January 2019
Intermediate to advanced
390 pages
9h 16m
English
Content preview from Hands-On Artificial Intelligence for IoT
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Deterministic and analytic methods
When the objective function is smooth with a continuous second derivative, then we know from the knowledge of calculus that at a local minimum the following are true:
- The gradient of the objective function at minima x*, that is, f'(x*) = 0
- The second derivative (Hessian H(x*) = ∇2f(x)) is positively definite
In such conditions, for some problems, it is possible to find the solution analytically by determining the zeros of the gradient and verifying the positive definiteness of the Hessian matrix at the zeros. So, in these cases, we can explore the search space iteratively for the minima of the objective function. There are various search methods; let's see them.
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