Logistic Regression, Stochastic Gradient, Regularization.
here is to get σ(zi) ≈ 1 when yi = 1 and σ(zi) ≈ 0 when yi = 0. when yi = 0 then if σ(zi) ≈ 0 then: L = -0*log(0) — (1–0)log(1–0) = -(1)log(1) when yi = 1 then if σ(zi) ≈ 1 then: L = -1*log(1) — (1–1)log(1–1) = -(1)log(1) So, when yi and σ(zi) are close we get closer to having log(1), which is 0.