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 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.
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.
c-lasso is a Python tool for robust and sparse regression with linear constraints.
problem Sparse and robust linear regression with linear constraints.
method Estimates coefficients and scale under linear constraints using perspective M-estimators.
result Provides estimators for various loss functions with linear constraints.
Proposes CLasso for high-dimensional regression with low-dimensional components.
problem Estimation and confidence intervals for low-dimensional parameters in high-dimensional models.
method Solves two estimating equations: zero-bias constraint and ℓ1-penalized procedure. result CLasso estimator is asymptotically normal and attains Cramér-Rao lower bound.
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…
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.
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
problem Learning a sparse undirected graph from multivariate data under Laplacian-related constraints.
method Modifications to penalized log-likelihood approaches to enforce total positivity and lasso/adaptive lasso penalties using ADMM.
result The proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches.
Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected beha…
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.
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods where feature selection is effected via mixed-norms. Several mixed-norm based spar…
The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.
problem Estimation of high-dimensional piecewise-constant regression coefficients.
method Formulated a restricted isometry condition for the fused lasso estimator and derived estimation bounds.
result The estimation error can be dominated by either the lasso or the fused lasso rate, depending on the number of non-zero coefficients and piece-wise constant segments.
The Lasso is suboptimal in sparse linear regression due to design matrix constraints.
problem The suboptimality of the Lasso estimator in sparse linear regression.
method Characterization of optimal estimation rates and analysis of the Lasso estimator.
result The Lasso is provably minimax rate-suboptimal when the minimum singular value is small.
New clustering method handles heavy-tailed, asymmetric data.
problem Robust clustering of high-dimensional, heavy-tailed data.
method Sparse mixture of generalized hyperbolic distributions with gamma-lasso penalty.
result Improved clustering performance on heavy-tailed data.
A new estimator learns sparse linear models with context-dependent coefficients.
problem Sparse linear models lack flexibility compared to deep neural networks for handling feature groups.
method Contextual lasso estimator using a deep neural network with lasso regularization.
result Learned models can be sparser than standard lasso without sacrificing predictive power.
Constrained least squares regression is an essential tool for high-dimensional data analysis. Given a partition G of input variables, this paper considers a particular class of nonconvex constraint functions that encourage the linear model to select a small number of variables from a small number of groups …
A new method solves sparse regularization problems efficiently and robustly.
problem Sparse regularization in machine learning problems.
method Iteratively reweighted least square (IRLS) with bilevel resolution and BFGS solver.
result Achieves top performances on various sparsity and regularization problems.
New method controls false detections in brain activity localization.
problem Statistical control of false detections in brain activity localization.
method Adapted Lasso estimator for spatio-temporal MEG/EEG data.
result Offers statistical guarantees and adaptive method for thresholding.
A new method resolves permutation issues in shuffled linear regression for large-scale applications.
problem Estimating latent features through linear transformation with unknown permutations.
method Spectral matching method to align spectral components of measurement and feature covariances.
result Achieves accurate estimates in shuffled LS and LASSO settings with sufficient samples.
Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by incorporating regularized approaches, such as the lasso in VAR estimation. Traditional a…
Paper studies quantized LRMR with random dithering for correlated tasks.
problem Estimating coefficient matrix in quantized multivariate regression.
method Uniform quantization with random dithering, constrained and regularized Lasso estimators.
result Achieves minimax optimal rate with dithering, slightly worsens quantization effect.
The paper introduces a dynamic MVP model using high-frequency financial data.
problem Capturing the dynamics of minimum variance portfolio weights in financial markets.
method Imposes autoregressive structure on MVP processes and uses CLIME and LASSO for estimation.
result Proposes DR-MVP model with established asymptotic properties.
Unified approach to linear regression using covariance fitting for optimal weights.
problem Finding optimal weights for linear regression models when weights are unknown.
method Covariance fitting SPICE-methodology to obtain data-adaptive weights.
result Tuned versions of known regularized estimators are unified under a common approach.
New framework for identifying unimportant variables in convex optimization.
problem Identifying unimportant variables in convex optimization problems.
method Two-step approach: gather information on optimal solution structure, then produce screening rules.
result New screening rules for various optimization problems.
New algorithms improve sampling from constrained distributions.
problem Sampling from distributions constrained to convex bodies.
method Penalized Langevin Dynamics and Underdamped Monte Carlo methods.
result Improved convergence rates for constrained sampling problems.
We develop a first order expansion for convex penalized estimators in high-dimensional regression.
problem High-dimensional regression problems with random designs.
method Construct a first order expansion η of the penalized estimator β^. result The risk of β^ is asymptotically the same as the risk of η. Method extracts features from signals for classification with explainability.
problem Lack of interpretability in signal classification models.
method Combining scattering transform and multiclass logistic regression with zeroth-order optimization.
result Uncovered the meaning of scattering transform coefficients.
New bounds for Lasso and Group Lasso in high dimensions derived.
problem Estimation error bounds for Lasso and Group Lasso in high-dimensional settings.
method Recent advances in high-dimensional statistics to derive new L2 estimation upper bounds.
result Bounds match optimal minimax rate for Lasso and improve over existing results for Group Lasso.
The ℓ1-norm fails to produce sparse solutions in Laplacian constrained graphical models, leading to a complete graph.
problem Learning a sparse graph under Laplacian constrained Gaussian graphical models.
method Introduced a nonconvex sparsity penalty and proposed a new estimator using a sequence of weighted ℓ1-norm penalized sub-problems. Developed a projected gradient descent algorithm with linear convergence rate. result The proposed estimator can recover the edges correctly with high probability and is effective on both synthetic and real-world data sets.
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.
The paper examines Adaptive Lasso and Transfer Lasso, highlighting their differences and proposing a new method.
problem Comparing and contrasting Adaptive Lasso and Transfer Lasso.
method Theoretical analysis of asymptotic properties and introduction of a new method.
result The Transfer Lasso method reduces non-asymptotic estimation errors compared to Adaptive Lasso.
New proof shows weighted fused lasso has O(n^2) segments.
problem Proving the complexity of the weighted fused lasso.
method New proof showing the number of segments is O(n^2).
result The solution path of the weighted fused lasso has O(n^2) segments.
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.
DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.
problem Sparse-group lasso's computational expense and need for tuning.
method Dual Feature Reduction (DFR) using strong screening rules and dual norms.
result DFR drastically reduces computational cost without affecting solution optimality.
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.
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.
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…
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.
Transformers enable in-context learning with guarantees for a wide range of tasks.
problem How to enable in-context learning with transformers for various tasks.
method Developed a universal approximation theory integrating Barron's function approximation with transformer capabilities.
result Transformers can approximate any target function with vanishingly small risk using a few in-context examples.
Network Lasso improves graph signal learning from few samples.
problem Ensuring network Lasso accuracy for graph signal learning.
method Compressed sensing concepts applied to network Lasso.
result Precise conditions for network Lasso accuracy quantified.
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.
Forward stagewise regression follows a very simple strategy for constructing a sequence of sparse regression estimates: it starts with all coefficients equal to zero, and iteratively updates the coefficient (by a small amount ε) of the variable that achieves the maximal absolute inner product with the current residua…
LLM-Lasso uses LLMs to improve feature selection in Lasso regression.
problem Improving feature selection in Lasso regression with domain-specific knowledge.
method Combines LLMs with Lasso regularization to generate feature weights.
result Outperforms standard Lasso and feature selection baselines in biomedical studies.
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.
We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of L1-regularized regression for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Violators Algorithm as its proximal operator. The main ap…
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.
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider ℓ1 penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dim…
We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients (r), size of the parameter vector (β), …