Group Least Absolute Shrinkage And Selection Operator Research Articles

Sparse Group Penalties for bi-level variable selection.

Many data sets exhibit a natural group structure due to contextual similarities or high correlations of variables, such as lipid markers that are interrelated based on biochemical principles. Knowledge of such groupings can be used through bi-level selection methods to identify relevant feature groups and highlight their predictive members. One of the best known approaches of this kind combines the classical Least Absolute Shrinkage and Selection Operator (LASSO) with the Group LASSO, resulting in the Sparse Group LASSO. We propose the Sparse Group Penalty (SGP) framework, which allows for a flexible combination of different SGL-style shrinkage conditions. Analogous to SGL, we investigated the combination of the Smoothly Clipped Absolute Deviation (SCAD), the Minimax Concave Penalty (MCP) and the Exponential Penalty (EP) with their group versions, resulting in the Sparse Group SCAD, the Sparse Group MCP, and the novel Sparse Group EP (SGE). Those shrinkage operators provide refined control of the effect of group formation on the selection process through a tuning parameter. In simulation studies, SGPs were compared with other bi-level selection methods (Group Bridge, composite MCP, and Group Exponential LASSO) for variable and group selection evaluated with the Matthews correlation coefficient. We demonstrated the advantages of the new SGE in identifying parsimonious models, but also identified scenarios that highlight the limitations of the approach. The performance of the techniques was further investigated in a real-world use case for the selection of regulated lipids in a randomized clinical trial.

Interpretability of bi-level variable selection methods.

Variable selection is usually performed to increase interpretability, as sparser models are easier to understand than full models. However, a focus on sparsity is not always suitable, for example, when features are related due to contextual similarities or high correlations. Here, it may be more appropriate to identify groups and their predictive members, a task that can be accomplished with bi-level selection procedures. To investigate whether such techniques lead to increased interpretability, group exponential LASSO (GEL), sparse group LASSO (SGL), composite minimax concave penalty (cMCP), and least absolute shrinkage, and selection operator (LASSO) as reference methods were used to select predictors in time-to-event, regression, and classification tasks in bootstrap samples from a cohort of 1001 patients. Different groupings based on prior knowledge, correlation structure, and random assignment were compared in terms of selection relevance, group consistency, and collinearity tolerance. The results show that bi-level selection methods are superior to LASSO in all criteria. The cMCP demonstrated superiority in selection relevance, while SGL was convincing in group consistency. An all-round capacity was achieved by GEL: the approach jointly selected correlated and content-related predictors while maintaining high selection relevance. This method seems recommendable when variables are grouped, and interpretation is of primary interest.

High-dimensional multivariate autoregressive model estimation of human electrophysiological data using fMRI priors

Multivariate autoregressive (MVAR) model estimation enables assessment of causal interactions in brain networks. However, accurately estimating MVAR models for high-dimensional electrophysiological recordings is challenging due to the extensive data requirements. Hence, the applicability of MVAR models for study of brain behavior over hundreds of recording sites has been very limited. Prior work has focused on different strategies for selecting a subset of important MVAR coefficients in the model to reduce the data requirements of conventional least-squares estimation algorithms. Here we propose incorporating prior information, such as resting state functional connectivity derived from functional magnetic resonance imaging, into MVAR model estimation using a weighted group least absolute shrinkage and selection operator (LASSO) regularization strategy. The proposed approach is shown to reduce data requirements by a factor of two relative to the recently proposed group LASSO method of Endemann et al (Neuroimage 254:119057, 2022) while resulting in models that are both more parsimonious and more accurate. The effectiveness of the method is demonstrated using simulation studies of physiologically realistic MVAR models derived from intracranial electroencephalography (iEEG) data. The robustness of the approach to deviations between the conditions under which the prior information and iEEG data is obtained is illustrated using models from data collected in different sleep stages. This approach allows accurate effective connectivity analyses over short time scales, facilitating investigations of causal interactions in the brain underlying perception and cognition during rapid transitions in behavioral state.

Application of lasso for identification of functional groups with significant contributions to antioxidant activities of Centella asiatica

High-dimensional data has more variables than observations (p>>n). In this case, modeling with regression analysis becomes ineffective because it will violate the multicollinearity assumption. The least absolute shrinkage and selection operator (LASSO) can handle high-dimensional data and multicollinearity because LASSO works by reducing the parameters of variables with significant effects and selecting variables with minor effects. In its application, several variables have the same characteristics. Reducing and selecting variables in the form of groups can solve the problem so that the group LASSO can be used as a solution. This study used data on antioxidant activity in C. asiatica. It is a plant that contains antioxidants. The spectroscopic technique can find important information about antioxidants, namely the Fourier transformed infrared spectrophotometer (FTIR). FTIR is a spectroscopic technique based on molecular vibrations subjected to infrared so that it can characterize molecules with functional groups. FTIR data has large dimensions and multicollinearity. This study has 1866 explanatory variables (p) and 15 predictor variables (n). So, this study aimed to implement LASSO and the group LASSO to identify functional groups that major affect the antioxidant. This study concluded that group LASSO was better than the LASSO with modification of the LAR algorithm in identifying functional groups that had a major contribution to antioxidant activity. The results showed that the functional groups that had a major effect on the antioxidant activity of C. asiatica were –NH –OH, and C –O. In general, the functional groups that had a major effect on the antioxidant activity of C. asiatica came from phenolic compounds.

MP-LASSO chart: a multi-level polar chart for visualizing group LASSO analysis of genomic data.

Penalized regression has been widely used in genome-wide association studies for jointanalyses to find genetic associations. Among penalized regression models, the least absolute shrinkage and selection operator (Lasso) method effectively removes some coefficientsfrom the model by shrinking them to zero. To handle group structures, such as genes andpathways, several modified Lasso penalties have been proposed, including group Lasso andsparse group Lasso. Group Lasso ensures sparsity at the level of pre-defined groups, eliminating unimportant groups. Sparse group Lasso performs group selection as in group Lasso,but also performs individual selection as in Lasso. While these sparse methods are useful inhigh-dimensional genetic studies, interpreting the results with many groups and coefficients is not straightforward. Lasso's results are often expressed as trace plots of regressioncoefficients. However, few studies have explored the systematic visualization of group information. In this study, we propose a multi-level polar Lasso (MP-Lasso) chart, which caneffectively represent the results from group Lasso and sparse group Lasso analyses. An Rpackage to draw MP-Lasso charts was developed. Through a real-world genetic data application, we demonstrated that our MP-Lasso chart package effectively visualizes the resultsof Lasso, group Lasso, and sparse group Lasso.

Assessment of Various Machine Learning Models for Peach Maturity Prediction Using Non-Destructive Sensor Data.

To date, many machine learning models have been used for peach maturity prediction using non-destructive data, but no performance comparison of the models on these datasets has been conducted. In this study, eight machine learning models were trained on a dataset containing data from 180 ‘Suncrest’ peaches. Before the models were trained, the dataset was subjected to dimensionality reduction using the least absolute shrinkage and selection operator (LASSO) regularization, and 8 input variables (out of 29) were chosen. At the same time, a subgroup consisting of the peach ground color measurements was singled out by dividing the set of variables into three subgroups and by using group LASSO regularization. This type of variable subgroup selection provided valuable information on the contribution of specific groups of peach traits to the maturity prediction. The area under the receiver operating characteristic curve (AUC) values of the selected models were compared, and the artificial neural network (ANN) model achieved the best performance, with an average AUC of 0.782. The second-best machine learning model was linear discriminant analysis with an AUC of 0.766, followed by logistic regression, gradient boosting machine, random forest, support vector machines, a classification and regression trees model, and k-nearest neighbors. Although the primary parameter used to determine the performance of the model was AUC, accuracy, F1 score, and kappa served as control parameters and ultimately confirmed the obtained results. By outperforming other models, ANN proved to be the most accurate model for peach maturity prediction on the given dataset.

Extracting relevant predictors of the severity of mental illnesses from clinical information using regularisation regression models

AbstractMental disorders are common non-communicable diseases whose occurrence rises at epidemic rates globally. The determination of the severity of a mental illness has important clinical implications and it serves as a prognostic factor for effective intervention planning and management. This paper aims to identify the relevant predictors of the severity of mental illnesses (measured by psychiatric rating scales) from a wide range of clinical variables consisting of information on both laboratory test results and psychiatric factors. The laboratory test results collectively indicate the measurements of 23 components derived from vital signs and blood tests results for the evaluation of the complete blood count. The 8 psychiatric factors known to affect the severity of mental illnesses are considered, viz. the family history, course and onset of an illness, etc. Retrospective data of 78 patients diagnosed with mental and behavioural disorders were collected from the Lady Hardinge Medical College & Smt. S.K, Hospital in New Delhi, India. The observations missing in the data are imputed using the non-parametric random forest algorithm. The multicollinearity is detected based on the variance inflation factor. Owing to the presence of multicollinearity, regularisation techniques such as ridge regression and extensions of the least absolute shrinkage and selection operator (LASSO), viz. adaptive and group LASSO are used for fitting the regression model. Optimal tuning parameter λ is obtained through 13-fold cross-validation. It was observed that the coefficients of the quantitative predictors extracted by the adaptive LASSO and the group of predictors extracted by the group LASSO were comparable to the coefficients obtained through ridge regression.

ML3 LASSO (Least Absolute Shrinkage and Selection Operator) and XGBoost (eXtreme Gradient Boosting) Models for Predicting Depression-Related Work Impairment in US Working Adults

Work productivity loss among adults with depression are associated with multiple patient characteristics. The current study examined predicted total work impairments as a result of absenteeism and presenteeism using regularized linear regression and decision-tree-based ensemble algorithm. Data on employed US adults (18-64 years old) were analyzed from the 2019 National Health and Wellness Survey. Analysis sample included respondents who self-reported diagnosis of depression or having experienced depression in the past 12 months. Work productivity loss was derived from Work Productivity and Activity Impairment questionnaire. Group LASSO with Nesterov’s method and XGBoost regression were used separately to predict work impairments and to extract model feature importance views. Given the count-like nature of productivity loss, poisson distribution was specified in both LASSO and XGBoost. Variable selection was based on model fit statistics Akaike Information Criterion (AIC) (LASSO) and the gain in feature importance (XGBoost). Forty variables on respondent demographics, health behavior (e.g., smoking and alcohol use), depression-related variables, comorbidities, and doctor visits were entered into both models. Data was split into training, validation, and testing datasets. Hyperparameters were tuned based on the validation data. Root mean squared errors (RMSE) for the testing data were compared to assess model performance. Among 11,478 working adults with depression, XGBoost made more accurate predictions compared with LASSO (RMSE=26.6 and 27.6, respectively). Overestimation of impairment was slightly greater in the LASSO model compared with that from XGBoost (mean impairment=33% and 30%, respectively). The LASSO model selected more demographic and health behavior variables than XGBoost which ranked comorbidity variables (arthritis, sleep conditions, migraine, liver or renal diseases) as the most important features in predicting productivity loss. In a broadly representative US population of working adults with depression, XGBoost model was found to better predict productivity loss compared with LASSO.

A study on group lasso for grouped variable selection in regression model

Estimation of regression parameters using the Least Squares (LS) method could not be performed when the number of explanatory variables exceeds the number of observations. An approach that can solve the problem is the LASSO (Least Absolute Shrinkage and Selection Operator) method. This method produces a stable model but with slight bias as the trade-off. Yuan and Lin [6] introduced the Group LASSO method which can be used when there are grouped structure in the variables. This current paper provided a study of the performance of the Group LASSO method through a simulation with several different scenarios. Furthermore, the Group LASSO method was applied to the Human Development Index (HDI) data of Bengkulu Province in 2019. The simulation yieled that the Group LASSO analysis was better than LASSO in term of its Mean Squared Error of Prediction (MSEP), False Negative Rate (FNR) and R-Squared. In the application of the approach to the HDI data, our result was in line with the simulation results that the analysis of Group LASSO was better than LASSO with MSEP Group LASSO of 0.25 and R-Squared of 98%.

Fused Group Lasso: A New EEG Classification Model With Spatial Smooth Constraint for Motor Imagery-Based Brain–Computer Interface

The traditional group sparse optimization method can simultaneously achieve the channel selection and classification for the motor imagery electroencephalogram (EEG) signals, but it doesn’t consider the spatial structure information between the electrode channels. Combining the group sparsity and spatial smoothness of EEG signals, a new EEG classification model is proposed, which is an improvement of group least absolute shrinkage and selection operator (LASSO). We call it fused group LASSO. First, group LASSO is used to model the group sparsity of EEG signals, the features of the same channel are assigned the same weights. Then, based on group LASSO, channel weights are regularized by total variation norm (TV-norm), which constrains the weights of adjacent channels to the same or similar, thereby the spatial smoothness modeling of EEG signals can be achieved. Using the primal-dual theory, an optimization algorithm for the new model is given. In order to verify the effectiveness of the new model, experiments were performed on two public brain-computer interface (BCI) competition data sets and one self-collected data set. Compared with the existing sparse optimization methods, the proposed method has achieved the highest average classification accuracy of 79.24%, 86.64% and 81.09%, respectively, and with better physiological interpretability. Compared with spatial filtering methods with smooth constraints, the proposed method realized global spatial smooth in a data-driver manner, and achieved the highest average classification accuracy of 84.96% in two competition data sets. All the experimental results showed that the proposed method can significantly improve the performance of BCI systems.

Model selection techniques for sparse weight‐based principal component analysis

AbstractMany studies make use of multiple types of data that are collected for the same set of samples, resulting in so‐called multiblock data (e.g., multiomics studies). A popular analysis framework is sparse principal component analysis (PCA) of the concatenated data. The sparseness in the component weights of these models is usually induced by penalties. A crucial factor in the use of such penalized methods is a proper tuning of the regularization parameters used to give more or less weight to the penalties. In this paper, we examine several model selection procedures to tune these regularization parameters for sparse PCA. The model selection procedures include cross‐validation, Bayesian information criterion (BIC), index of sparseness, and the convex hull procedure. Furthermore, to account for the multiblock structure, we present a sparse PCA algorithm with a group least absolute shrinkage and selection operator (LASSO) penalty added to it, to either select or cancel out blocks of data in an automated way. Also, the tuning of the group LASSO parameter is studied for the proposed model selection procedures. We conclude that when the component weights are to be interpreted, cross‐validation with the one standard error rule is preferred; alternatively, if the interest lies in obtaining component scores using a very limited set of variables, the convex hull, BIC, and index of sparseness are all suitable.

Home environmental and lifestyle factors associated with asthma, rhinitis and wheeze in children in Beijing, China

BackgroundThe prevalence of asthma and allergic diseases has increased rapidly in urban China since 2000. There has been limited study of associations between home environmental and lifestyle factors with asthma and symptoms of allergic disease in China. MethodsIn a cross-sectional analysis of 2214 children in Beijing, we applied a two-step hybrid Least Absolute Shrinkage and Selection Operator (LASSO) algorithm to identify environmental and lifestyle-related factors associated with asthma, rhinitis and wheeze from a wide range of candidates. We used group LASSO to select variables, using cross-validation as the criterion. Effect estimates were then calculated using adaptive LASSO. Model performance was assessed using Area Under the Curve (AUC) values. ResultsWe found a number of environmental and lifestyle-related factors significantly associated with asthma, rhinitis or wheeze, which changed the probability of asthma, rhinitis or wheeze from −5.76% (95%CI: −7.74%, −3.79%) to 27.4% (95%CI: 16.6%, 38.3%). The three factors associated with the largest change in probability of asthma were short birth length, carpeted floor and paternal allergy; for rhinitis they were maternal smoking during pregnancy, paternal allergy and living close to industrial area; and for wheeze they were carpeted floor, short birth length and maternal allergy. Other home environmental risk factors identified were living close to a highway, industrial area or river, sharing bedroom, cooking with gas, furry pets, cockroaches, incense, printer/photocopier, TV, damp, and window condensation in winter. Lifestyle-related risk factors were child caretakers other than parents, and age<3 for the day-care. Other risk factors included use of antibiotics, and mother’s occupation. Major protective factors for wheeze were living in a rural/suburban region, air conditioner use, and mother’s occupation in healthcare. ConclusionsOur findings suggest that changes in lifestyle and indoor environments associated with the urbanization and industrialization of China are associated with asthma, rhinitis, and wheeze in children.

Exploring the associations of serum concentrations of PCBs, PCDDs, and PCDFs with walking speed in the U.S. general population: Beyond standard linear models

Studies have shown that persistent organic pollutants (POPs) can have various health effects. However, little is known about the effects of multiple chemicals with possible common sources of exposure on walking speed, a proxy index reflecting lower limb neuromuscular function and physical function. We simultaneously applied multiple linear and nonlinear statistical models to explore the complex exposure-response relationship between a mixture of 22 selected POPs and walking speed. A total of 14 polychlorinated biphenyls (PCBs), 3 polychlorinated dibenzo-p-dioxins (PCDDs), and 5 polychlorinated dibenzofurans (PCDFs) were measured in the serum of participants in the National Health and Nutrition Examination Survey (NHANES) from 1999 to 2002. Walking speed was measured during a physical examination. Linear regression (LR), least absolute shrinkage and selection operator (LASSO), and group LASSO were used to evaluate the linearity of mixtures, while restricted cubic spline (RCS) regression, random forest (RF), and Bayesian kernel machine regression (BKMR) models were used to evaluate the nonlinearity of mixtures. Potential confounders were adjusted in the above models. A total of 436 subjects were included in our final analysis. The results of the LR model did not identify any POP exposure that was significantly associated with walking speed. The LASSO results revealed an inverse association of one PCDD congener and two PCDF congeners with walking speed, while the group LASSO analysis identified PCDFs at the exposure level and at the group level. In the RCS analysis, two PCB congeners presented significant overall associations with walking speed. The PCB congener PCB194 showed statistically significant effects on the outcome (P = 0.01) when a permutation-based RF was used. The BKMR analysis suggested that PCBs and PCDFs (probabilities = 0.887 and 0.909, respectively) are potentially associated with walking speed. Complex statistical models, such as RCS regression, RF and BKMR models, can detect the nonlinear and nonadditive relationships between PCBs and walking speed, while LASSO and group LASSO can identify only the linear relationships between PCDFs and walking speed. Fully considering the influence of collinearity in each method during modelling can increase the comprehensiveness and reliability of conclusions in studies of multiple chemicals.

Estimation of parameters on Texas reservoirs using least absolute shrinkage and selection operator

This paper is to analyze and estimate Texas reservoirs of monitored water supply reservoirs about 89.8% full until December 26, 2018 using LASSO methods and predict its water reservoirs. Data collects January 2017, April 2017, July 2017, October 2017, January 2018, April 2018, July 2018, October 2018 and December 26, 2018 for 118 lakes or dams from Texas, USA. Variables include percent full, water level, height above conservation pool, reservoir storage, conservation storage, conservation capacity, and surface area. The least absolute shrinkage and selection operator (LASSO) methods are stepwise selections, net and external cross validation, group LASSO, and adaptive LASSO. Elastic net selection find the minimum validation average square error, conservation storage; stepwise selection picks the minimum values of adjust R2 (adjust R2 statistic), Akaike’s information criterion, corrected Akaike’s information criterion, Bayesian information criterion, Cp statistic, Schwarz Bayesian information criterion in the model. The results reveal that height above conservation pool along with conservation capacity has very strong significant level for percent full among all of variables to be chosen in the model. The percent full at Texas reservoirs of monitored water supply reservoirs is affected directly by the height above conservation pool. It has a trend for the height above conservation pool with quadratic pattern in the future.

High-Dimensional LASSO-Based Computational Regression Models: Regularization, Shrinkage, and Selection

Regression models are a form of supervised learning methods that are important for machine learning, statistics, and general data science. Despite the fact that classical ordinary least squares (OLS) regression models have been known for a long time, in recent years there are many new developments that extend this model significantly. Above all, the least absolute shrinkage and selection operator (LASSO) model gained considerable interest. In this paper, we review general regression models with a focus on the LASSO and extensions thereof, including the adaptive LASSO, elastic net, and group LASSO. We discuss the regularization terms responsible for inducing coefficient shrinkage and variable selection leading to improved performance metrics of these regression models. This makes these modern, computational regression models valuable tools for analyzing high-dimensional problems.

Analysis of genotype by methylation interactions through sparsity-inducing regularized regression

In this paper, we consider the use of the least absolute shrinkage and selection operator (LASSO)-type regression techniques to detect important genetic or epigenetic loci in genome-wide association studies (GWAS) and epigenome-wide association studies (EWAS). We demonstrate how these techniques can be adapted to provide quantifiable uncertainty using stability selection, including explicit control of the family-wise error rate. We also consider variants of the LASSO, such as the group LASSO, to study genetic and epigenetic interactions. We use these techniques to reproduce some existing results on the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) data set, which collects from 991 individuals blood triglyceride and differential methylation at 464,000 cytosine-phosphate-guanine (CpG) sites and 761,000 single-nucleotide polymorphisms (SNPs), and to identify new research directions. Epigenome-wide and genome-wide models based on the LASSO are considered, as well as an interaction model limited to chromosome 11. The analyses replicate findings concerning 2 CpGs in carnitine palmitoyltransferase 1A (CPT1A). Some suggestions are made regarding potentially interesting directions for the analysis of genetic and epigenetic interactions.

Appearance-Based Localization of Mobile Robots Using Group LASSO Regression

Appearance-based localization is a robot self-navigation technique that integrates visual appearance and kinematic information. To analyze the visual appearance, we need to build a regression model based on extracted visual features from raw images as predictors to estimate the robot's location in two-dimensional (2D) coordinates. Given the training data, our first problem is to find the optimal subset of the features that maximize the localization performance. To achieve appearance-based localization of a mobile robot, we propose an integrated localization model that consists of two main components: the group least absolute shrinkage and selection operator (LASSO) regression and sequential Bayesian filtering. We project the output of the LASSO regression onto the kinematics of the mobile robot via sequential Bayesian filtering. In particular, we examine two candidates for the Bayesian estimator: the extended Kalman filter (EKF) and particle filter (PF). Our method is implemented in both indoor mobile robot and outdoor vehicle equipped with an omnidirectional camera. The results validate the effectiveness of our proposed approach.

The linearized alternating direction method of multipliers for sparse group LAD model

While the least absolute shrinkage and selection operator (LASSO) became a popular method due to its wide applications in high dimensional settings, some generalized LASSO models were developed. The sparse group LASSO is one of the important lasso-type methods, which aims to solve the linear regression problems with grouped covariates and tends to produce a solution with sparse effects both on a group and within group level. At the same time, we know that the least absolute deviation (LAD) is a useful and robust method when the noise distribution may be heavy-tailed or heterogeneous. In this paper, we combine these two classical ideas together to develop sparse group LAD model. We show that the sparse group LAD estimator achieves near oracle performance, i.e., with high probability, the $$L_2$$ norm of the estimation error is of order $$O(\sqrt{k\text{ log }p/n}).$$ Moreover, with the help of the linearization technique we propose the linearized alternating direction method of multipliers to solve the sparse group LAD estimator and establish its convergence. Numerical experiments are reported to illustrate the efficiency of the proposed algorithm.

Toward Probabilistic Diagnosis and Understanding of Depression Based on Functional MRI Data Analysis with Logistic Group LASSO.

Diagnosis of psychiatric disorders based on brain imaging data is highly desirable in clinical applications. However, a common problem in applying machine learning algorithms is that the number of imaging data dimensions often greatly exceeds the number of available training samples. Furthermore, interpretability of the learned classifier with respect to brain function and anatomy is an important, but non-trivial issue. We propose the use of logistic regression with a least absolute shrinkage and selection operator (LASSO) to capture the most critical input features. In particular, we consider application of group LASSO to select brain areas relevant to diagnosis. An additional advantage of LASSO is its probabilistic output, which allows evaluation of diagnosis certainty. To verify our approach, we obtained semantic and phonological verbal fluency fMRI data from 31 depression patients and 31 control subjects, and compared the performances of group LASSO (gLASSO), and sparse group LASSO (sgLASSO) to those of standard LASSO (sLASSO), Support Vector Machine (SVM), and Random Forest. Over 90% classification accuracy was achieved with gLASSO, sgLASSO, as well as SVM; however, in contrast to SVM, LASSO approaches allow for identification of the most discriminative weights and estimation of prediction reliability. Semantic task data revealed contributions to the classification from left precuneus, left precentral gyrus, left inferior frontal cortex (pars triangularis), and left cerebellum (c rus1). Weights for the phonological task indicated contributions from left inferior frontal operculum, left post central gyrus, left insula, left middle frontal cortex, bilateral middle temporal cortices, bilateral precuneus, left inferior frontal cortex (pars triangularis), and left precentral gyrus. The distribution of normalized odds ratios further showed, that predictions with absolute odds ratios higher than 0.2 could be regarded as certain.

Linearized alternating direction method of multipliers for sparse group and fused LASSO models

The least absolute shrinkage and selection operator (LASSO) has been playing an important role in variable selection and dimensionality reduction for linear regression. In this paper we focus on two general LASSO models: Sparse Group LASSO and Fused LASSO, and apply the linearized alternating direction method of multipliers (LADMM for short) to solve them. The LADMM approach is shown to be a very simple and efficient approach to numerically solve these general LASSO models. We compare it with some benchmark approaches on both synthetic and real datasets.