Neural modeling fields: Difference between revisions

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Romanilin (talk | contribs)
Romanilin (talk | contribs)
Line 46:
First, assign any values to unknown parameters, {S<sub>m</sub>}. Then, compute association variables f(m|n),
 
:<big>f(m|n) = r(m) l(X(n)|m) / &sum;<sub>m'=1..M</sub> r(m') l(X(n)|m').</big>
 
Equation for f(m|n) looks like the Bayes formula for a posteriori probabilities; if l(n|m) in the result of learning become conditional likelihoods, f(m|n) become Bayesian probabilities for signal n originating from object m. The dynamic logic of the Modeling Fields (MF) is defined as follows
 
 
:<big>df(m|n)/dt = f(m|n) &sum;<sub>m'=1..M</sub> {[&delta;<sub>mm'</sub> - f(m'|n)] • [&part;ln l(n|m')/&part;M<sub>m'</sub>] &part;M<sub>m'</sub>/&part;S<sub>m'</sub> dS<sub>m'</sub>/dt,</big>
 
:<big>dSm/dt = &sum;<sub>n=1..N</sub> f(m|n)[&part;ln l(n|m)/&part;M<sub>m</sub>]&part;M<sub>m</sub>/&part;S<sub>m</sub>,</big>