Why not a straight line? Default (0 or 1) against card balance, 600 simulated customers
β₀ (intercept)
β₁ (per dollar of balance)
maximum likelihood
show the least-squares line
logistic p(x) = 1 / (1 + e^−(β₀ + β₁x))
least squares on 0/1
customer (0 = paid, 1 = defaulted; jittered)
Bayes' theorem as a classifier: one predictor, two Gaussian classes
mean of class 0
mean of class 1
common standard deviation σ
prior π₁ = Pr(class 1)
the dividend example
equal priors
π₀ f₀(x)
π₁ f₁(x)
Pr(class 1 | x)
decision boundary
Logistic regression, LDA, QDA and naive Bayes on the same 100 training points
new training set
class 0
class 1
One score, many classifiers: the threshold, the confusion matrix and the ROC curve
threshold on the predicted probability
predicted probability by true class
ROC curve: every threshold at once