NLP C1_W1 Math Derivation in Cost function

Hi, can anyone give me a clearer explanation in Optional Logistic Regression: Cost Function:

  • what is the likelihood score and why do we use it in this case?
  • I see that we need to maximize h(θ,x (i) ) in L(\theta)L(θ), but I cannot understand why do we maximize h(θ,x (i) ), because it is just the output/prediction of the model?
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