DEMetropolis: tune lambda instead of epsilon

[michaelosthege]

Our DEMetropolis tunes the scaling factor of the noise distribution:
https://github.com/pymc-devs/pymc3/blob/1c30a6f487afaeef73464a98320e35961b11873f/pymc3/step_methods/metropolis.py#L572-L581

My feeling these days is that tuning the noise distribution is a bit pointless after the first few iterations & could obscure the warmup, or even lead to slingshots if it overshoots.

Instead, we could tune lambda parameter. It's optimal value depends on the (dimensionality of the) target density (ter Braak (2006)), so it should be a good candidate for tuning.
This approach is described in Nelson et al. (2013), section 4.1.2.

[michaelosthege]

On my test problem (50-dim MvNormal) the tuning converges to the same rule of thumb that was used before (2.38 / sqrt(2*ndim)).
Here the progression of the tuned parameter (3000 tuning its)

I also see no significant difference in the effective sample size...

I'm thinking to ditch tuning of scaling/lambda alltogether. What do you think?
cc @junpenglao

[junpenglao]

Could you try on a ODE example?

[michaelosthege]

Could you try on a ODE example?

I tried with Demetris benchmark example, but it was very slow & inefficient (--> noisy) while having just 2 dimensions.

[junpenglao]

Do you mean slower than no tuning?

[michaelosthege]

Do you mean slower than no tuning?

No the sampling was just slow/inefficient because it's an ODE. Also DifferentialEquation computes sensitivities that DEMetropolis doesn't use.
So I'd have to wait very long for the benchmark results to give a significant answer.

I could also implement a kwarg like DEMetropolis(tune_par=x) with x in {None, 'epsilon', 'lambda'} where None is the default because tuning epsilon is a bit pointless & tuning lambda is not necessarily better than lambda = 2.38 / sqrt(2*ndim).

Maybe the result of my testing is simply that DEMetropolis doesn't need hyperparameter tuning. (Needs warmup/burnin though.)

[junpenglao]

I see. Thanks! Feel free to close.