match_support: Match datasets

In jagterberg/nonparGraphTesting: Nonparametric Testing for Random Graphs

Description

Function to iterate over a decreasing sequence of lambdas, the penalization parameters. If lambda is big, the function is more concave, so we iterate, starting from Lambda = .5, and decreasing each time by alpha. This method takes longer, but is more likely to converge to the true solution, since we start from a more concave problem and iteratively solve it by setting lambda = alpha * lambda, for alpha in (0,1).

Usage

match_support(X, Y, Q = NULL, lambda_init = 0.5, lambda_final = 0.01,
  alpha = 0.95, eps = 0.01, numReps = 100, eps_OT = 0.01,
  p = dim(X)[2], q = 0)

Arguments

X	an n x d dataset of vectors
Y	an m x d dataset of vectors
Q	an initial guess
lambda_init	the initial value of lambda for penalization
lambda_final	For termination
alpha	the parameter for which lambda is multiplied by
eps	the tolerance for the iterative optimal transport problem
numReps	the number of reps for each subiteration
eps_OT	the tolerance for the individual optimal transport problem
p	the dimension of the positive component
q	the dimension of the negative component

Value

a list of the final orthogonal matrix and the assignment matrix

Examples

library(rstiefel)
set.seed(2030)
X <- matrix(rnorm(100,1,.2),ncol= 4)
Y <- rbind(X,X)
W <- rustiefel(4,4)
Y <- Y %*% W
test <- match_support(X,Y,numReps = 10,Q = diag(c(1,-1,-1,1)))
#cheating a bit by starting with Q with the diagonals equal to
# the sign of the true matrix
# others have pointed out that initializing Q at all 2^d sign matrices ( diagonal matrices
 # whose entries are plus or minus one) might have better global
 # convergence
set.seed(2010)
X <- matrix(rnorm(100,.2,.02),ncol= 5)
Y <- rbind(X,X)
W <- rustiefel(5,5)
Y <- Y %*% W
test2 <- match_support(X,Y)
norm(test2$Q - W)

jagterberg/nonparGraphTesting documentation built on Feb. 4, 2022, 1:31 a.m.