GaussianMixture & TableOfReal: Get likelihood value...


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

Maximum likelihood
ML = Σ_{i=1..n} log (Σ_{m=1..k} α_{k} p_{ik}) 

Minimum message length
DL = ML  0.5(N·Σ_{m=1..k} log(nα_{m}/12) k·log(n/12) k(N+1)) 

Bayes information

Akaike information

Akaike corrected
AICc = 2(ML  k·N·n/(nk·N1)) 

Completedata ML
Σ_{i=1..n}Σ_{m=1..k} γ_{im} log (γ_{im}) 
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 α_{k} are the mixing probabilities, the p_{ik} are the probabilities for the ith data vector in the kth component. The γ_{ik} are defined as
γ_{im}= α_{m}·p_{im} /(Σ_{j=1..k} α_{j}·p_{ij}). 
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© djmw, November 25, 2010