InformationCriteria4GMM {AdaptGauss}

Information Criteria For GMM

Description

Calculates the AIC and BIC criteria

Usage

InformationCriteria4GMM(Data, Means, SDs, Weights, IsLogDistribution)

Arguments

Data

vector (1:N) of data points

Means

vector[1:L] of Means of Gaussians (of GMM),L == Number of Gaussians

SDs

vector of standard deviations, estimated Gaussian Kernels, has to be the same length as Means

Weights

vector of relative number of points in Gaussians (prior probabilities), has to be the same length as Means

IsLogDistribution

Optional, ==1 if distribution(i) is a LogNormal, default vector of zeros of length L, LogNormal Modes are at this point only experimental

Details

AIC = 2*k -2*LogLikelihood, k = nr. of model parameter = 3*Nr. of Gaussians One Gaussian: K=2 (Weight is then not an parameter!) SMALL SAMPLE CORRECTION: for n= nr of Data and n < 40 * k, AIC is adjusted to AIC=AIC+ (2*k*(k+1))/(n-k-1)

BIC = k* log(n) - 2*LogLikelihood

Only for a Gaussian Mixture Model (GMM) verified, for the Log Gaussian, Gaussian, Log Gaussian (LGL) Model only experimental

Value

List with

K

Number of gaussian mixtures

AIC

Akaike Informations criterium

BIC

Bayes Information criterium

LogLikelihood

LogLikelihood of GMM, see LogLikelihood4Mixtures

PDFmixture

probability density function of GMM, see Pdf4Mixtures

LogPDFdata

log(PDFmixture)

Author(s)

Michael Thrun

References

Aubert, A. H., Thrun, M. C., Breuer, L., & Ultsch, A.: Knowledge discovery from data structure: hydrology versus biology controlled in-stream nitrate concentration, Scientific reports, Vol. (in revision), pp., 2016.

Aho, K., Derryberry, D., & Peterson, T.: Model selection for ecologists: the worldviews of AIC and BIC. Ecology, 95(3), pp. 631-636, 2014.