Homonym: Hessian (Fabric)
The Hessian is a square matrix of second-order partial derivatives of a scalar-valued function. It provides information about the local curvature of the function, which is useful in optimization problems. By analyzing the Hessian, one can determine whether a critical point is a local minimum, local maximum, or a saddle point.
In the context of machine learning and statistics, the Hessian matrix plays a crucial role in algorithms like Newton's method for finding optimal solutions. It helps in assessing how changes in input variables affect the output, thereby guiding the optimization process more effectively than using first derivatives alone.