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Financial Machine Learning / Classification and Generalized Linear Models

Derivation — Newton's Method for Maximizing the Logistic Log-Likelihood

Gradient ascent on the logistic log-likelihood from the parent note converges, but slowly and with a hand-tuned learning rate. Newton's method uses second-order (curvature) information to take much larger, self-scaling steps, typically converging in single-digit iterations on well-conditioned problems. This note derives the update and its per-iteration cost.

In this lesson

  1. Learning objectives
  2. Newton's method
  3. The Hessian of the logistic log-likelihood
  4. Worked example

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