Why is the covariance normalization step included in _estimate_wishart_full(_Bayesian_mixture.py)?
#30759
Replies: 0 comments
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Uh oh!
There was an error while loading. Please reload this page.
-
I am reviewing the _estimate_wishart_full function in _Bayesian_mixture.py, and I noticed the following comment and line of code:
Contrary to the original bishop book, we normalize the covariances
self.covariances_ /= self.degrees_of_freedom_[:, np.newaxis, np.newaxis]
I understand that this step is normalizing the covariance matrices by the degrees of freedom, but I would like to gain a clearer understanding of why this is necessary.
In Bishop’s Pattern Recognition and Machine Learning (PRML), the Wishart distribution is typically parameterized without this explicit normalization step.
The previous lines in the function construct self.covariances_ by adding the prior covariance, weighted sample covariance, and a term involving the prior mean.
Could someone clarify the reasoning behind this normalization step? Is it related to ensuring a proper estimate of the posterior covariance under the Bayesian Gaussian mixture framework?
Any insights would be greatly appreciated!
Beta Was this translation helpful? Give feedback.
All reactions