HSDiC_ADMM: Homogeneity Detection Incorporating Prior Constraint...

In HSDiC: Homogeneity and Sparsity Detection Incorporating Prior Constraint Information

Description

simultaneous homogeneity detection and variable selection incorporating prior constraint by ADMM algorithm. The problem turn to solving quadratic programming problems of the form min(-d^T b + 1/2 b^T D b) with the constraints A^T b >= b_0. The penalty is the pairwise fusion with p(p-1)/2 number of penalties.

Usage

HSDiC_ADMM(X, Y, A.eq, A.ge, A.lbs, A.ubs, b.eq, b.ge, b.lbs, b.ubs,
  penalty = c("MCP", "SCAD", "adlasso", "lasso"), lambda2,
  admmScale1 = 1/nrow(X), admmScale2 = 1, admmAbsTol = 1e-04,
  admmRelTol = 1e-04, nADMM = 2000, admmVaryScale = FALSE)

Arguments

X	n-by-p design matrix.
Y	n-by-1 response matrix.
A.eq	equality constraint matrix.
A.ge	inequality constraint matrix.
A.lbs	low-bounds matrix on variables, see examples.
A.ubs	upper-bounds matrix on variables, see examples.
b.eq	equality constraint vector.
b.ge	inequality constraint vector.
b.lbs	low-bounds on variables, see details.
b.ubs	upper-bounds on variables, see details.
penalty	The penalty to be applied to the model. Either "lasso" (the default), "SCAD", or "MCP".
lambda2	penalty tuning parameter for thresholding function.
admmScale1	first ADMM scale parameter, 1/nrow(X) is default.
admmScale2	second ADMM scale parameter, 1 is default.
admmAbsTol	absolute tolerance for ADMM, 1e-04 is default.
admmRelTol	relative tolerance for ADMM, 1e-04 is default.
nADMM	maximum number of iterations for ADMM, 2000 is default.
admmVaryScale	dynamically chance the ADMM scale parameter, FALSE is default

Value

betahat	solution vector.
stats.ADMM_inters	number of iterations.

References

'Pairwise Fusion Approach Incorporating Prior Constraint Information' by Yaguang Li

See Also

solve.QP

Examples

## data generation
set.seed(111)
n=100
p=50
r <- 1 #0.5, 0.8, 1

beta <- r*c(sample(rep(1:2, each = 10)), rep(0,10), -sample(rep(1:2, each = 10)) )
X <- matrix(rnorm(n*p),nrow = n)
sigma = 1
Y <- X %*% beta + sigma * rnorm(n, 0, 1)


# equalities
A.eq <- rbind(rep(1,p))
b.eq <- c(0)

# inequalities
A.ge <- diag( c(rep(1,30), rep(-1,20)) )
b.ge <- rep(0,p)

# lower-bounds
A.lbs <- diag(1, p)
b.lbs <- rep(-2, p)

# upper-bounds on variables
A.ubs <- diag(-1, p)
b.ubs <- rep(-2, p)

ptm <- proc.time()
fit <- HSDiC_ADMM(X, Y, A.eq, A.ge, A.lbs, A.ubs, b.eq, b.ge, b.lbs, b.ubs,
                 penalty = "adlasso", lambda2 = 0.8, admmScale2 = 1)
proc.time() - ptm

## table(round(fit$beta,1))

plot(beta, type="p", pch = 20, cex = 1)
points(fit$beta, col = 3)

HSDiC documentation built on May 1, 2019, 8:05 p.m.