I am wondering why there is twice the product over k in the formula below… isn't it sufficient to have the double product over n and k at the beginning and not adding again a product over k for the pi_k at the end? I don't see the logic!
Thank you for your help!!
I think that the second product over k is outside of the first one and is just the definition of p(z_n|pi).
You could remove the second product and extend the first one without problem. It is just written this way so we understand what is p(x_n|z_k,µ_k,sigma_k) and p(z_n|pi)
Gaussian mixture models joint distribution
Hello,
I am wondering why there is twice the product over k in the formula below… isn't it sufficient to have the double product over n and k at the beginning and not adding again a product over k for the pi_k at the end? I don't see the logic!
Thank you for your help!!
Hi,
I think that the second product over k is outside of the first one and is just the definition of p(z_n|pi).
You could remove the second product and extend the first one without problem. It is just written this way so we understand what is p(x_n|z_k,µ_k,sigma_k) and p(z_n|pi)
1
I confirm, the second product is outside the first one.
1
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