Thursday, February 8, 2024

Solution 1.11 - On Gaussian Distribution and it's Log Likelihood (Pattern Recognition and ML by Christopher Bishop)

Can you give me the equation for Gaussian distribution?

Can you give me it's log likelihood function?

Note: This is already given as part of the problem statement.

Can you show the detailed steps how you arrived at it?

Some paperwork

In the next slide we will solve for the below expression:

Some Logarithm Properties we would use:

Can you maximize the log likelihood expression w.r.t. mu and show the detailed steps?

Some paperwork for derivative of:

We will prove it next:

Some ‘Differentiation’ identities we would see next

And now maximize log likelihood w.r.t. sigma-squared and show the detailed steps

Identity:

References

https://chat.openai.com/share/4278db33-9b76-4d8b-9586-4e1e78844433

Tags: Mathematical Foundations for Data Science,Machine Learning,

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