Revision

**49cb69c5a18fdb262964fbfeb47ab2099eb32c5c**authored by Wesley Tansey on**03 May 2018, 19:46:59 UTC**, committed by Wesley Tansey on**03 May 2018, 19:46:59 UTC** ADMM_cholcache.R

```
# Fits the weighted fused lasso by ADMM where D is the discrete difference operator on a graph
# D is a sparse matrix of class 'dgCMatrix' [package "Matrix"]
fit_graphfusedlasso_cholcache = function(y, lambda, D, chol_factor = NULL, weights=NULL, initial_values = NULL, iter_max = 10000, rel_tol = 1e-4, alpha=1.0, inflate=2, adaptive=FALSE) {
require(Matrix)
n = length(y)
m = nrow(D)
a = 2*lambda # step-size parameter
if(missing(weights)) {
weights = rep(1, n)
}
# Check if we need a Cholesky decomp of system involving graph Laplacian
if(missing(chol_factor)) {
L = Matrix::crossprod(D)
chol_factor = Matrix::Cholesky(L + Matrix::Diagonal(n))
}
# Initialize primal and dual variables from warm start
if(missing(initial_values)) {
x = rep(0, n) # likelihood term
z = rep(0, n) # slack variable for likelihood
r = rep(0, m) # penalty term
s = rep(0, m) # slack variable for penalty
u_dual = rep(0,n) # scaled dual variable for constraint x = z
t_dual = rep(0,m) # scaled dual variable for constraint r = s
} else {
x = initial_values$x
z = initial_values$z
r = initial_values$r
s = initial_values$s
t_dual = initial_values$t_dual
u_dual = initial_values$u_dual
}
primal_trace = NULL
dual_trace = NULL
converged = FALSE
counter = 0
while(!converged & counter < iter_max) {
# Update x
x = {weights * y + a*(z - u_dual)}/{weights + a}
x_accel = alpha*x + (1-alpha)*z
# Update constraint term r
arg = s - t_dual
if(adaptive) {
local_lambda = 1/{1+(lambda)*abs(arg)} # Minimax-concave penalty instead?
} else {
local_lambda = lambda
}
r = softthresh(arg, local_lambda/a)
r_accel = alpha*r + (1-alpha)*s
# Projection to constraint set
arg = x_accel + u_dual + Matrix::crossprod(D, r_accel + t_dual)
z_new = drop(Matrix::solve(chol_factor, arg))
s_new = as.numeric(D %*% z_new)
dual_residual_u = a*(z_new - z)
dual_residual_t = a*(s_new - s)
z = z_new
s = s_new
# Dual update
primal_residual_x = x_accel - z
primal_residual_r = r_accel - s
u_dual = u_dual + primal_residual_x
t_dual = t_dual + primal_residual_r
# Check convergence
primal_resnorm = sqrt(mean(c(primal_residual_x, primal_residual_r)^2))
dual_resnorm = sqrt(mean(c(dual_residual_u, dual_residual_t)^2))
if(dual_resnorm < rel_tol && primal_resnorm < rel_tol) {
converged=TRUE
}
primal_trace = c(primal_trace, primal_resnorm)
dual_trace = c(dual_trace, dual_resnorm)
counter = counter+1
# Update step-size parameter based on norm of primal and dual residuals
if(primal_resnorm > 5*dual_resnorm) {
a = inflate*a
u_dual = u_dual/inflate
t_dual = t_dual/inflate
} else if(dual_resnorm > 5*primal_resnorm) {
a = a/inflate
u_dual = inflate*u_dual
t_dual = inflate*t_dual
}
}
list(x=x, r=r, z=z, s=s, u_dual=u_dual, t_dual=t_dual,
primal_trace = primal_trace, dual_trace=dual_trace, counter=counter)
}
```

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