Please explain how the following is calculated
Q8. Likelihood Estimation in Logistic Regression
Suppose, there are 6 training (x1…x6) points, and hypothesis value comes out to be as follows -
Remember hθ(x) = sigmoid(wT.x + b), where w and b are weights and bias learned by the model after training.
hθ(x1) = 0.6
hθ(x2) = 0.4
hθ(x3) = 0.7
hθ(x4) = 0.1
hθ(x5) = 0.4
hθ(x6) = 0.9
The maximum likelihood estimation is defined as the product of the probabilities p(yi|xi). Assuming 100% correct classification, the likelihood value(without log) for the above case would be -
Logistic regression Quiz Q8
Hey @sanandasaha3 , the likelihood is product of Bernoulli distribution. So, in your case, assuming 100% correct classification and you are keeping 0.5 as the threshold and hθ(x) is the probability of label being 1 then,
The likelihood = 0.6 × (1 - 0.4) × 0.7 × (1 - 0.1) × (1 - 0.4) × 0.9 = 0.122472
Note : remember, likelihood = Py × (1 - P)(1 - y)
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