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The “log-likelihood function” is a probabilistic function.

<MATH> \sum_{i=1}^{N}(1-X_i^i)log(1-Pr[1|B_1^1,B_2^2,\dots,B_k^k])+X_i^i.log(Pr[1|B_1^1,B_2^2,\dots,B_k^k]) </MATH>

The “log-likelihood function” is also referred to as the cross-entropy