fmlcd: Estimates a Log-Concave Density

In fmlogcondens: Fast Multivariate Log-Concave Density Estimation

Description

fmlcd returns a MLE estimate of a log-concave density for X. After obtaining an initial parameter estimate the MLE objective with log-concavity and normalization constraint is optimized using a quasi-Newton approach for large scale optimization (BFGS-L). The logarithm of the optimal density f(x) is a piecewise-linear function. Its parametrization in terms of a set of hyperplanes is returned.

Usage

fmlcd(X, w = rep(1/nrow(X), nrow(X)), init = "", verbose = 0,
  intEps = 0.001, objEps = 1e-07, offset = 0.1, maxIter = 10000)

Arguments

X	Matrix of data points (one sample per row)
w	Vector of sample weights (default: uniform weights)
init	String that sets the initialization approach. 'kernel' based on kernel density, 'smooth' based on smooth log-concave density, ” compares both and takes the optimal one. (default: ”)
verbose	Int determining the verboseness of the code; 0 = no output to 3. (default: 0)
intEps	Stopping criteria for the numerical integration accuracy Optimization stops if both measurements are smaller than intEps and objEps Modification of this value is not recommended. (default: 1e-3)
objEps	Stopping criteria for the change in the objective function Optimization stops if both measurements are smaller than intEps and objEps Modification of this value is not recommended. (default: 1e-7)
offset	Smaller values correspond to slower hyperplane reduction. Offset should be a value smaller than 1. Modification of this value is not recommended. (default: 1e-1)
maxIter	Number of iterations in the main optimization (default: 1e4)

Value

Parametrization of f(x) in terms of hyperplanes and function evaluations y = log(f(x))

aOpt, bOpt	Analytically normalized parameters of f(x).
logLike	Log-likelihood of f(x)
y	Vector with values y_i = log(f(X_)) of the normalized density (logLike = ∑(y_i)).
aOptSparse, bOptSparse	Sparse parametrization normalized on the integration grid.

Examples

# draw samples from normal distribution
X <- matrix(rnorm(200),100,2) 
# calculate parameters of convex hull of X
r <- calcCvxHullFaces(X)
# draw random parameters of 10 hyperplanes
a <- matrix(runif(10*2),10,2)
b <- runif(10)

# calculate parameters of convex hull of X
params <- correctIntegral(X,rep(0,2),a,b,r$cvh)

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