paramFitGammaOne: Parameter Initialization Based on a Smooth Log-Concave...

In fmlogcondens: Fast Multivariate Log-Concave Density Estimation

Description

paramFitGammaOne fits in a first step a log-concave density to data points X with weights w using a smoothness parameter of gamma=1. In a second step, it calculates the upper convex hull of the set X and log(y), where y_i is the smooth log-concave density evaluated at X_i. It returns the hyperplane parameters of the faces of this upper convex hull.

Usage

paramFitGammaOne(X, w, ACVH, bCVH, cvh)

Arguments

X	Set of data points (one sample per row)
w	Vector with weights for X (sum(w)==1)
ACVH	Matrix where each row constitutes the normal vector of a face of conv(X)
bCVH	Vector where each entry constitutes the intercept for a face of conv(X)
cvh	Matrix where each row is a set of indices of points in X describing one face of conv(X)

Value

A list containing the description of the upper convex hull of (X,log(y)) in term of hyperplane parameters:

a	A matrix where each row constitutes a hyperplane normal
b	A vector where each entry constitutes the intercept of a hyperplane

Note the difference

Examples

# draw samples from normal distribution
X <- matrix(rnorm(200),100,2) 
# calculate parameters of convex hull of X
r <- calcCvxHullFaces(X)
# find initial hyperplane parameters based on a smooth log-concave density
params <- paramFitGammaOne(X, rep(1 / nrow(X), nrow(X)), r$ACVH, r$bCVH, r$cvh)

fmlogcondens documentation built on May 2, 2019, 8:29 a.m.