Matlab toolbox to calculate least angle regression (LAR) for general convex loss funtions. It can calculate LAR and LASSO solution paths for various models, including generalized linear model, recurrent event data, panel count data, Ada-boost and gaussian graphical model. Weighted LAR (LASSO) and group LAR (LASSO) are also included.
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convexLAR.m: fucntion to compute the ConvexLAR (weighted ConvexLAR) solution path of general convex function, including generalized linear model (glm), recurrent event data (recurrent), panel count data (panel) and Ada-boost (ada).
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convexLASSO.m: function to compute the ConvexLASSO (weighted ConvexLASSO) solution path of general convex function, including generalized linear model (glm), recurrent event data (recurrent), panel count data (panel) and Ada-boost (ada).
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convexGLAR.m: funtion to compute the group LAR solution path of general convex function, including generalized linear model (glm), recurrent event data (recurrent), panel count data (panel) and Ada-boost (ada).
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convexGLASSO.m: function to calculate the group LASSO solution path of general convex function, including generalized linear model (glm), recurrent event data (recurrent), panel count data (panel) and Ada-boost (ada).
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graphLAR.m: function to compute the ConvexLAR solution path of gaussian graphical model.
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graphLASSO.m: function to compute the ConvexLASSO solution path of gaussian graphical model.
See the paper for details
If you use this toolbox in any way, please cite the following publication.
@article{XIAOWUZHOU15ConvexLAR,
author = {Wei Xiao and Yichao Wu and Hua Zhou},
title = {ConvexLAR: An Extension of Least Angle Regression},
journal = {Journal of Computational and Graphical Statistics},
volume = {24},
number = {3},
pages = {603-626},
year = {2015},
doi = {10.1080/10618600.2014.962700},
URL = {http://dx.doi.org/10.1080/10618600.2014.962700},
eprint = {http://dx.doi.org/10.1080/10618600.2014.962700}
}
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Least square case (a simulated data set)
clear; % read matrices x, y from a simulated data set (n=100, p=6) x=dlmread('./data/lscase_x.dat'); y=dlmread('./data/lscase_y.dat'); model='glm'; % specify model distname='normal'; % specify distribution weight=ones(size(x,2),1); % specify weight % LAR solution path [TP_LAR_normal, FP_LAR_normal]=convexLAR(x, y, model, distname, weight); % LASSO solution path [TP_LASSO_normal, FP_LASSO_normal]=convexLASSO(x, y, model, distname, weight); % plot solution paths plot_path(TP_LAR_normal, FP_LAR_normal, ... 'ConvexLAR solution path for least square example'); plot_path(TP_LASSO_normal, FP_LASSO_normal, ... 'ConvexLASSO solution path for least square example');
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Poisson model (the diabetes data set)
clear; % read matrices x, y from the diabetes data set x=dlmread('./data/diabetesx.dat'); y=dlmread('./data/diabetesy.dat'); % Calculate LARS solution path model='glm'; % specify model distname='poisson'; % specify distribution weight=ones(size(x,2),1); % specify weight % LAR solution path [TP_LAR_pois, FP_LAR_pois]=convexLAR(x, y, model, distname, weight); % LASSO solution path [TP_LASSO_pois, FP_LASSO_pois]=convexLASSO(x, y, model, distname, weight); % plot solution paths plot_path(TP_LAR_pois, FP_LAR_pois, ... 'ConvexLAR solution path for possion model'); plot_path(TP_LASSO_pois, FP_LASSO_pois, ... 'ConvexLASSO solution path for possion model'); % Calculate weighted LARS solution path beta_ini=glmfit(x, y, distname, 'constant', 'on'); weight=abs(beta_ini(2:(size(x,2)+1))); % LAR solution path [TP_adaLAR_pois, FP_adaLAR_pois]=convexLAR(x, y, model, distname, weight); % LASSO solution path [TP_adaLASSO_pois, FP_adaLASSO_pois]=convexLASSO(x, y, model, distname, weight); % plot solution paths plot_path(TP_adaLAR_pois, FP_adaLAR_pois, ... 'Weighted ConvexLAR solution path for possion model'); plot_path(TP_adaLASSO_pois, FP_adaLASSO_pois, ... 'Weighted ConvexLASSO solution path for possion model');
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Recurrent event data (CGD data set, Tong et al., 2009b)
clear; % read matrices x, y from CGD date set with added interaction effect terms x=dlmread('./data/cgd_x.dat'); y=dlmread('./data/cgd_y.dat'); x1=[x x(:,3).^2 x(:,4).^2 x(:,5).^2 x(:,3).*x(:,4) x(:,3).*x(:,5) x(:,4).*x(:,5)]; % Calculate ConvexLARS solution paths recurrent'; % specify model distname=''; weight=ones(size(x1,2),1); % specify weight % LAR solution path [TP_LAR_cgd2, FP_LAR_cgd2]=convexLAR(x1, y, model, distname, weight); % LASSO solution path [TP_LASSO_cgd2, FP_LASSO_cgd2]=convexLASSO(x1, y, model, distname, weight); % plot solution paths plot_path(TP_LAR_cgd2, FP_LAR_cgd2, ... 'ConvexLAR solution path for recurrent event data'); plot_path(TP_LASSO_cgd2, FP_LASSO_cgd2, ... 'ConvexLASSO solution path for recurrent event data'); % Weighted ConvexLARS solution paths weight=abs(TP_LAR_cgd2(1:17,18)); % specify weight % LAR solution path [TP_adaLAR_cgd2, FP_adaLAR_cgd2]=convexLAR(x1, y, model, distname, weight); % LASSO solution path [TP_adaLASSO_cgd2, FP_adaLASSO_cgd2]=convexLASSO(x1, y, model, distname, weight); % plot solution paths plot_path(TP_adaLAR_cgd2, FP_LAR_cgd2, ... 'Weighted ConvexLAR solution path for recurrent event data'); plot_path(TP_adaLASSO_cgd2, FP_LASSO_cgd2, ... 'Weighted ConvexLASSO solution path for recurrent event data');
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Panel count data (Bladder data set, Sun and Wei, 2000)
clear; x=dlmread('./data/bladder_x.dat'); y=dlmread('./data/bladder_y.dat'); model='panel'; % specify model distname=''; weight=ones(size(x,2),1); % specify weight % calculate LAR solution path [TP_LAR_bladder, FP_LAR_bladder]=convexLAR(x, y, model, distname, weight); % calculate LASSO solution path [TP_LASSO_bladder, FP_LASSO_bladder]=convexLASSO(x, y, model, distname, weight); % plot solution paths plot_path(TP_LAR_bladder, FP_LAR_bladder, ... 'LAR solution path for panel count data'); plot_path(TP_LASSO_bladder, FP_LASSO_bladder, ... 'LASSO solution path for panel count data');
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Gaussian graphical model (math score data, Mardia et. al., 1979)
clear; x=dlmread('./data/scoreGraph_x.dat'); % calculate LAR solution path [TP_LAR_math, FP_LAR_math]=graphLAR(x); % calculate LASSO solution path [TP_LASSO_math, FP_LASSO_math]=graphLASSO(x); % plot solution paths plot_path(TP_LAR_math, FP_LAR_math, ... 'LAR solution path for graphical model'); plot_path(TP_LASSO_math, FP_LASSO_math, ... 'LASSO solution path for graphical model');
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Ada-boost (WDBC data, Frank and Asuncion, 2010)
clear; % read matrics x, y from the WDBC data set (this data set has the singularity issue) x=dlmread('./data/wdbc.data', ',', 0, 2); x=(x-repmat(mean(x, 1), size(x,1),1))./repmat(std(x, 1), size(x, 1), 1); [temp1, tmp2]=textread('./data/wdbc.data', '%f%s%*[^\n]', 'delimiter', ','); y=zeros(length(tmp2),1); for i=1:length(tmp2) if(strcmp(tmp2(i), 'M')) y(i)=1; elseif(strcmp(tmp2(i),'B')) y(i)=0; else y(i)=-100; end end y1=y*2-1; index=repmat(1:10, 1, 3)'; % index set to classify covariates into 10 groups. Members of the same group share the same numbers. model='ada'; % specify model distname=''; % specify distribution % Calculate GroupConvexLAR-L2 solution path method='grouplarl2'; % specify method [TP_GLARL2_wdbc, FP_GLARL2_wdbc]=convexGLAR(x, y1, model, distname, index, method); [r,c]=find(isnan(TP_GLARL2_wdbc)); TP_GLARL2_wdbc(:,c)=[]; p=(size(TP_GLARL2_wdbc,1)-1)/2; FP_GLARL2_wdbc=FP_GLARL2_wdbc(:,FP_GLARL2_wdbc(p+1,:)<TP_GLARL2_wdbc(p+1,end)); % plot solution paths plot_path(TP_GLARL2_wdbc, FP_GLARL2_wdbc, ... 'GroupLARL2 solution path for WDBC data'); % Calculate GroupConvexLAR-L1 solution path method='grouplarl1'; % specify method [TP_GLARL1_wdbc, FP_GLARL1_wdbc]=convexGLAR(x, y1, model, distname, index, method); [r,c]=find(isnan(TP_GLARL1_wdbc)); TP_GLARL1_wdbc(:,c)=[]; p=(size(TP_GLARL1_wdbc,1)-1)/2; FP_GLARL1_wdbc=FP_GLARL1_wdbc(:,FP_GLARL1_wdbc(p+1,:)<=TP_GLARL1_wdbc(p+1,end)); % plot solution paths plot_path(TP_GLARL1_wdbc, FP_GLARL1_wdbc, ... 'GroupLARL1 solution path for WDBC data'); % Calculate GroupConvexLAR solution path method='grouplar'; % specify method % calculate GroupLAR solution path [TP_GLAR_wdbc, FP_GLAR_wdbc]=convexGLAR(x, y1, model, distname, index, method); [r,c]=find(isnan(TP_GLAR_wdbc)); TP_GLAR_wdbc(:,c)=[]; p=(size(TP_GLAR_wdbc,1)-1)/2; FP_GLAR_wdbc=FP_GLAR_wdbc(:,FP_GLAR_wdbc(p+1,:)<=TP_GLAR_wdbc(p+1,end)); % plot solution paths plot_path(TP_GLAR_wdbc, FP_GLAR_wdbc, ... 'GroupLAR solution path for WDBC data'); % Calculate GroupConvexLASSO solution path method='grouplar'; % specify method % calculate GroupLASSO solution path [TP_GLASSO_wdbc, FP_GLASSO_wdbc]=convexGLASSO(x, y1, model, distname, index, method); [r,c]=find(isnan(TP_GLASSO_wdbc)); TP_GLASSO_wdbc(:,c)=[]; p=(size(TP_GLASSO_wdbc,1)-1)/2; FP_GLASSO_wdbc=FP_GLASSO_wdbc(:,FP_GLASSO_wdbc(p+1,:)<=TP_GLASSO_wdbc(p+1,end)); % plot solution paths plot_path(TP_GLASSO_wdbc, FP_GLASSO_wdbc, ... 'GroupLASSO solution path for WDBC data');
Wei Xiao wxiao0421@gmail.com