fusedLassoProximal {fuser}

Fused lasso optimisation with proximal-gradient method. (Chen et al. 2010)

Description

Fused lasso optimisation with proximal-gradient method. (Chen et al. 2010)

Usage

fusedLassoProximal(X, Y, groups, lambda, gamma, G, mu = 1e-04, tol = 1e-06,
  num.it = 1000, lam.max = NULL, c.flag = FALSE, intercept = TRUE,
  penalty.factors = NULL, conserve.memory = p >= 10000, scaling = TRUE)

Arguments

X

matrix of covariates (n by p)

Y

vector of responses (length n)

groups

vector of group indicators (length n)

lambda

Sparsity hyperparameter (accepts scalar value only)

gamma

Fusion hyperparameter (accepts scalar value only)

G

Matrix of pairwise group information sharing weights (K by K)

mu

Smoothness parameter for proximal optimization

tol

Tolerance for optimization

num.it

Number of iterations

lam.max

Maximal eigenvalue of t(X) %*% X (will be calculate if not provided)

c.flag

Whether to use Rcpp for certain calculations (see Details).

intercept

Whether to include a (group-specific) intercept term.

penalty.factors

Weights for sparsity penalty.

conserve.memory

Whether to calculate XX and XY on the fly, conserving memory at the cost of speed. (True by default iff p >= 10000)

scaling

if TRUE, scale the sum-squared loss for each group by 1/n_k where n_k is the number of samples in group k.

Details

The proximal algorithm uses t(X) %*% X and t(X) %*% Y. The function will attempt to pre-calculate these values to speed up computation. This may not always be possible due to memory restrictions; at present this is only done for p < 10,000. When p > 10,000, crossproducts are calculated explicitly; calculation can be speeded up by using Rcpp code (setting c.flag=TRUE).

Value

A matrix with the linear coefficients for each group (p by k).

Examples

set.seed(123)
# Generate simple heterogeneous dataset
k = 4 # number of groups
p = 100 # number of covariates
n.group = 15 # number of samples per group
sigma = 0.05 # observation noise sd
groups = rep(1:k, each=n.group) # group indicators
# sparse linear coefficients
beta = matrix(0, p, k)
nonzero.ind = rbinom(p*k, 1, 0.025/k) # Independent coefficients
nonzero.shared = rbinom(p, 1, 0.025) # shared coefficients
beta[which(nonzero.ind==1)] = rnorm(sum(nonzero.ind), 1, 0.25)
beta[which(nonzero.shared==1),] = rnorm(sum(nonzero.shared), -1, 0.25)

X = lapply(1:k,
           function(k.i) matrix(rnorm(n.group*p),
                                n.group, p)) # covariates
y = sapply(1:k,
           function(k.i) X[[k.i]] %*% beta[,k.i] +
                           rnorm(n.group, 0, sigma)) # response
X = do.call('rbind', X)

# Pairwise Fusion strength hyperparameters (tau(k,k'))
# Same for all pairs in this example
G = matrix(1, k, k)

# Use L1 fusion to estimate betas (with near-optimal sparsity and
# information sharing among groups)
beta.estimate = fusedLassoProximal(X, y, groups, lambda=0.01, tol=3e-3,
                                   gamma=0.01, G, intercept=FALSE,
                                   num.it=500)