## How log likelihood value is calculated in EM?

The engine.
snowave
Posts: 22
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: 1325
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: 22
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: 1325
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: 22
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: 391
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: 22
Joined: Mon Jan 25, 2016 1:27 pm

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

cool, very much appreciated.
snowave
Posts: 22
Joined: Mon Jan 25, 2016 1:27 pm

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

Hi experts, if the model has high tree-width, i.e., the inference querying posterior joint distributions can't be performed by exact methods like JT due to memory constraint, what approximate algorithm is used in EM learning? Are they relevance based decomposition and/or sampling methods?

Many Thanks
marek [BayesFusion]
Posts: 391
Joined: Tue Dec 11, 2007 4:24 pm

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

GeNIe/SMILE do not switch to approximate algorithms automatically -- it is the user's responsibility to designate the default inference algorithm. If exact algorithms fail, I recommend the EPIS sampling algorithm, which is quite likely the state of the art algorithm for approximate inference in discrete Bayesian networks.
I hope this helps,

Marek
snowave
Posts: 22
Joined: Mon Jan 25, 2016 1:27 pm

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

Thanks a lot.
snowave
Posts: 22
Joined: Mon Jan 25, 2016 1:27 pm

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

Hi Experts,

I use Genie to do EM learning and switch between JT inference and EPIS sampling algorithms. Why the parameter learned are exactly the same (even for the decimals)? Though the marginal results are different. It seems like the parameter learning is tied to an exact method. Only at the marginal updating step the EPIS is used.

Thanks
shooltz[BayesFusion]