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…
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48 results for “robust matrix elastic net”
Enhanced Elastic-Net with box-constraint improves support recovery in noisy measurements.
problem Support recovery of sparse signals from noisy measurements.
method Box-Elastic Net (Box-EN) method with mean squared error and probability of support recovery analysis.
result The Box-Elastic Net outperforms the standard Elastic-Net in support recovery.
Paper introduces RMEN-CCA for multi-view unsupervised learning.
problem Combining multiple data views for unsupervised learning.
method Robust matrix elastic net (RMEN) integrated with canonical correlation analysis (CCA).
result RMEN-CCA outperforms state-of-the-art methods on multiple datasets.
New SVM model balances sparsity and robustness in noisy data.
problem Noise sensitivity and lack of sparsity in traditional SVM models.
method Combines elastic net loss with robust loss framework, integrates with SVM, uses half-quadratic algorithm.
result Proves sparsity and robustness, outperforms traditional SVMs in noisy environments.
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
Robust support vector model based on bounded asymmetric elastic net loss for binary classificationstat.ML
BAEN-SVM improves SVM robustness to noisy data.
problem Noise and geometric irrationalities in SVM.
method Bounded asymmetric elastic net loss combined with SVM.
result BAEN-SVM is robust to noise and geometrically well-defined.
Renet: Principled and Efficient Relaxation for the Elastic Net via Dynamic Objective Selectionstat.ME
Renet improves Elastic Net by dynamically selecting between convex blending and refitting, enhancing prediction accuracy.
problem Elastic Net's shrinkage bias limits its prediction accuracy in high-dimensional settings.
method Adaptive relaxation procedure that dynamically dispatches between convex blending and efficient sub-path refitting.
result Renet consistently outperforms standard Elastic Net and Adaptive Elastic Net in high-dimensional, low signal-to-noise ratio, and high-multicollinearity scenarios.
SMM preserves matrix data structure for SVM classification.
problem Preserving spatial correlations in matrix data for SVM.
method SMM uses spectral elastic net combining nuclear and Frobenius norms.
result SMM improves SVM performance on matrix data.
FedElasticNet reduces communication costs and handles client drift in FL.
problem Expensive communication costs and client drift issues in federated learning.
method Leverages elastic net regularizers to sparsify local updates and limit client drift.
result FedElasticNet effectively resolves communication cost and client drift problems.
RENT selects stable features for robust model interpretation.
problem Stability in feature selection for robust model interpretation.
method RENT uses an ensemble of elastic net models trained on distinct subsets of data.
result RENT selects features with high stability improving model robustness.
New method selects features using graph-based interactions and elastic net.
problem Loss of feature relationships in vector-based feature selection.
method Graph-based structurally interacting elastic net method.
result Preserves feature relationships and selects informative features.
The paper improves NBR for count data using elastic-net regularization, achieving consistency and weak signal detection.
problem Sparse negative binomial regression for count data with non-asymptotic advantages.
method Elastic-net estimator with oracle inequalities derived under Compatibility Factor Condition and Stabil Condition.
result Sign consistency and grouping effect with high probability, and true variable set recovery under certain conditions.
Paper develops algorithms for sparse linear regression with generalized elastic net penalty.
problem Sparse linear regression with robust penalty for high-dimensional data.
method Iterative Reweighted Framework based on ADMM and PMM with SNN.
result Efficient algorithms provide superior performance in both simulated and real data.
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…
New algorithm selects genes for cancer classification using adaptive elastic net and conditional mutual information.
problem Selecting informative genes for microarray cancer classification.
method Adaptive Elastic Net with Conditional Mutual Information (AEN-CMI).
result AEN-CMI achieves the best classification performance with fewer genes.
Paper proposes robust estimators for heavy-tailed data with infinite variance.
problem Developing robust estimators for heavy-tailed data with infinite variance.
method Proposes two robust estimators: ridge log-truncated M-estimator and elastic net log-truncated M-estimator.
result Demonstrates robustness of log-truncated estimations over standard estimations through simulations and real data analysis.
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…
Maximizes stock portfolio predictability using machine learning.
problem Improving stock portfolio performance through predictive modeling.
method Optimal constrained weights in the MPP constructed using Elastic Net, Random Forest, and Support Vector Regression models.
result MPP portfolios can outperform or underperform the index based on the time period.
Study on Transfer Elastic Net error bounds and grouping effect.
problem Estimation error and grouping effect in Transfer Elastic Net.
method Derives non-asymptotic error bound and examines grouping effect scenarios.
result Effective error bounds and grouping effect observed in Transfer Elastic Net.
A new method fills missing labels in multi-label classification problems.
problem Missing feature and label values in multi-label classification.
method Proposes co-completion (COCO) algorithm based on subgradient descent.
result Demonstrates theoretical and practical effectiveness of COCO.
Efficiently solves Elastic Net in high dimensions with Newton method.
problem Feature selection in high-dimensional data with non-negligible collinearity.
method Semi-smooth Newton Augmented Lagrangian Method.
result Significantly reduces computational cost compared to competitors.
A fast method estimates group-adaptive elastic net penalties using co-data.
problem Computational inefficiency in estimating group-adaptive elastic net penalties.
method Derive low-dimensional representation of Taylor approximation for marginal likelihood and its derivative for group-adaptive ridge penalties; approximate elastic net marginal likelihood by ridge; transform ridge penalties to elastic net penalties.
result Significantly decreases computation time and outperforms other methods.
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…
This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and develop an iterative algorithm to solve the convex minimization problem. The itera…
ARGEN method improves variable selection and regularization in high-dimensional sparse models.
problem Constrained variable selection and regularization in high-dimensional sparse linear models.
method ARGEN penalty method, variable selection and regularization.
result ARGEN method has variable selection and estimation consistency under certain conditions.
Generalised elastic netsq-bio.NC
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…
Network Elastic Net identifies smoking-specific gene expression for lung cancer prognosis.
problem Identifying smoking-specific gene expression biomarkers in lung cancer prognosis.
method Introduces Network Elastic Net, a method that clusters and regresses on graphs based on smoking behavior.
result Shows efficacy of clusters in identifying cancer stages using gene expression and smoking behavior.
A new method for semi-supervised learning of sparse features using elastic-net.
problem Semi-supervised learning of sparse features in generalized linear models.
method Generalized Semi-Supervised Elastic-Net (s2net) framework.
result The s2net framework improves upon supervised elastic-net methods for semi-supervised learning.
Proposes fwelnet to improve prediction using feature information.
problem Improving prediction accuracy in supervised learning settings.
method fwelnet uses feature-weighted elastic net to adapt feature penalties.
result fwelnet outperforms lasso in test MSE and feature selection.
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 penalty. We show that this new {\em -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 …
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 …
We investigate the learning rate of multiple kernel learning (MKL) with and elastic-net regularizations. The elastic-net regularization is a composition of an -regularizer for inducing the sparsity and an -regularizer for controlling the smoothness. We focus on a sparse setting where the total …
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 , or nuclear norms. regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no conne…
A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computingstat.ML
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…
ME-Net defends neural nets against adversarial attacks by reconstructing images.
problem Adversarial attacks on deep neural networks.
method ME-Net uses matrix estimation to preprocess images, destroying adversarial noise while preserving global structure.
result ME-Net consistently outperforms state-of-the-art defenses on various benchmarks.
Improves parameter selection for denoising with elastic net.
problem Challenges in selecting optimal parameters for denoising.
method Combines statistical learning theory and regularisation theory to approximate optimal elastic net parameters.
result Explicit error bounds on accuracy of approximated parameter and regularisation solution.
We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an -regularizer for inducing the sparsity and an -regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non…
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the - and -norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
A new method for multi-target regression robust to outliers.
problem Outliers in regression data affect the performance of ELM-based methods.
method Generalized Outlier Robust ELM (GOR-ELM) using norm and Elastic Net theory.
result GOR-ELM outperforms other ELM-based techniques in datasets with outliers.
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…
A new method tracks index using topological data analysis for sparse portfolios.
problem Sparse index tracking with robust risk management.
method Topological learning via Vietoris-Rips filtration for sparse regularization.
result The method outperforms state-of-the-art techniques in various market conditions.
Paper proves robust M-estimators' coordinates' normality in high dimensions.
problem High-dimensional robust M-estimators' asymptotic normality.
method Develops Stein formulae for high-dimensional random vectors on the sphere.
result Asymptotic normality holds for most coordinates of robust M-estimators with convex penalty.
Enhanced ECCD speeds up elastic net model training.
problem Efficiently solving generalized linear models with elastic net constraints.
method Redesigned cyclic coordinate descent with Taylor expansion and batched computations.
result Empirically shows consistent performance improvement over state-of-the-art solvers.
EAD creates -distorted adversarial examples to improve DNN security.
problem Vulnerability of deep neural networks to adversarial examples.
method Formulated as an elastic-net regularized optimization problem.
result EAD yields distinct adversarial examples with small distortion.
New framework uses EEG to detect brain atrophy in AD, validated on large AD trial.
problem Diagnosis of Alzheimer's disease relies on subjective clinical interpretations.
method Combines Riemannian tangent space mapping and elastic net regression.
result Developed brain atrophy markers validated on large AD trial.
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.
problem Violation of constant error variance in high-dimensional regression.
method HDBEN framework using hierarchical Bayesian priors with and penalties.
result Achieves posterior concentration, variable selection consistency, and asymptotic normality.