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.
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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.
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.
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…
New Lasso algorithm recovers sparse signals on graphs.
problem Signal recovery from graph measurements.
method Combines compressed sensing and graph Fourier analysis.
result Non-convex, non-smooth Lasso outperforms standard Lasso.
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.
Proximal algorithms work well for SQRT-Lasso despite its nonsmooth loss.
problem Tackles the optimization of SQRT-Lasso regression.
method Applies proximal algorithms without concern for nonsmooth loss.
result Proximal algorithms converge fast with high probability.
A new algorithm speeds up and broadens the graph-fused lasso method.
problem Efficiently estimating parameters under graph structure assumptions.
method Decompose graph into trails, solve each trail using 1D fused lasso, alternate between primal and dual updates.
result Faster and more flexible GFL method compared to previous approaches.
Efficient algorithms for clustered Lasso and OSCAR reduce computational costs.
problem High dimensional regression with feature clustering.
method Efficient path algorithms for clustered Lasso and OSCAR, reducing computational costs.
result Proposed algorithms are more efficient than existing methods in numerical experiments.
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.
Two New Algorithms for Solving Covariance Graphical Lasso Based on Coordinate Descent and ECMstat.CO
Covariance graphical lasso applies a lasso penalty on the elements of the covariance matrix. This method is useful because it not only produces sparse estimation of covariance matrix but also discovers marginal independence structures by generating zeros in the covariance matrix. We propose and explore two new algorith…
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.
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 Lasso is a very well known penalized regression model, which adds an penalty with parameter on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an penalty with parameter on the difference of neighboring coefficients, assuming the…
PLS-Lasso integrates dimension reduction into regression for financial index tracking.
problem Dimension reduction and regression are traditionally treated separately in multivariate data analysis.
method PLS-Lasso integrates dimension reduction directly into the regression process, presenting two formulations: PLS-Lasso-v1 and PLS-Lasso-v2.
result PLS-Lasso-v1 and PLS-Lasso-v2 outperform Lasso in financial index tracking.
A two-phase algorithm identifies the best arm in sparse linear bandits with fixed budget.
problem Best arm identification in sparse linear bandits with limited budget.
method Lasso and Optimal-Design (Lasso-OD) based linear best-arm identification.
result Lasso-OD achieves significant performance improvement for sparse and high-dimensional linear bandits.
Optimizes UoI_LASSO and UoI_VAR for scalable statistical estimation of large datasets.
problem Statistical estimation of large, complex scientific data.
method Two-step UoI framework, optimized for scalability on supercomputers.
result Enabled estimation of largest VAR model (1000 nodes) for neurophysiology data.
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…
Optimizes Lasso hyperparameters using leave-one-out CV.
problem Finding optimal hyperparameters for Lasso regression.
method Develops an algorithm to compute exact or approximate leave-one-out CV.
result Algorithm finds optimal hyperparameters for Lasso.
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.
New algorithm speeds up Lasso computation by proving faster convergence.
problem Lasso estimator's slow convergence rate due to penalty.
method Homotopic approach using surrogate functions.
result Proves convergence rate for Lasso computation.
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.
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
problem Lasso's sensitivity to outliers and heavy-tailed noise in high-dimensional statistics.
method Integrates an exponential-type loss function into the Lasso framework.
result Achieves strong statistical convergence rates robust to heavy-tailed contamination.
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…
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.
Thresholded Lasso Banditstat.ML
Thresholded Lasso bandit minimizes regret in sparse linear bandits.
problem Sparse stochastic contextual linear bandits with large feature vectors.
method Uses Lasso framework with thresholding to estimate reward function and its sparse support.
result Non-asymptotic regret upper bounds scaling as .
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.
A new algorithm improves GLasso for sparse precision matrix estimation.
problem Efficiently estimating sparse precision matrices in high-dimensional data.
method A new reparametrization and iterative block coordinate descent algorithm.
result Improved performance comparable to DP-GLasso with a simpler optimization target.
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.
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmet…
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose where satisfies the restricted isometry property (RIP) with a sufficiently small constant, and . Then minimizing subject to $\Vert y - Az \Ver…
Improves Group Lasso for categorical data by reducing dimensionality and selecting models.
problem Sparse modelling of categorical data is challenging, especially for high dimensions.
method Two-step procedure: first, reduce dimensionality using Group Lasso; second, select final model using an information criterion on clustered levels.
result The method produces a sparse solution and performs better than state-of-the-art algorithms in prediction accuracy and model dimension.
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.
Stability Selection improves structured variable selection but requires careful tuning.
problem Finding a right-sized model or controlling false positives in structured selection problems.
method Stability Selection applied to group lasso and structured input-output lasso.
result Stability Selection often increases power but reduces error control reliability in structured settings.
The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the l_{1,2} and the l_{1,\infty} version have been studied in detail and efficient algorithms exist, there are still open questions regarding other l_{1,p} variants. We characterize conditions for solutions of the l_{1,p} G…
Recursive Group lassostat.ME
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 exact update of the optimal -penalized recursive least squares (R…
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.
Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some small computational effort to locate inactive atoms and remove them from the dictio…
Quantum algorithm speeds up Lasso regression by quadratically faster per iteration.
problem Efficiently solving high-dimensional linear regression with L1-penalty.
method Pathwise LARS algorithm adapted for quantum computing, using minimum-finding subroutines.
result Quadratic speedup in computation time for both number of features and observations.
Automatically selects important variables for malaria risk prediction using Lasso method.
problem Identifying the most relevant variables for predicting malaria risk using empirical knowledge.
method Uses Lasso method for automatic feature selection and prediction, combining double and simple cross-validation.
result Stable and consistent estimators of optimal variable subsets for malaria risk prediction.
Bayesian model improves sparsity in regression coefficients.
problem Sparsity in regression coefficients.
method Bayesian generalized fused lasso modeling using NEG distribution.
result The proposed method produces more sparse solutions than the ordinary fused lasso.
Paper analyzes adaptive ISTA with MAD for LASSO problem.
problem Finding solutions to LASSO problems without tuning .
method Adaptive ISTA with median absolute deviation (MAD) for estimating noise level.
result Local linear convergence and global convergence of the algorithm.
Paper links network Lasso to network flow optimization.
problem Joint clustering and optimization of networked data.
method Exploration of duality between network Lasso and network flow optimization.
result nLasso is equivalent to a minimum-cost flow problem on the data network structure.
Improved Lasso method for high-dimensional regression with noise estimation.
problem Sparse structure in high-dimensional settings with unknown noise level.
method Smoothed Concomitant Lasso, incorporating noise estimation and efficient solver.
result Increased numerical stability and computational efficiency compared to original formulation.
New convergence analysis for Lasso l1 reweighting improves practical performance.
problem Theoretical convergence of Lasso l1 reweighting methods is limited.
method Biconvex analysis for an alternated convex search.
result Numerical convergence of the algorithm sequence for practical purposes.
New guarantees for Group LASSO in sparse convex optimization.
problem Sparse convex optimization with vector-valued features.
method Group LASSO regularization and analysis of gradient norms.
result Group LASSO selects the same features as Orthogonal Matching Pursuit.
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.
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.