We introduce an application of the group lasso to design of experiments. Note that we are NOT trying to explain experimental design for the group lasso. Conversely, we explain how we can use the idea of the group lasso in experimental design, showing that the problem of constructing an optimal design matrix can be tran…
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48 results for “LASSO Problem”
New algorithm solves clustered lasso problem efficiently.
problem Learning group structure in regression parameters.
method Inexact semismooth Newton augmented Lagrangian algorithm with efficient Jacobian computation.
result The {\sc Ssnal} algorithm outperforms existing methods.
This paper is a survey of dictionary screening for the lasso problem. The lasso problem seeks a sparse linear combination of the columns of a dictionary to best match a given target vector. This sparse representation has proven useful in a variety of subsequent processing and decision tasks. For a given target vector, …
New hybrid rules improve lasso optimization efficiency.
problem Efficiently solving lasso problems with ultrahigh-dimensional data.
method Hybrid safe-strong rules (HSSR) incorporating safe screening into sequential strong rules.
result HSSR outperforms existing rules in synthetic and real data sets.
Proposes MM-DUST for efficient generalized lasso solution paths.
problem Efficiently solve generalized lasso problems in large-scale and non-linear models.
method Majorization-minimization dual stagewise algorithm incorporating quadratic majorizers and stagewise learning.
result Established the uniform convergence of approximated solution paths.
The paper compares methods for solving constrained lasso problems.
problem Handling linear constraints in lasso regression.
method Quadratic programming, ADMM, and solution path algorithm.
result Efficiency and accuracy recommendations for different data sizes.
The Lasso's complexity is polynomial in problem size with intrinsic noise.
problem Understanding the Lasso's complexity in various settings.
method Smoothed analysis with a tiny amount of intrinsic noise.
result The Lasso's complexity is polynomial in problem size.
A fast method for Lasso and Logistic Lasso problems.
problem Solving Lasso and Logistic Lasso regression problems efficiently.
method Iterative active set approach using solver updates.
result 31.41 times faster on average for compressed sensing.
The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifi…
A new method speeds up overlapping group lasso computations.
problem Time-consuming optimization of overlapping group lasso on large-scale problems.
method Non-overlapping statistical approximation to overlapping group lasso.
result The proposed penalty is statistically equivalent to overlapping group lasso.
Paper reveals how lasso screening can be simplified.
problem Efficiently solving the lasso problem for large datasets.
method Uses the projection of features onto subspace spanned by normals of half spaces to reduce dimensionality.
result Optimization problem in high dimensions can be simplified to lower dimensions.
Bayesian approach improves network lasso for multi-task learning.
problem Improving the determination of relational coefficients in network lasso.
method Proposes a Bayesian approach to solve multi-task learning problems using network lasso.
result Objective determination of relational coefficients through Bayesian estimation.
Network Lasso improves semi-supervised regression on network data.
problem Improving regression accuracy on network data with limited labeled examples.
method Applying network Lasso to semi-supervised regression problems, leveraging message passing over an empirical graph.
result Network Lasso's accuracy is linked to the existence of large network flows over the empirical graph.
New method for tuning Graphical Lasso hyperparameters.
problem Tuning hyperparameters of Graphical Lasso.
method Bilevel optimization with first-order method.
result Derivation of Graphical Lasso Jacobian.
This review summarizes five Lasso optimization algorithms.
problem Optimizing the Lasso objective function.
method Five representative algorithms: ISTA, FISTA, CGDA, SLA, PFA.
result Comparison of convergence rates and strengths/weaknesses.
We study the property of the Fused Lasso Signal Approximator (FLSA) for estimating a blocky signal sequence with additive noise. We transform the FLSA to an ordinary Lasso problem. By studying the property of the design matrix in the transformed Lasso problem, we find that the irrepresentable condition might not hold, …
Proposes finding missing features in Lasso solutions.
problem Lasso overlooks features not selected in its optimal solution.
method Computes alternate features efficiently without redundant computations.
result Reasonable alternate features found in 20 newsgroup data.
Efficient method solves constrained Lasso problems.
problem Variable selection with prior information.
method Inexact augmented Lagrangian method exploiting second-order sparsity.
result Superior performance compared to first-order methods.
We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization problems are equivalent, in the following sense. Given any instance of an $\ell…
Improves LASSO by scaling to reduce bias and enhance model selection.
problem LASSO's bias issue affecting sparse model selection.
method Introducing a scaling method to expand LASSO estimator.
result Empirical scaling improves LASSO and enhances model selection.
Exclusive Group Lasso improves feature selection in correlated biological data.
problem Correlated features hinder Lasso performance in biological classification problems.
method Proposes and solves the exclusive group Lasso, combining stability selection and random group allocation.
result Exclusive Group Lasso outperforms Lasso in comprehensive selection of informative features.
Efficient algorithms solve joint graphical lasso problems.
problem Learning graphical models from sparse data.
method Proximal gradient procedures with ADMM backtracking option.
result Proposed algorithms achieve high accuracy and precision.
Bayesian Lasso Sparse model provides sparse estimates in linear and nonlinear regression.
problem Sparse learning in regression models.
method Develops a new sparse learning model using type-II maximum likelihood procedure.
result The BLS model provides sparse estimates and is more precise, especially with noisy data.
Network Lasso classifies partially labeled data with high-dimensional features.
problem Classifying data points with limited labeled data and high-dimensional features.
method Logistic Network Lasso using total variation regularization and primal-dual splitting.
result Accurate classification achieved from limited labeled data via network structure.
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter . Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at is decomposed into connected components. We show that the vertex-partition induced by the thresh…
A new method for solving many lasso problems with a fixed regularization parameter.
problem Solving many lasso problems with a fixed regularization parameter when the dictionary is large.
method Feedback-controlled sequential screening to adaptively select problems.
result The method can solve many lasso problems efficiently with a fixed regularization parameter.
New solver speeds up Lasso-type problems by using screening rules and working sets.
problem Efficiently solving large-scale Lasso-type problems.
method Combining Gauss-Southwell rule with aggressive Gap Safe screening rules and working set strategy.
result Achieves state-of-the-art performance on sparse learning problems.
Proposes a new Lasso method for high missing rate data.
problem Handling high-dimensional data with many missing values.
method Integrates mean imputed covariance to overcome estimation bias.
result Effective even with high missing rates, improving upon CoCoLasso.
New method solves sparse approximation problem using trimmed lasso and generalized soft-min penalties.
problem Sparse approximation or best subset selection problem.
method Regularized approach with trimmed lasso and generalized soft-min penalties.
result The trimmed lasso provides sparse recovery guarantees and a practical optimization algorithm.
Lasso is a widely used regression technique to find sparse representations. When the dimension of the feature space and the number of samples are extremely large, solving the Lasso problem remains challenging. To improve the efficiency of solving large-scale Lasso problems, El Ghaoui and his colleagues have proposed th…
We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani and Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the special cases of trend filte…
Paper improves Lasso for S&P500 index tracking with post-selection inference.
problem Index tracking for S&P500 with many applications.
method Used Lasso for dimension reduction and post-selection inference.
result Lasso method for S&P500 index tracking shows high performance.
We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various decays of the regularization parameter, we compute asymptotic equivalents of the …
Recently, to solve large-scale lasso and group lasso problems, screening rules have been developed, the goal of which is to reduce the problem size by efficiently discarding zero coefficients using simple rules independently of the others. However, screening for overlapping group lasso remains an open challenge because…
A new method solves large-scale sparse group square-root Lasso problems efficiently.
problem Large-scale linearly constrained sparse group square-root Lasso problems.
method Dual semismooth Newton based augmented Lagrangian method (ALM).
result The proposed method efficiently solves the problem with numerical experiments demonstrating its effectiveness.
Trimmed Lasso offers sparse modeling with robustness control.
problem Sparse modeling in linear regression with robustness.
method Trimmed Lasso penalty function and its analysis.
result Trimmed Lasso offers exact sparsity control and robustness.
New method proves neural networks can select features consistently.
problem Feature selection for deep neural networks is challenging.
method Adaptive Group Lasso selection procedure with Group Lasso as the base estimator.
result Adaptive Group Lasso is selection-consistent for a wide class of neural networks.
Introduces screening rules for non-convex Lasso problems.
problem Efficiently solving non-convex Lasso problems with theoretical guarantees.
method Iterative majorization-minimization strategy with screening rule.
result Significant computational gain compared to classical methods.
The paper examines how to protect LASSO-based feature selection from adversarial attacks.
problem Adversarial attacks on LASSO-based feature selection.
method Formulated as a bi-level optimization problem, reformulated LASSO with linear inequality constraints, solved using interior-point method, and modified using projected gradient descent.
result Demonstrated the effectiveness of the proposed method in protecting LASSO-based feature selection from adversarial attacks.
Lasso with Latents: Efficient Estimation, Covariate Rescaling, and Computational-Statistical Gapsstat.ML
Lasso performs poorly with correlated covariates, but a rescaled approach fixes this.
problem Lasso's performance degrades with correlated covariates, leading to inefficiency.
method Proposes a rescaling method for Lasso to handle correlated covariates effectively.
result Rescaled Lasso provides strong provable guarantees for estimation with quadratic sample complexity.
We consider a joint processing of independent sparse regression problems. Each is based on a sample of \iid observations from $y_{i1}=x_{i1}\tβ_i+\eps_{i1}$, , , , and $\eps_{i1}\dist N(0,\sig^2)$, say. is large enough so that the…
The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…
The study approximates nearly optimal Lasso solutions using convex hulls.
problem Finding diverse yet nearly optimal Lasso solutions.
method Formulate problem as approximating nearly optimal solutions with a convex hull of sampled extreme points. Use a greedy algorithm to select a small number of points.
result The proposed algorithm can approximate the solution set well and obtain diverse Lasso solutions.
Proposes a new Lasso method with performance constraints.
problem No control over prediction accuracy for certain individuals.
method Adds quadratic performance constraints to Lasso-based objective functions.
result Defines a constrained sparse regression model through nonlinear optimization.
We analyze coresets for regularized regression problems and propose a modified lasso that yields smaller coresets.
problem Analyzing coresets for regularized regression problems.
method Examined coresets for ridge regression and proposed a modified lasso problem.
result No coreset for regularized regression can be smaller than the unregularized version when .
Robust Lasso-Zero handles missing covariates and sparse corruptions.
problem Sparse corruptions and missing covariates in sparse linear models.
method Extension of Lasso-Zero to handle sparse corruptions, with theoretical guarantees on sign recovery.
result Robust Lasso-Zero can handle missing values without specifying a parametric model.
We consider the least-square linear regression problem with regularization by the -norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in low-dimensional settings. For various decays of the regularization parameter, w…
New screening test for LASSO reduces complexity.
problem Efficient screening for LASSO problems.
method Joint screening test for LASSO problem, applied to sphere and dome regions.
result Effective screening of atoms reduces computational complexity.