Fits a regularization path for MultiClass Sparse Discriminant Analysis
Description
Fits a regularization path for MultiClass Sparse Discriminant Analysis at a sequence of regularization parameters lambda.
Usage
1 2 3 4 5 
Arguments
x 
matrix of predictors, of dimension N*p; each row is an observation vector. 
y 
response variable. This argument should be a factor for classification. 
nlambda 
the number of 
lambda.factor 
The factor for getting the minimal lambda in 
lambda 
a user supplied 
dfmax 
limit the maximum number of variables in the model. Useful for very large p, if a partial path is desired. Default is n. 
pmax 
limit the maximum number of variables ever to be nonzero. For example once β enters the model, no matter how many times it exits or reenters model through the path, it will be counted only once. Default is 
pf 
L1 penalty factor of length p. Separate L1 penalty weights can be applied to each coefficient of theta to allow
differential L1 shrinkage. Can be 0 for some variables, which implies
no L1 shrinkage, and results in that variable always being included in the
model. Default is 1 for all variables (and implicitly infinity for
variables listed in 
eps 
convergence threshold for coordinate descent. Each inner
coordinate descent loop continues until the relative change in any
coefficient. Defaults value is 
maxit 
maximum number of outerloop iterations allowed at fixed lambda value. Default is 1e6. If models do not converge, consider increasing 
sml 

verbose 
whether to print out computation progress. The default is 
perturb 
a scalar number. If it is specified, the number will be added to each diagonal element of the sigma matrix as perturbation. The default is 
Details
Note that for computing speed reason, if models are not converging or running slow, consider increasing eps
and sml
, or decreasing
nlambda
, or increasing lambda.factor
before increasing
maxit
. Users can also reduce dfmax
to limit the maximum number of variables in the model.
Value
An object with S3 class msda
.
theta 
a list of length(lambda) for fitted coefficients theta, each one corresponding to one lambda value, each stored as a sparse matrix ( 
df 
the number of nonzero coefficients for each value of

obj 
the fitted value of the objective function for each value of

dim 
dimension of each coefficient matrix at each lambda. 
lambda 
the actual sequence of 
x 
matrix of predictors. 
y 
response variable. 
npasses 
total number of iterations (the most inner loop) summed over all lambda values 
jerr 
error flag, for warnings and errors, 0 if no error. 
sigma 
estimated sigma matrix. 
delta 
estimated delta matrix. delta[k] = mu[k]mu[1]. 
mu 
estimated mu vector. 
prior 
prior probability that y belong to class k, estimated by mean(y that belong to k). 
call 
the call that produced this object 
Author(s)
Qing Mai <mai@stat.fsu.edu>, Yi Yang <yiyang@umn.edu>, Hui Zou <hzou@stat.umn.edu>
Maintainer: Yi Yang <yiyang@umn.edu>
References
Mai, Q.*, Yang, Y.*, and Zou, H. (2014), "Multiclass Sparse Discriminant Analysis." Submitted to Journal of the American Statistical Association. (* cofirst author)
URL: https://github.com/emeryyi/msda
See Also
cv.msda
, predict.msda
Examples
1 2 3 4 