Hessian Matrix
Gist
Looking to understand the curvature of a function? Useful for optimization
Definition
For a scalar-valued function, the Hessian matrix calculates the second partial derivative.
Usage
You can figure out if you’re at a maximum/minimum point by calculating the Hessian
For Maximum- likelihood
Properties
- Positive definite Hessian → local minimum
- Negative definite Hessian → local maximum
- Indefinite Hessian → saddle point
- Zero determinant → test is inconclusive
Association with the Taylor Series
The Hessian matrix arises naturally in the second-order Taylor Series of a scalar function: