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Gradient-based techniques

 

The gradient of L(Theta) is obtained by computing, for each thetaij:

pdL(Theta)/pdthetaij = dlogp(xq = a, e)/dthetaij - dlogp(e)/dthetaij.

This expression (derivation can be found in [10]) is:

  dL(Theta)/dthetaij = p(z'i = j|xq = a, e)/thetaij - p(z'i = j|e)/thetaij,

which can be obtained through standard Bayesian network algorithms using local computations. A conjugate gradient descent can be constructed by selecting an initial value for Theta and, at each step, normalizing the values of Theta to ensure they represent proper distributions [31].



© Fabio Cozman[Send Mail?]

Fri May 30 15:55:18 EDT 1997