Introduces Temporal Group LASSO for healthcare time series prediction.
problem Predicting response variables over time in healthcare.
method Multi-task, regularized regression approach for time series data.
result Reduces overfitting, selects predictors, learns smooth patterns over time.
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.
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.
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.
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…
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.
This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is …
SyGlasso models tensor data dependencies using Sylvester equations.
problem Capturing multiway dependencies in tensor-valued data.
method Based on Sylvester equation, uses nodewise regression for estimation.
result Demonstrates simultaneous estimation of brain connectivity and temporal dependencies.
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.
Paper proposes a method to efficiently estimate structural breaks in cointegrating regressions.
problem Estimating structural breaks in cointegrating regressions is challenging due to inconsistency of group lasso.
method Adaptive group lasso procedure using a first step group lasso estimation of diverging breakpoint candidates to produce weights for a second estimation.
result The adaptive group lasso estimator delivers consistent parameter changes and oracle properties.
New screening rules speed up Sparse-Group Lasso solving.
problem Efficiently solving Sparse-Group Lasso in high dimensions.
method Adapted safe screening rules for Sparse-Group Lasso.
result Significant speed-ups in computing time for coordinate descent.
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…
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…
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…
Bayesian method discovers PDEs with variable coefficients robustly.
problem Discovering PDEs from noisy data is challenging.
method Bayesian sparse learning with tBGL-SS and Gibbs sampler.
result Method enhances robustness and model selection criteria.
Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or not selected. In many applications, however, this can be too restrictive. In th…
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
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.
Selective inference for group lasso estimators across various distributions and covariates.
problem Developing selective inference methods for group lasso estimators.
method Randomized group-regularized optimization problem with post-selection likelihood.
result Selective point estimator and Wald-type confidence regions for regression parameters.
We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the usual group Lasso penalty on a set of latent variables. A detailed analysis of th…
Sparse group Lasso optimizes sparse and grouped parameters in high-dimensional data.
problem Simultaneously sparse and grouped parameters in high-dimensional linear regression.
method Sparse group Lasso, debiased sparse group Lasso, statistical inference.
result Matching upper and lower bounds on sample complexity and estimation error.
New method corrects selection bias in post-selective inference for Group LASSO.
problem Inference after Group LASSO selection is unreliable.
method Develops a consistent, post-selective Bayesian method to adjust for selection bias.
result Corrects bias in recovering effects of selected variables.
ACL method selects variables and clusters correlated ones in high-dimensional models.
problem Variable selection and clustering in high-dimensional, correlated data.
method Three-stage procedure: Lasso initial selection, variable clustering, and sparse estimation.
result ACL is consistent and efficient in finding true group structure.
We present a data dependent generalization bound for a large class of regularized algorithms which implement structured sparsity constraints. The bound can be applied to standard squared-norm regularization, the Lasso, the group Lasso, some versions of the group Lasso with overlapping groups, multiple kernel learning a…
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.
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose y=Az+η where A satisfies the restricted isometry property (RIP) with a sufficiently small constant, and ∥η∥2≤ε. Then minimizing ∥z∥1 subject to $\Vert y - Az \Ver…
Improves robustness of high-dimensional regression with rank objective and group lasso regularization.
problem Heavy-tailed noise and outliers in high-dimensional regression.
method Non-smooth Wilcoxon score based rank objective, group lasso regularization, data-driven tuning rule, proximal augmented Lagrangian method.
result Robust estimator with finite-sample error bound and efficient computational method.
New model reveals evolving stock interactions over time.
problem Understanding time-varying relationships among stocks.
method LOcal Group Graphical Lasso Estimation (loggle) with ADMM algorithm.
result Loggle reveals evolving stock interactions over time.
Exclusive Lasso improves survival prediction in cancer datasets.
problem Enhanced survival prediction in cancer datasets with high-dimensional genomic and clinical data.
method Proposes Exclusive Lasso regularization for feature selection in Cox regression models for grouped variables.
result Demonstrates improved survival prediction performance using Exclusive Lasso compared to standard Cox regression.
Study high-dimensional Granger causality tests for VIX and financial news.
problem Testing Granger causality in high-dimensional time series data.
method Regularized regressions, sparse-group LASSO, HAC estimation of variance.
result Valid time series inference for Granger causality tests in high dimensions.
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…
The paper improves support recovery guarantees for the group Lasso.
problem Estimating group-sparse signals from noisy measurements.
method Establishes new conditions for accurate group-level support estimation using the group Lasso.
result Allows for nearly as many recoverable nonzero groups as the total number of groups.
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.
Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group…
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 ℓ1,∞-penalized recursive least squares (R…
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.
In this paper we consider the problem of grouped variable selection in high-dimensional regression using ℓ1−ℓq regularization (1≤q≤∞), which can be viewed as a natural generalization of the ℓ1−ℓ2 regularization (the group Lasso). The key condition is that the dimensionality pn can…
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…
Standardization boosts sparse group lasso performance for categorical variables.
problem Improving performance of sparse group lasso with categorical variables.
method Column-wise scaling and re-scaling of coefficients, without orthonormalization.
result Column-wise scaling and re-scaling of coefficients achieves the same effect as orthonormalization.
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.
Paper introduces machine learning for time series data, improving nowcasting accuracy.
problem Improving accuracy in nowcasting US GDP growth using machine learning.
method Sparse-group LASSO estimator for high-dimensional time series data, considering different sampling frequencies and financial/macroeconomic data tail properties.
result Sparse-group LASSO outperforms unstructured LASSO in nowcasting US GDP growth.
Estimates VAR models with correlated data using structured norms.
problem Estimating VAR models with dependent data and structured norms.
method Structured VAR models with various norms, using Lasso-type techniques.
result Error bounds for structured VAR parameters are comparable to independent data settings.
Unified approach for error bounds in group sparse compressed sensing.
problem Error bounds for group sparse vectors in compressed sensing.
method Unified approach using decomposable and γ-decomposable norms.
result Bounds for various group sparse norms derived.
A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function ωwith a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and man…
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.
A new model identifies genetic risk factors using gene-level priors.
problem Identifying genetic risk factors from nucleotide-level genetic variants.
method Sparse Group Lasso with Group-level Graph structure (SGLGG) model.
result SGLGG effectively identifies phenotype-associated risk SNPs.
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.
Paper develops a new estimator for high-dimensional panel data with common shocks.
problem Cross-sectionally dependent errors driven by common shocks in high-dimensional panel data.
method Factor-augmented sparse-group LASSO estimator combining MIDAS aggregation with latent factors.
result The estimator outperforms standard LASSO for prediction and estimation in settings with cross-sectional dependence.