A finite stationary point is a global maximiser
Theorem taught in Logistic regression, part of Statistical learning
A finite stationary point is a global maximiser
| Type | Theorem |
| Taught in | Logistic regression |
| Part | Statistical learning |
At every finite coefficient vector the weights p_i(1-p_i) are positive. The Hessian -X^\top W X is negative semi-definite, so \ell is concave. If X has full column rank, W is positive definite on the column space of X and the Hessian is negative definite, so \ell is strictly concave. Any finite stationary point is then the unique global maximiser.
Used in
- Taught in Logistic regression, where the derivation and examples are.
- All 7 questions on Logistic regression
See also
Positive definite matrix · Binary logistic regression · From a linear model to class probabilities · Logistic and probit models · Likelihood, score, and fitting · Score and Hessian of logistic regression · Iteratively reweighted least squares · Interpretation and the decision boundary