold standard', with its use being restricted only by its NP-hard nature. Alternatives such as the…

Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…

Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…