arXiv research

Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper,…

Study on Transfer Elastic Net error bounds and grouping effect.

Efficiently solves Elastic Net in high dimensions with Newton method.

A fast method estimates group-adaptive elastic net penalties using co-data.

Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. By a simulation study, we s…

ARGEN method improves variable selection and regularization in high-dimensional sparse models.

The elastic net was introduced as a heuristic algorithm for combinatorial optimisation and has been applied, among other problems, to biological modelling. It has an energy function which trades off a fitness term against a tension term. In the original formulation of the algorithm the tension term was implicitly based…

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to the elastic net model. Specifically, we robustify the covariance matrix by trimm…

A new method for semi-supervised learning of sparse features using elastic-net.

New SVM model balances sparsity and robustness in noisy data.

Paper develops algorithms for sparse linear regression with generalized elastic net penalty.

Proposes fwelnet to improve prediction using feature information.

We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1 regularization (inducing sparse kernel combination), block-l2 regularization (inducing un…

We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an $\ell_2$ penalty. We show that this new {\em $k$-support norm} provides a tighter relaxation than the elastic net and is thus a good replacement for the Lasso or the elastic net in sparse prediction problems. Through …

In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the Box-Elastic Net (Box-EN). We assume independent identically distributed (iid) r…

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie for the selection of groups of correlated variables. To investigate on the statistical properties of this scheme and in particular on its consistency properties, we set up …

It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the…

Renet improves Elastic Net by dynamically selecting between convex blending and refitting, enhancing prediction accuracy.

We investigate the learning rate of multiple kernel learning (MKL) with $\ell_1$ and elastic-net regularizations. The elastic-net regularization is a composition of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total …

The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many h…

Study on spectral asymptotics in elasticity on smooth manifolds.

Study on elasticity with mixed boundary conditions, proving spectral asymptotics.

We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non…

Skew parallelogram nets factorize, encompassing discrete differential geometry.

This papers introduces an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. The algorithm compares very favourably in terms of time and space complexity to existing approaches and can be implemented with simple code that does not rely on external l…

FedElasticNet reduces communication costs and handles client drift in FL.

SMM preserves matrix data structure for SVM classification.

Survival month for non-small lung cancer patients depend upon which stage of lung cancer is present. Our aim is to identify smoking specific gene expression biomarkers in the prognosis of lung cancer patients. In this paper, we introduce the network elastic net, a generalization of network lasso that allows for simulta…

BAEN-SVM improves SVM robustness to noisy data.

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracl…

The spectral asymptotics for linear elasticity with mixed boundary conditions are shown to be old results.

Enhanced ECCD speeds up elastic net model training.

RENT selects stable features for robust model interpretation.

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \ci…

Multiple kernel learning (MKL), structured sparsity, and multi-task learning have recently received considerable attention. In this paper, we show how different MKL algorithms can be understood as applications of either regularization on the kernel weights or block-norm-based regularization, which is more common in str…

Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.

In this paper, the elastic Dirichlet-to-Neumann map $Ξ_g$ is studied for the stationary elasticity system in a compact Riemannian manifold $(Ω,g)$ with smooth boundary $\partial Ω$. By overcoming methodological difficulties, we explicitly get matrix-valued full symbol for the elastic Dirichlet-to-Neumann map $Ξ_g$. We …

IEN speeds up T-Rex+GVS for fast, efficient GWAS.

Corrects errors in previous work on spectral asymptotics in elasticity.

This paper provides theoretical guarantees for SPCA using the Elastic Net.

Recent studies have highlighted the vulnerability of deep neural networks (DNNs) to adversarial examples - a visually indistinguishable adversarial image can easily be crafted to cause a well-trained model to misclassify. Existing methods for crafting adversarial examples are based on $L_2$ and $L_\infty$ distortion me…

This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our experiments demonstrate that this strategy, implemented on the elastic-net, is computatio…

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associ…

Proposes novel wSVMs for sparse learning and accurate probability estimation.

Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems wi…

Optimizing quantum graphs yields geodesic nets on surfaces.

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no conne…

The diagnosis of Alzheimer's disease (AD) in routine clinical practice is most commonly based on subjective clinical interpretations. Quantitative electroencephalography (QEEG) measures have been shown to reflect neurodegenerative processes in AD and might qualify as affordable and thereby widely available markers to f…