Package 'msda'

Cross-validation for msda

Description

Does k-fold cross-validation for msda, returns a value for lambda.

Usage

cv.msda(x, y, nfolds = 5, lambda = NULL, lambda.opt = "min", ...)

Arguments

x	matrix of predictors, of dimension $N \times p$; each row is an observation vector.
y	response variable. This argument should be a factor for classification.
nfolds	number of folds - default is 5. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3.
lambda	optional user-supplied lambda sequence; default is NULL, and msda chooses its own sequence.
lambda.opt	If choose "min", the smallest lambda that gives minimum cross validation error cvm will be returned. If choose "max", the largest lambda that gives minimum cross validation error cvm will be returned.
...	other arguments that can be passed to msda.

Details

The function runs msda nfolds+1 times; the first to get the lambda sequence, and then the remainder to compute the fit with each of the folds omitted. The average error and standard deviation over the folds are computed.

Value

an object of class cv.msda is returned, which is a list with the ingredients of the cross-validation fit.

lambda	the values of lambda used in the fits.
cvm	the mean cross-validated error - a vector of length length(lambda).
cvsd	estimate of standard error of cvm.
lambda.min	the optimal value of lambda that gives minimum cross validation error cvm.
lambda.1se	the largest value of lambda such that error is within 1 standard error of the minimum.
msda.fit	a fitted msda object for the full data.

Author(s)

Qing Mai <[email protected]>, Yi Yang <[email protected]>, Hui Zou <[email protected]>
Maintainer: Yi Yang <[email protected]>

References

Mai, Q.*, Yang, Y.*, and Zou, H. (2014), "Multiclass Sparse Discriminant Analysis." Submitted to Journal of the American Statistical Association. (* co-first author)

URL: https://github.com/emeryyi/msda

See Also

msda

Examples

data(GDS1615)
x<-GDS1615$x
y<-GDS1615$y
obj.cv<-cv.msda(x=x,y=y,nfolds=5,lambda.opt="max")
lambda.min<-obj.cv$lambda.min
id.min<-which(obj.cv$lambda==lambda.min)
pred<-predict(obj.cv$msda.fit,x)[,id.min]

---

GDS1615 data introduced in Burczynski et al. (2012).

Description

The dataset is a subset of the dataset available on Gene Expression Omnibus with the accession number GDS1615. The original dataset contains 22283 gene expression levels and the disease states of the observed subjects. In Mai, Yang and Zou, the dimension of the original dataset was first reduced to 127 by F-test screening.

Usage

data(GDS1615)

Value

This data frame contains the following:

x	gene expression levels.
y	Disease state that is coded as 1,2,3. 1: normal; 2: ulcerative colitis; 3: Crohn's disease.

References

M. E. Burczynski, R. L Peterson, N. C. Twine, K. A. Zuberek, B. J. Brodeur, L. Casciotti, V. Maganti, P. S. Reddy, A. Strahs, F. Immermann, W. Spinelli, U. Schwertschlag, A. M. Slager, M. M. Cotreau, and A. J. Dorner. (2012), "Molecular classification of crohn's disease and ulcerative colitis patients using transcriptional profiles in peripheral blood mononuclear cells". Journal of Molecular Diagnostics, 8:51–61.

Mai, Q.*, Yang, Y.*, and Zou, H. (2014), "Multiclass Sparse Discriminant Analysis." Submitted to Journal of the American Statistical Association. (* co-first author)

URL: https://github.com/emeryyi/msda

Examples

data(GDS1615)

---

Fits a regularization path for Multi-Class Sparse Discriminant Analysis

Description

Fits a regularization path for Multi-Class Sparse Discriminant Analysis at a sequence of regularization parameters lambda.

Usage

msda(x, y, nlambda = 100, 
lambda.factor = ifelse((nobs - nclass) <= nvars, 0.2, 0.001), 
lambda = NULL, dfmax = nobs, pmax = min(dfmax * 2 + 20, nvars), 
pf = rep(1, nvars), eps = 1e-04, maxit = 1e+06, sml = 1e-06, 
verbose = FALSE, perturb = NULL)

Arguments

x	matrix of predictors, of dimension $N \times p$; each row is an observation vector.
y	response variable. This argument should be a factor for classification.
nlambda	the number of lambda values - default is 100.
lambda.factor	The factor for getting the minimal lambda in lambda sequence, where min(lambda) = lambda.factor * max(lambda). max(lambda) is the smallest value of lambda for which all coefficients are zero. The default depends on the relationship between $N$ (the number of rows in the matrix of predictors) and $p$ (the number of predictors). If $N > p$, the default is 0.0001, close to zero. If $N<p$, the default is 0.2. A very small value of lambda.factor will lead to a saturated fit. It takes no effect if there is user-defined lambda sequence.
lambda	a user supplied lambda sequence. Typically, by leaving this option unspecified users can have the program compute its own lambda sequence based on nlambda and lambda.factor. Supplying a value of lambda overrides this. It is better to supply a decreasing sequence of lambda values than a single (small) value, if not, the program will sort user-defined lambda sequence in decreasing order automatically.
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 $\beta$ enters the model, no matter how many times it exits or re-enters model through the path, it will be counted only once. Default is min(dfmax*1.2,p).
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 exclude).
eps	convergence threshold for coordinate descent. Each inner coordinate descent loop continues until the relative change in any coefficient. Defaults value is 1e-8.
maxit	maximum number of outer-loop iterations allowed at fixed lambda value. Default is 1e6. If models do not converge, consider increasing maxit.
sml
verbose	whether to print out computation progress. The default is FALSE.
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 NULL.

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 (dgCMatrix class, the standard class for sparse numeric matrices in the Matrix package.). To convert it into normal type matrix use as.matrix().
df	the number of nonzero coefficients for each value of lambda.
obj	the fitted value of the objective function for each value of lambda.
dim	dimension of each coefficient matrix at each lambda.
lambda	the actual sequence of lambda values used.
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 <[email protected]>, Yi Yang <[email protected]>, Hui Zou <[email protected]>
Maintainer: Yi Yang <[email protected]>

References

Mai, Q.*, Yang, Y.*, and Zou, H. (2014), "Multiclass Sparse Discriminant Analysis." Submitted to Journal of the American Statistical Association. (* co-first author)

URL: https://github.com/emeryyi/msda

See Also

cv.msda, predict.msda

Examples

data(GDS1615)
x<-GDS1615$x
y<-GDS1615$y
obj <- msda(x = x, y = y)

---

Plot coefficients from a "msda" object

Description

Produces a coefficient profile plot of the coefficient paths for a fitted msda object.

Usage

## S3 method for class 'msda'
plot(x, xvar = c("norm", "lambda"), ...)

Arguments

x	fitted msda model
xvar	the variable on the X-axis. The option "norm" plots the coefficients against the L1-norm of the coefficients, and the option "lambda" plots the coefficient against the log-lambda sequence.
...	other graphical parameters to plot

Details

A coefficient profile plot is produced.

Author(s)

Qing Mai <[email protected]>, Yi Yang <[email protected]>, Hui Zou <[email protected]>
Maintainer: Yi Yang <[email protected]>

References

Mai, Q.*, Yang, Y.*, and Zou, H. (2014), "Multiclass Sparse Discriminant Analysis." Submitted to Journal of the American Statistical Association. (* co-first author)

URL: https://github.com/emeryyi/msda

Examples

data(GDS1615)
x<-GDS1615$x
y<-GDS1615$y
obj <- msda(x = x, y = y)
plot(obj)

---

make predictions from a "msda" object.

Description

This functions predicts class labels from a fitted msda object.

Usage

## S3 method for class 'msda'
predict(object, newx, ...)

Arguments

object	fitted msda model object.
newx	matrix of new values for x at which predictions are to be made. NOTE: newx must be a matrix, predict function does not accept a vector or other formats of newx.
...	Not used. Other arguments to predict.

Value

predicted class label(s) at the entire sequence of the penalty parameter lambda used to create the model.

Author(s)

Qing Mai <[email protected]>, Yi Yang <[email protected]>, Hui Zou <[email protected]>
Maintainer: Yi Yang <[email protected]>

References

Mai, Q.*, Yang, Y.*, and Zou, H. (2014), "Multiclass Sparse Discriminant Analysis." Submitted to Journal of the American Statistical Association. (* co-first author)

URL: https://github.com/emeryyi/msda

See Also

msda

Examples

data(GDS1615)
x<-GDS1615$x
y<-GDS1615$y
obj <- msda(x = x, y = y)
pred<-predict(obj,x)

---