kernel_density_outliers <- function(traintrain_dists,
traintest_dists=NULL, trainrandom_dists=NULL, outlier_fraction=0,
kernel='gaussian', kernel_h0=1,estimate_kernel_h0=T,bandwidth=NULL,
pval_cutoff=NULL,use_random_trees=T,pathbase=".",
use_iterative_outliers=F, normalize_kernels=F,
normalize_preds=T,kernel_h0_step=0.1,starting_h0=0.6)

Standard usage:

traintrain_dists: matrix of pairwise distances between input trees
traintest_dists =  NULL
train_random_dists:  matrix of distances between input trees and
random trees (one row for each input tree)
outlier_fraction:  fraction of outliers to attempt to remove from the
distribution estimation
kernel:  Either 'laplace', 'gaussian', 'gaussian1_5', 'gaussian2'
which correspond to delta = 1,2,3,4 in the manuscript
kernel_h0 = 1
estimate_kernel_h0 = T
bandwidth = NULL
pval_cutoff = NULL
use_random_trees = T
pathbase: path where messages file should be printed
use_iterative_outliers = F
normalize_kernels = F
normalize_preds = T
kernel_h0_step:  Hill-climbing optimization of bandwidth will
increase/decrease bandwidth by a factor of (1 + kernel_h0_step) at
each step
starting_h0:  Starting value of bandwidth will be starting_h0 times
the square-root of second moment of pairwise distances between input
trees

Output:  List with members

unbiased_density_sums:  Probability estimate for each input tree,
times number of all possible tree topologies (i.e., likelihood ratio
versus uniform random distribution on trees)
estimated_kernel_h0:  ML estimate of bandwidth multiplier.  (ML
bandwidth is estimated_kernel_h0 times the square-root of second
moment of pairwise distances between input trees)