BFGS+EM for optimising model parameters

[iqtree]

BFGS+EM for optimising model parameters

[bqminh]

tagging @thomaskf here for discussions.
That's interesting. What Lars and Thomas did, was not exactly about log-likelihoods but about accuracy. So they simulated a bunch of alignments and free-rates, and ask whether BFGS or EM most frequently obtained the the true rates back. And the answer was EM.
I remember that, I also did a bunch of empirical alignments, and observed that none of them always obtained higher likelihood than the other. Sometimes BFGS got higher likelihood, sometimes EM.
@roblanf 's suggestion is sensible. I believe Thomas put such code in IQ-TREE after our meeting. Thomas, can you pls test this data set?

[roblanf]

@thomaskf if you can post the relevant commandline here, I can test it on this dataset (it's a GISAID dataset so hard to share).

[roblanf]

Also I'm not totally convinced about simulating data and then asking whether we get the 'true' rates back. We only expect to get the 'true' rates if we have infinite species (well, infinite tree length really) and infinite sites.

E.g. if the number of species is limited, more and more sites will look like constant sites rather than sites from a 'true' low rate category. Because of these limitations, I tend to think that in ML software we should really consider the methods (within reason, of course!) that give us the best likelihood. If that disagrees with simulation conditions, it will often be because of some other limitation.

[thomaskf]

@roblanf sorry for the late reply. I agree with your point. I have updated the codes last Saturday so that in each iteration 1-BFGS->EM is performed, and the iteration will be repeated until the convergence is reached. I am uploading the codes soon so that you can have a test. Meanwhile, I still need a bit more time to finalize the paper with Allen and I will work at full speed on the project starting from next week. Apology for the delay and the inconvenience caused.

[roblanf]

Hi @thomaskf, that sounds good. Just make sure that the three algorithms are available as different flags:

1. one for EM only
2. one for BFGS only
3. one for EM/BFGS combined

[bqminh]

@thomaskf : I don't think 1-BFGS->EM a good approach, because after doing BFGS, you will be in a local optimum. If you now start EM from that local optimum, I don't see how it help to escape it, except for moving a bit around it. It's better to have independent starting points, with/without different algorithms. Since this is quite a long time with no sensible solution, I recommend that we close this discussion, also because everyone is busy with other projects and we don't really have person to pursue it further, esp. in testing different approaches.