Numerical problems with complex RTMB model

[Jan-Ole Koslik]

Hi,

I am trying to fit a rather complicated non-linear and non-Gaussian state space model.

Specifically, the model is a state-switching continuous-time correlated random walk with measurement error. For each state, I have an integrated OU process and I am jointly modelling latent locations and velocities, which need to be integrated out by RTMB.

Due to the complexity, I wasn't expecting anything to run smoothly, but nonetheless I wanted to ask for tips. 

The issue I have is that the nested optimisation looks good for the most part, i.e. first 20-30 iterations. Inner gradients become zero in each outer iteration and the outer mgc also becomes fairly small. But then at some point, I'm always getting a lot of line searches, followed by the gradient "exploding", i.e. just becoming larger and larger from that point on.

The crazy thing is, if I just let it run, the estimated model in the end is not bad. Positions are also filtered pretty nicely.

So I just wanted to ask if people have tips for numerically stabilising this optimisation, or if it's just a terrible idea to fit this with TMB in general.

Cheers,

Ole

[Hans Skaug]

I have had similar situations, where I believe the problem has been that the Laplace approximation is inaccurate in some part of the (outer) parameter space, and the optimizer gets attracted to this area due to error in the likelihood approximation. This can be really hard (and time consuming) to diagnose. My attempt has been to fix one parameter at the time, and see if the problems go away. This would indicate which part of the model is causing the problem, but it is not solving the problem.

When you say “non-Gaussian state space model” I believe that the prior distribution for each latent variable (random effect) is Gaussian, still. Otherwise that is a candidate for the culprit.

[Cole Monnahan - NOAA Federal]

This is what the experimental feature "ridge.correct" in RTMB tries to fix. Try setting it to TRUE. I couldn't find any documentation but I know there is at least a presentation where Kasper introduces the concept and shows how it works. But I can't seem to find it online.

[Matt Cheng]

I believe this was partly discussed during the 2024 ICES MGWG?

[Cole Monnahan - NOAA Federal]

Also there's a test which could be worth a look:

https://github.com/kaskr/RTMB/blob/master/RTMB/inst/tinytest/test-ridge_correct.R

[marks...@gmail.com]

Just chiming in to say this looks incredibly useful. I have run into the issue described in the Kasper's slides several times and it can be really frustrating and difficult to troubleshoot. 

[Imai-Eaton, Jeffrey W]

Thanks for sharing these slides — this has been a longstanding intermittent issue for us, with limited traction on addressing.

To confirm, can the ridge correction be tested in ‘normal’ TMB (not RTMB) simply by specifying the argument below?

obj <- MakeADFun(..., ridge.correct=TRUE)​

Thanks,

Jeff

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[Kasper Kristensen]

Jeff, so far the method is only available in RTMB.