Prediction of primary cancer site based on microRNA measurements, see Modeling tissue contamination to improve molecular identification of the primary tumor site of metastases for more details.
Load data containing N samples and p features (covariates):
x <- # load design matrix (of size N x p) classes <- # load class labels (a vector of size N)
For the purpose of this tutorial we will load a data set consisting of microRNA normalized expression measurements of primary cancer samples.
data(PrimaryCancers) x[1:5,1:5] dim(x) table(classes)
Hence, p = 384, N = 165 and the number of classes K = 9, this implies that the multinomial classification model has 9*(384+1) = 3465 parameters.
Let us take out a small test set:
idx <- 1:10 x.test <- x[idx,] x <- x[-idx,] classes.test <- classes[idx] classes <- classes[-idx]
lambda (fraction of lambda.max) and
alpha = 1 for lasso,
alpha = 0 for group lasso and
alpha in the range (0,1) for sparse group lasso.
msgl::cv to estimate the error for each lambda in a sequence decreasing from the data derived lambda.max to
lambda * lambda.max.
Lambda.max is the lambda at which the first penalized parameter becomes non-zero.
lambda will take longer to fit and include more features.
The following code will run a 10 fold cross validation for each lambda value in
the lambda sequence using 2 parallel units (using the foreach and doParallel packages.
cl <- makeCluster(2) registerDoParallel(cl) fit.cv <- msgl::cv(x, classes, fold = 10, alpha = 0.5, lambda = 0.1, use_parallel = TRUE) stopCluster(cl)
We have now cross validated the models corresponding to the lambda values, one model for each lambda value. We can summarize the validation as follows.
Hence, the best model is obtained using lambda index
r best_model(fit.cv) and it has a cross validation error of
r round(Err(fit.cv)[best_model(fit.cv)],2). The expected number of selected features is
r colMeans(features_stat(fit.cv))[best_model(fit.cv)] and the expected number of parameters is
Use msgl to fit a final model.
fit <- msgl::fit(x, classes, alpha = 0.5, lambda = 0.1)
As we saw in the previous step the model with index
r best_model(fit.cv) had the best cross validation error, we may take a look at the included features using the command:
features(fit)[[best_model(fit.cv)]] # Non-zero features in best model
r length(features(fit)[[best_model(fit.cv)]]) features are included in the model, this is close to the expected number based on the cross validation estimate.
The sparsity structure of the parameters belonging to these
r length(features(fit)[[best_model(fit.cv)]]) features may be viewed using
We may also take a look at the estimate parameters (or coefficients)
coef(fit, best_model(fit.cv))[,1:5] # First 5 non-zero parameters of best model
If we count the total number of non-zero parameters in the model we get in this case
r sum(parameters(fit)[[best_model(fit.cv)]]), which is close to the expected based on the cross validation estimate.
Load test data containing M samples and p features.
x.test <- # load matrix with test data (of size M x p)
Use the final model to predict the classes of the M samples in
res <- predict(fit, x.test) res$classes[,best_model(fit.cv)] # Classes predicted by best model classes.test # True classes
We may also get the estimated probabilities for each of the classes
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