GaussianMixture & TableOfReal: Get likelihood value...

Calculates how well the GaussianMixture model fits the data according to a criterion.

Settings

Maximum likelihood
ML = Σi=1..n log (Σm=1..k αk pik)
Minimum message length
DL = ML - 0.5(N·Σm=1..k log(nαm/12) -k·log(n/12) -k(N+1))
Bayes information
BIC = 2·ML - k·N·log(n)
Akaike information
AIC = 2(ML - k·N)
Akaike corrected
AICc = 2(ML - k·N·n/(n-k·N-1))
Complete-data ML
Σi=1..nΣm=1..k γim log (γim)

In the formulas above n is the number of data points, k is the number of mixture components, N is the number of parameters in one component, i.e. d + d(d+1)/2 for a full covariance matrix of dimension d with means. The αk are the mixing probabilities, the pik are the probabilities for the i-th data vector in the k-th component. The γik are defined as

γim= αm·pim /(Σj=1..k αj·pij).

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© djmw, November 25, 2010