orthopen: Solver for a general problem of the form: min (loss +...

In kevinVervier/orthopen: Learning Matrices with Orthogonal Columns or Disjoint Supports

Description

orthopen

Usage

orthopen(X, Y, lambda = 1, step_size = 0.1, verbose = 0,
  stop_no_improve = 100, max_iter = 1e+06, K = NULL, disjoint = TRUE,
  logistic = FALSE, enet = FALSE)

Arguments

X	MxP observations matrix (features are in columns)
Y	MxT observed output matrix for T different tasks
lambda	a regularization parameter (default 1)
step_size	step for gradient descent (default 0.1)
verbose	option (default 0)
stop_no_improve	number of gradient descent steps without improvment before stopping (default: 100)
max_iter	maximum number of iterations before stopping optimization (default: 1000000)
K	PxP orthogonality constraints matrix (default: diagonal matrix –> no orthogonality constraint)
disjoint	if TRUE add contraints for disjoint supports (default: TRUE)
logistic	if TRUE change loss function to logistic loss (for classification problems)
enet	if TRUE, add a L1 penalization to the L2 penalization, using elastic net formula (single parameter lambda, assuming enet = 0.5*L2 + 0.5*L1)

Value

a list containing three elements

• W: optimal PxT matrix for objective function minimum

• obj: objective function value at W

• imax: number of steps before reaching optimum

Examples

#solve orthogonal columns problem 
# min_W 1/2 norm( X%*%W - Y )^2 + lambda ||W||_orthopen
NVAR=10
NTRAIN=100
T=3
K = matrix(1,nrow=T,ncol=T)
# Generate random data and random model
X <- matrix(rnorm(NTRAIN*NVAR),nrow=NTRAIN,ncol=NVAR)
# Random orthogonal matrix
W <- qr.Q(qr(matrix(rnorm(NVAR*T),nrow=NVAR,ncol=T)))
Y <- X %*% W + matrix(rnorm(NTRAIN*T),nrow=NTRAIN)
set.seed(42)
res <- orthopen(X,Y,lambda = 0.1,K = K,disjoint = FALSE)

kevinVervier/orthopen documentation built on May 20, 2019, 9:07 a.m.