replace term 'EM' to 'SVD based approach'

[Cartman0]

Reference Issues/PRs

replaced term "EM" -> "SVD based approach" for #14317 .

What does this implement/fix? Explain your changes.

Any other comments?

[amueller]

Can you please explain your change?
It looks like the algorithm is an EM algorithm where the E step is an SVD, right?

[Cartman0]

the method with EM algorithm is in BRML 2017 p.448-449.

generally should calculate posterior distributions of hidden variable each observation data in E-step,
and should estimate parameters maximizing lower bound using these posterior distributions in M-step in EM algorithm.

i can't see calculating the posterior dist of hidden variable in a E-step and
estimating parameters using the posterior dist in M-step in this implementation.

i think that the method of this implementation is "SVD-based approach", not "EM algorithm".

(maybe "EM" you say is actually just "MLE(Maximize Likelihood Estimation)" ?)

[jnothman]

It's definitely not a stopping tolerance for the svd. It's tolerance of the log likelihood that is being maximised by em

[Cartman0]

i don't know whether this description is exact or not.
however, because SVD based approach also need to iterate, i think it need this stop tolerance.

do you have a idea for better description ?

[jnothman]

"Stopping tolerance for log-likelihood increase"?

[Cartman0]

i think that's fine. should i change it ?

[jnothman]

Please do if you think it's good

[Cartman0]

i persit em algorithm is not used in BRML Algorithm 21.1.

[amueller]

@Cartman0 ok, looked it up, I agree!

[jnothman]

Otherwise this is fine by me

[jnothman]

Thanks @Cartman0