## How log likelihood value is calculated in EM?

The engine.
snowave
Posts: 19
Joined: Mon Jan 25, 2016 1:27 pm

### How log likelihood value is calculated in EM?

Hi,

Can anyone explain how the log likelihood value in EM learning is calculated in Genie? Suppose the underline inference algorithm is Junction Tree.
In my understanding the log P(x) is calculated by multiplying and dividing cliques, is that correct?

many thanks

shooltz[BayesFusion]
Posts: 1255
Joined: Mon Nov 26, 2007 5:51 pm

### Re: How log likelihood value is calculated in EM?

The primary algorithm for calculating the probability of evidence is based on the junction tree cliques. If the junction tree cannot be created due to memory constraints, the algorithm switches to chain rule (slower, but potentially less memory-intensive).

snowave
Posts: 19
Joined: Mon Jan 25, 2016 1:27 pm

### Re: How log likelihood value is calculated in EM?

many thanks, so the log p(x)=log (product of cliques/product of sepsets)?
Could you please explain a bit more on chain rule calculation of the log p(x)?

best

shooltz[BayesFusion]
Posts: 1255
Joined: Mon Nov 26, 2007 5:51 pm

### Re: How log likelihood value is calculated in EM?

log p(x)=log (product of cliques/product of sepsets)?
It's more complicated algorithm. We run relevance decomposition which may create a forest of junction trees (the same approach is used for the main exact inference algorithm).

See this post for the explanation of the chain rule algorithm and P(e)
viewtopic.php?f=3&t=4687&start=15#p10449

snowave
Posts: 19
Joined: Mon Jan 25, 2016 1:27 pm

### Re: How log likelihood value is calculated in EM?

I think I understand the chain rule algorithm.

But I can't understand the "Relevant decomposition of JT". Is there a link or more detailed explanation for that? appreciate a lot.
Last edited by snowave on Tue Jul 28, 2020 9:43 am, edited 2 times in total.

marek [BayesFusion]
Posts: 284
Joined: Tue Dec 11, 2007 4:24 pm

### Re: How log likelihood value is calculated in EM?

Here is the article introducing the relevance-based decomposition algorithm:

http://www.pitt.edu/~druzdzel/psfiles/uai97.pdf

I hope this helps,

Marek

snowave
Posts: 19
Joined: Mon Jan 25, 2016 1:27 pm

### Re: How log likelihood value is calculated in EM?

cool, very much appreciated.