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glmnet.m
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glmnet.m
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function fit = glmnet(x, y, family, options)
%--------------------------------------------------------------------------
% glmnet.m: fit an GLM with lasso or elasticnet regularization
%--------------------------------------------------------------------------
%
% DESCRIPTION:
% Fit a generalized linear model via penalized maximum likelihood. The
% regularization path is computed for the lasso or elasticnet penalty
% at a grid of values for the regularization parameter lambda. Can deal
% with all shapes of data, including very large sparse data matrices.
% Fits linear, logistic and multinomial, Poisson, and Cox regression
% models.
%
% USAGE:
% fit = glmnet(x, y)
% fit = glmnet(x, y, family)
% fit = glmnet(x, y, family, options)
% (Use empty matrix [] to apply the default value, eg. fit = glmnet(x,
% y, [], options))
%
%
% EXTERNAL FUNCTIONS:
% options = glmnetSet; provided with glmnet.m
%
% INPUT ARGUMENTS:
% x Input matrix, of dimension nobs x nvars; each row is an
% observation vector. Can be in sparse matrix format.
% y Response variable. Quantitative (column vector) for family =
% 'gaussian', or family = 'poisson'(non-negative counts). For
% family = 'binomial' should be either a column vector with two
% levels, or a two-column matrix of counts or proportions. For
% family = 'multinomial', can be a column vector of nc>=2
% levels, or a matrix with nc columns of counts or proportions.
% For family = 'cox', y should be a two-column matrix with the
% first column for time and the second for status. The latter
% is a binary variable, with 1 indicating death, and 0
% indicating right censored. For family = 'mgaussian', y is a
% matrix of quantitative responses.
% family Reponse type. (See above). Default is 'gaussian'.
% options A structure that may be set and altered by glmnetSet.
% Default values for some often used options:
% options.alpha = 1.0 (elastic-net mixing parameter)
% options.nlambda = 100 (number of lambda values)
% options.lambda depends on data, nlambda and
% lambda_min(user spplied lambda sequence)
% options.standardize = true (variable standardization)
% options.weights = all ones vector (observation weights)
% For more details, type help glmnetSet.
%
% OUTPUT ARGUMENTS:
% fit A structure.
% fit.a0 Intercept sequence of length length(fit.lambda).
% fit.beta For "elnet" and "lognet" models, a nvars x length(lambda)
% matrix of coefficients. For "multnet", a list of nc such
% matrices, one for each class.
% fit.lambda The actual sequence of lambda values used.
% fit.dev The fraction of (null) deviance explained (for "elnet", this
% is the R-square).
% fit.nulldev Null deviance (per observation).
% fit.df The number of nonzero coefficients for each value of lambda.
% For "multnet", this is the number of variables with a nonzero
% coefficient for any class.
% fit.dfmat For "multnet" only. A matrix consisting of the number of
% nonzero coefficients per class.
% fit.dim Dimension of coefficient matrix (ices).
% fit.npasses Total passes over the data summed over all lambda values.
% fit.offset a logical variable indicating whether an offset was included
% in the model.
% fit.jerr Error flag, for warnings and errors (largely for internal
% debugging).
% fit.class Type of regression - internal usage.
% fit.call a cell including the names of all the input variables in the
% parent environment.
%
% DETAILS:
% The sequence of models implied by lambda is fit by coordinate descent.
% For family='gaussian' this is the lasso sequence if alpha=1, else it
% is the elasticnet sequence. For the other families, this is a lasso or
% elasticnet regularization path for fitting the generalized linear
% regression paths, by maximizing the appropriate penalized
% log-likelihood (partial likelihood for the 'cox' model). Sometimes the
% sequence is truncated before nlambda values of lambda have been used,
% because of instabilities in the inverse link functions near a
% saturated fit. glmnet(...,family='binomial') fits a traditional
% logistic regression model for the log-odds.
% glmnet(...,family='multinomial') fits a symmetric multinomial model,
% where each class is represented by a linear model (on the log-scale).
% The penalties take care of redundancies. A two-class 'multinomial'
% model will produce the same fit as the corresponding 'binomial' model,
% except the pair of coefficient matrices will be equal in magnitude and
% opposite in sign, and half the 'binomial' values. Note that the
% objective function for 'gaussian' is
%
% 1/2 RSS / nobs + lambda * penalty,
%
% and for the logistic models it is
%
% -loglik / nobs + lambda * penalty.
%
% Note also that for 'gaussian', glmnet standardizes y to have unit
% variance before computing its lambda sequence (and then unstandardizes
% the resulting coefficients); if you wish to reproduce/compare results
% with other software, best to supply a standardized y. The latest two
% features in glmnet are the family='mgaussian' family and the
% mtype='grouped' in options for multinomial fitting. The former
% allows a multi-response gaussian model to be fit, using a "group
% -lasso" penalty on the coefficients for each variable. Tying the
% responses together like this is called "multi-task" learning in some
% domains. The grouped multinomial allows the same penalty for the
% family='multinomial' model, which is also multi-responsed. For both of
% these the penalty on the coefficient vector for variable j is
%
% (1-alpha)/2 * ||beta_j||_2^2 + alpha * ||beta_j||_2
%
% When alpha=1 this is a group-lasso penalty, and otherwise it mixes
% with quadratic just like elasticnet.
%
% LICENSE: GPL-2
%
% DATE: 30 Aug 2013
%
% AUTHORS:
% Algorithm was designed by Jerome Friedman, Trevor Hastie and Rob Tibshirani
% Fortran code was written by Jerome Friedman
% R wrapper (from which the MATLAB wrapper was adapted) was written by Trevor Hasite
% The original MATLAB wrapper was written by Hui Jiang (14 Jul 2009),
% and was updated and is maintained by Junyang Qian (30 Aug 2013) junyangq@stanford.edu,
% Department of Statistics, Stanford University, Stanford, California, USA.
%
% REFERENCES:
% Friedman, J., Hastie, T. and Tibshirani, R. (2008) Regularization Paths for Generalized Linear Models via Coordinate Descent,
% http://www.jstatsoft.org/v33/i01/
% Journal of Statistical Software, Vol. 33(1), 1-22 Feb 2010
%
% Simon, N., Friedman, J., Hastie, T., Tibshirani, R. (2011) Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent,
% http://www.jstatsoft.org/v39/i05/
% Journal of Statistical Software, Vol. 39(5) 1-13
%
% Tibshirani, Robert., Bien, J., Friedman, J.,Hastie, T.,Simon, N.,Taylor, J. and Tibshirani, Ryan. (2010) Strong Rules for Discarding Predictors in Lasso-type Problems,
% http://www-stat.stanford.edu/~tibs/ftp/strong.pdf
% Stanford Statistics Technical Report
%
% SEE ALSO:
% glmnetPrint, glmnetPlot, glmnetCoef, glmnetPredict,
% glmnetSet, glmnetControl and cvglmnet.
%
% EXAMPLES:
% % Gaussian
% x=randn(100,20);
% y=randn(100,1);
% fit1 = glmnet(x,y);
% glmnetPrint(fit1);
% glmnetPredict(fit1,[],0.01,'coef') %extract coefficients at a single value of lambda
% glmnetPredict(fit1,x(1:10,:),[0.01,0.005]') %make predictions
%
% % Multivariate Gaussian:
% y=randn(100,3);
% fit1m=glmnet(x,y,'mgaussian');
% glmnetPlot(fit1m,[],[],'2norm');
%
% % Binomial:
% g2=randsample(2,100,true);
% fit2=glmnet(x,g2,'binomial');
%
% % Multinomial:
% g4=randsample(4,100,true);
% fit3=glmnet(x,g4,'multinomial');
% opts=struct('mtype','grouped');
% fit3a=glmnet(x,g4,'multinomial',opts);
%
% % Poisson:
% N=500; p=20;
% nzc=5;
% x=randn(N,p);
% beta=randn(nzc,1);
% f=x(:,1:nzc) * beta;
% mu=exp(f);
% y=poissrnd(mu,N,1);
% fit=glmnet(x,y,'poisson');
% glmnetPlot(fit);
% pfit=glmnetPredict(fit,x,0.001,'response');
% plot(pfit,y,'o');
%
% % Cox:
% N=1000; p=30;
% nzc=p/3;
% x=randn(N,p);
% beta=randn(nzc,1);
% fx=x(:,1:nzc)*beta/3;
% hx=exp(fx);
% ty=exprnd(1./hx,N,1);
% tcens=binornd(1,0.3,N,1);
% y=cat(2,ty,1-tcens);
% fit=glmnet(x,y,'cox');
% glmnetPlot(fit);
%
% % Sparse:
% n=10000;p=200;
% nzc=fix(p/10);
% x=randn(n,p);
% iz=randsample(n*p,n*p*0.85,false);
% x(iz)=0;
% sx=sparse(x);
% beta=randn(nzc,1);
% fx=x(:,1:nzc)*beta;
% eps=randn(n,1);
% y=fx+eps;
% px=exp(fx);
% px=px./(1+px);
% ly=binornd(1,px,length(px),1);
% tic;
% fit1=glmnet(sx,y);
% toc;
% tic;
% fit2n=glmnet(x,y);
% toc;
%
% DEVELOPMENT:
% 14 Jul 2009: Original version of glmnet.m written.
% 30 Aug 2013: Updated glmnet.m with more options and more models
% (multi-response Gaussian, cox and Poisson models) supported.
% 29 Dec 2013: Fixed a bug in the return value of CVerr.fit_preval,
% pointed out by Leon Peshkin from Harvard University.
%
% OLDER UPDATES:
% 26 Jan 2010: Fixed a bug in the description of y, pointed out by
% Peter Rijnbeek from Erasmus University.
% 09 Mar 2010: Fixed a bug of printing "ka = 2", pointed out by
% Ramon Casanova from Wake Forest University.
% 25 Mar 2010: Fixed a bug when p > n in multinomial fitting, pointed
% out by Gerald Quon from University of Toronto
% 25 Jul 2010: Check for input matrix format and size
% 27 Sep 2010: Fixed a bug of undefined "df" in multinomial fitting,
% pointed by Jeff Howbert from Insilicos.
if nargin < 2
error('more input arguments needed.');
end
if nargin < 3 || isempty(family)
family = 'gaussian';
end
if nargin < 4 || isempty(options)
options = glmnetSet;
end
%Get the names of input variables
out_x = inputname(1); out_y = inputname(2);
out_family = mat2str([]); out_options = mat2str([]);
if nargin > 2
if ~isempty(inputname(3))
out_family = inputname(3);
else
out_family = family;
end
end
if nargin > 3
if ~isempty(inputname(4))
out_options = inputname(4);
end
end
%match the family, abbreviation allowed
fambase = {'gaussian','binomial','poisson','multinomial','cox','mgaussian'};
famind = find(strncmp(family,fambase,length(family)),1);
if isempty(famind)
error('family should be one of ''gaussian'', ''binomial'', ''poisson'', ''multinomial'', ''cox'', ''mgaussian''');
else
family = fambase{famind};
end
% Prepare parameters
options = glmnetSet(options);
if (options.alpha > 1)
warning('alpha >1; set to 1');
options.alpha = 1;
end
if (options.alpha < 0)
warning('alpha <0; set to 0');
options.alpha = 0;
end
parm = options.alpha;
nlam = options.nlambda;
[nobs,nvars] = size(x);
weights = options.weights;
if isempty(weights)
weights = ones(nobs,1);
else
if (length(weights) ~= nobs)
error('number of elements in weights (%d) not equal to the number of rows of x (%d)',length(weights),nobs);
end
end
nrowy = size(y, 1);
if (nrowy ~= nobs)
error('number of observations in y (%d) not equal to the number of rows of x (%d)',nrowy,nobs);
end
ne = options.dfmax;
if isempty(ne)
ne = nvars + 1;
end
nx = options.pmax;
if isempty(nx)
nx = min(ne * 2 + 20, nvars);
end
exclude = options.exclude;
if ~isempty(exclude)
exclude = unique(exclude);
if ~all(exclude > 0 & exclude <= nvars)
error('Some excluded variables out of range');
end
jd = [length(exclude); exclude];
else
jd = 0;
end
vp = options.penalty_factor;
if isempty(vp)
vp = ones(1,nvars);
end
inparms = glmnetControl();
cl = options.cl;
if any(cl(1,:) > 0)
error ('The lower bound should be non-positive');
end
if any(cl(2,:) < 0)
error ('The lower bound should be non-negative');
end
cl(1,cl(1,:)==-Inf) = -inparms.big;
cl(2,cl(2,:)==Inf) = inparms.big;
if (size(cl,2) < nvars)
if (size(cl,2) == 1)
cl = cl * ones(1,nvars);
else
error('Require length 1 or nvars lower and upper limits');
end
else
cl = cl(:,1:nvars);
end
exit_rec = 0;
if (any(cl(:)==0))
fdev = inparms.fdev;
if (fdev ~= 0)
optset.fdev = 0;
glmnetControl(optset);
exit_rec = 1;
end
end
isd = double(options.standardize);
intr = double(options.intr);
if (intr == true) && (strcmp(family, 'cox'))
warning('Cox model has no intercept');
end
jsd = options.standardize_resp;
thresh = options.thresh;
lambda = options.lambda;
lambda_min = options.lambda_min;
if isempty(lambda_min)
if nobs < nvars
lambda_min = 0.01;
else
lambda_min = 1e-4;
end
end
lempty = isempty(lambda);
if lempty
if (lambda_min >= 1)
error('lambda_min should be less than 1');
end
flmin = lambda_min;
ulam = 0.0;
else
flmin = 1.0;
if any(lambda < 0)
error ('lambdas should be non-negative');
end
ulam = sort(lambda,'descend');
nlam = length(lambda);
end
maxit = options.maxit;
gtype = options.gtype;
if isempty(gtype)
if (nvars < 500)
gtype = 'covariance';
else
gtype = 'naive';
end
end
ltype = options.ltype;
indl = find(strncmp(ltype,{'Newton','modified.Newton'},length(ltype)),1);
if (isempty(indl))
error('ltype should be one of ''Newton'', ''modified.Newton''');
else
kopt = indl - 1;
end
if strcmp(family,'multinomial')
mtype = options.mtype;
indm = find(strncmp(mtype,{'ungrouped','grouped'},length(mtype)),1);
if (isempty(indm))
error('mtype should be one of ''ungrouped'', ''grouped''');
else
if (indm == 2)
kopt = 2;
end
end
end
offset = options.offset;
is_sparse = false;
if issparse(x)
is_sparse = true;
[irs, jcs, x] = find(x);
pcs = [0;cumsum(histc(jcs, 1:nvars))] + 1;
else
irs = []; pcs = [];
end
if issparse(y)
y = full(y);
end
switch family
case 'gaussian'
fit = elnet(x,is_sparse,irs,pcs,y,weights,offset,gtype,parm,lempty,...
nvars,jd,vp,cl,ne,nx,nlam,flmin,ulam,thresh,isd,intr,maxit,family);
case {'binomial', 'multinomial'}
fit = lognet(x,is_sparse,irs,pcs,y,weights,offset,parm,nobs,nvars,...
jd,vp,cl,ne,nx,nlam,flmin,ulam,thresh,isd,intr,maxit,kopt,family);
case 'cox'
fit = coxnet(x,is_sparse,irs,pcs,y,weights,offset,parm,nobs,nvars,...
jd,vp,cl,ne,nx,nlam,flmin,ulam,thresh,isd,maxit,family);
case 'mgaussian'
fit = mrelnet(x,is_sparse,irs,pcs,y,weights,offset,parm,nobs,nvars,...
jd,vp,cl,ne,nx,nlam,flmin,ulam,thresh,isd,jsd,intr,maxit,family);
case 'poisson'
fit = fishnet(x,is_sparse,irs,pcs,y,weights,offset,parm,nobs,nvars,...
jd,vp,cl,ne,nx,nlam,flmin,ulam,thresh,isd,intr,maxit,family);
end
fit.call = {out_x, out_y, out_family, out_options};
if (exit_rec == 1)
optset.fdev = fdev;
glmnetControl(optset);
end
%------------------------------------------------------------------
% End function glmnet
%------------------------------------------------------------------