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The analysis of gradient descent and the choice of step size in every iteration is beyond the scope of this class, but the implementation of
The analysis of gradient descent and the choice of step size in every iteration is beyond the scope of this class, but the implementation of this algorithm requires one to compute gradients of the function at various points as given in Step of the algorithm. Hence, the computational complexity of gradient descent boils down to the complexity of evaluating the gradient of the function
Note: The above algorithm is a descent algorithm to minimize and find a local minimum of a given function. This is the reason why we used the conversion If one were to rewrite the algorithm without this conversion, we would have maximized and Step of the algorithm would be Such an algorithm is called a gradient ascent algorithm. It is more common in literature in optimization to use the descent version rather than the ascent version.
One Step of Gradient Ascent for the Poisson GLM
points possible graded
Let and let for some constant For the Poisson GLM recall that and we have
What is for any
Use Xi for and Yi for
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STANDARD NOTATION
Let
Step size
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