Description Usage Arguments Value Examples
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.
1 2 |
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) |
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. |
1 2 3 4 5 6 7 8 9 10 | # 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)
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