glmnet(x, y, family=c("gaussian","binomial","poisson","multinomial","cox","mgaussian"),
weights, offset=NULL, alpha = 1, nlambda = 100,
lambda.min.ratio = ifelse(nobs"sparseMatrix" as in package Matrix; not yet available for family="cox")family="gaussian",
or family="poisson" (non-negative counts). For
family="binomial" should be either a factor with two levels, or
a two-column matrix of counts or proportions (the second column is
treated as the target class; for a factor, the last level in
alphabetical order is the target class). For
family="multinomial", can be a nc>=2 level factor, or a
matrix with nc columns of counts or proportions.
For either "binomial" or "multinomial", if y is
presented as a vector, it will be coerced into a factor. For
family="cox", y should be a two-column matrix with
columns named 'time' and 'status'. The latter is a binary variable,
with '1' indicating death, and '0' indicating right censored. The
function Surv() in package survival produces such a
matrix. For family="mgaussian", y is a matrix of quantitative responses.nobs that is included in the linear predictor (a nobs x nc matrix for the "multinomial" family). Useful for the "poisson" family (e.g. log of exposure time), or for refining a model by starting at a current fit. Default is NULL. If supplied, then values must also be supplied to the predict function.alpha=1
is the lasso penalty, and alpha=0 the ridge penalty.lambda values - default is 100.lambda, as a fraction of
lambda.max, the (data derived) entry value (i.e. the smallest
value for which all coefficients are zero). The default depends on the
sample size nobs relative to the number of variables
nvars. If nobs > nvars, the default is 0.0001,
close to zero. If nobs < nvars, the default is 0.01.
A very small value of
lambda.min.ratio will lead to a saturated fit in the nobs <
nvars case. This is undefined for
"binomial" and "multinomial" models, and glmnet
will exit gracefully when the percentage deviance explained is almost
1.lambda sequence. Typical usage
is to have the
program compute its own lambda sequence based on
nlambda and lambda.min.ratio. Supplying a value of
lambda overrides this. WARNING: use with care. Do not supply
a single value for lambda (for predictions after CV use predict()
instead). Supply instead
a decreasing sequence of lambda values. glmnet relies
on its warms starts for speed, and its often faster to fit a whole
path than compute a single fit.standardize=TRUE.
If variables are in the same units already, you might not wish to
standardize. See details below for y standardization with family="gaussian".thresh
times the null deviance. Defaults value is 1E-7.nvars, if a partial path is desired.lambda to allow
differential shrinkage. Can be 0 for some variables, which implies
no shrinkage, and that variable is always included in the
model. Default is 1 for all variables (and implicitly infinity for
variables listed in exclude). Note: the penalty factors are
internally rescaled to sum to nvars, and the lambda sequence will
reflect this change.-Inf. Each
of these must be non-positive. Can be presented as a single value
(which will then be replicated), else a vector of length nvarsInf. See lower.limitsfamily="gaussian". The default when nvar<500 is
type.gaussian="covariance", and saves all
inner-products ever computed. This can be much faster than
type.gaussian="naive", which loops through nobs every
time an inner-product is computed. The latter can be far more efficient for nvar >>
nobs situations, or when nvar > 500."Newton" then the exact hessian is used
(default), while "modified.Newton" uses an upper-bound on the
hessian, and can be faster.family="mgaussian"
family, and allows the user to standardize the response variables"grouped" then a grouped lasso penalty
is used on the multinomial coefficients for a variable. This ensures
they are all in our out together. The default is "ungrouped""glmnet","*" , where "*" is
"elnet", "lognet",
"multnet", "fishnet" (poisson), "coxnet" or "mrelnet" for the various types of models.
length(lambda)"elnet", "lognet", "fishnet" and "coxnet" models, a nvars x
length(lambda) matrix of coefficients, stored in sparse column
format ("CsparseMatrix"). For "multnet" and "mgaussian", a list of nc such
matrices, one for each class.lambda values used. When
alpha=0, the largest lambda reported does not quite give the
zero coefficients reported (lambda=inf would in principle). Instead, the
largest lambda for alpha=0.001 is used, and the sequence
of lambda values is derived from this."elnet", this
is the R-square). The deviance calculations incorporate weights if
present in the model. The deviance is defined to be 2*(loglike_sat -
loglike), where loglike_sat is the log-likelihood for the saturated
model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.lambda. For "multnet", this is the number of variables
with a nonzero coefficient for any class."multnet" and "mrelnet" only. A matrix consisting of the
number of nonzero coefficients per classlambda 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 other 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 coefficients for any predictor variables
with zero variance are set to zero for all values of lambda.
The latest two features in glmnet are the family="mgaussian"
family and the type.multinomial="grouped" option 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.print, predict, coef and plot methods, and the cv.glmnet function.# Gaussian
x=matrix(rnorm(100*20),100,20)
y=rnorm(100)
fit1=glmnet(x,y)
print(fit1)
coef(fit1,s=0.01) # extract coefficients at a single value of lambda
predict(fit1,newx=x[1:10,],s=c(0.01,0.005)) # make predictions
#multivariate gaussian
y=matrix(rnorm(100*3),100,3)
fit1m=glmnet(x,y,family="mgaussian")
plot(fit1m,type.coef="2norm")
#binomial
g2=sample(1:2,100,replace=TRUE)
fit2=glmnet(x,g2,family="binomial")
#multinomial
g4=sample(1:4,100,replace=TRUE)
fit3=glmnet(x,g4,family="multinomial")
fit3a=glmnet(x,g4,family="multinomial",type.multinomial="grouped")
#poisson
N=500; p=20
nzc=5
x=matrix(rnorm(N*p),N,p)
beta=rnorm(nzc)
f = x[,seq(nzc)]%*%beta
mu=exp(f)
y=rpois(N,mu)
fit=glmnet(x,y,family="poisson")
plot(fit)
pfit = predict(fit,x,s=0.001,type="response")
plot(pfit,y)
#Cox
set.seed(10101)
N=1000;p=30
nzc=p/3
x=matrix(rnorm(N*p),N,p)
beta=rnorm(nzc)
fx=x[,seq(nzc)]%*%beta/3
hx=exp(fx)
ty=rexp(N,hx)
tcens=rbinom(n=N,prob=.3,size=1)# censoring indicator
y=cbind(time=ty,status=1-tcens) # y=Surv(ty,1-tcens) with library(survival)
fit=glmnet(x,y,family="cox")
plot(fit)
# Sparse
n=10000;p=200
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)
iz=sample(1:(n*p),size=n*p*.85,replace=FALSE)
x[iz]=0
sx=Matrix(x,sparse=TRUE)
inherits(sx,"sparseMatrix")#confirm that it is sparse
beta=rnorm(nzc)
fx=x[,seq(nzc)]%*%beta
eps=rnorm(n)
y=fx+eps
px=exp(fx)
px=px/(1+px)
ly=rbinom(n=length(px),prob=px,size=1)
system.time(fit1<-glmnet(sx,y))
system.time(fit2n<-glmnet(x,y))
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