# W1D4 What is closed form solution

Dear All,

I have difficulty in understanding the main problem of the poisson GLM that is the log likelihood is not a closed form solution which led us to apply optimization technique.
What is meant by closed form solution???

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A closed form solution is one that has a simple algebraic expression, so you can simply plug in numbers and get the result. Non-closed form solutions generally need to be computed, often through successive approximation. For example, Newton’s method or gradient descent.

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upon my intuition, using the example of the tutorial, closed form solution like linear model I can calculate theta because it is separable (theta in one side of equality and other variables lies in the other side), while not closed solution like the poisson GLM where I can’t separate theta from X, which led us to use optimization. Is that right?

Sorry, I don’t have access to Neuromatch materials (or, if they’re public, I don’t know about them), so I can’t speak with reference to them. I just saw this on the general questions.

But that seems right. If there’s no way to write the desired values as a finite sequence of operations depending only on input values, then some approximation method will be required. (Now I’m worried that there’s a well-known counter-example…)

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Yep, that’s right! Closed-form mean you can solve for theta.

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