npmr-package | R Documentation |
As an alternative to an l1- or l2-penalty on multinomial logistic regression, this package fits multinomial regression with a penalty on the nuclear norm of the fitted regression coefficient matrix. The result is often a matrix of reduced rank, leveraging structure among the response classes so that the likelihood of one class informs the likelihood of other classes. Proximal gradient descent is used to solve the NPMR optimization problem.
The primary functions in the package are npmr
, which solves
nuclear penalized multinomial regression for a sequence of input values for the
regularization parameter lambda, and cv.npmr
, which chooses the
optimal value of the regularization parameter lambda via cross validation. Both
npmr
and cv.npmr
have predict and plot methods.
Scott Powers, Trevor Hastie, Rob Tibshirani
Maintainer: Scott Powers <sspowers@stanford.edu>
Scott Powers, Trevor Hastie and Rob Tibshirani (2016). “Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball.” In prep.
# Fit NPMR to simulated data
K = 5
n = 1000
m = 10000
p = 10
r = 2
# Simulated training data
set.seed(8369)
A = matrix(rnorm(p*r), p, r)
C = matrix(rnorm(K*r), K, r)
B = tcrossprod(A, C) # low-rank coefficient matrix
X = matrix(rnorm(n*p), n, p) # covariate matrix with iid Gaussian entries
eta = X
P = exp(eta)/rowSums(exp(eta))
Y = t(apply(P, 1, rmultinom, n = 1, size = 1))
# Simulate test data
Xtest = matrix(rnorm(m*p), m, p)
etatest = Xtest
Ptest = exp(etatest)/rowSums(exp(etatest))
Ytest = t(apply(Ptest, 1, rmultinom, n = 1, size = 1))
# Fit NPMR for a sequence of lambda values without CV:
fit2 = npmr(X, Y, lambda = exp(seq(7, -2)))
# Print the NPMR fit:
fit2
# Produce a biplot:
plot(fit2, lambda = 20)
# Compute mean test error using the predict function (for each value of lambda):
getloss = function(pred, Y) {
-mean(log(rowSums(Y*pred)))
}
apply(predict(fit2, Xtest), 3, getloss, Ytest)
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