UseParallel for hessian?

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Jonne Guyt 2018-6-29

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https://ww2.mathworks.cn/matlabcentral/answers/408081-useparallel-for-hessian

评论： Jonne Guyt 2022-10-4

Will Matlab at some point support parallel computation of the finite difference Hessian? More specifically, I've been using UseParallel in my fminunc settings (which have a lot of parameters), but computing the Hessian takes a fair amount of time.

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Walter Roberson 2022-10-2

the option description is "When true, fminunc estimates gradients in parallel." but that is gradients not hessian

Jonne Guyt 2022-10-4

I've stopped using Matlab but simply monitoring the system usage (# of cores) as well as the slowness were giveaways that it's not calculating in parallel

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回答（1 个）

Matt J 2022-10-2

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编辑：Matt J 2022-10-2

I don't speak for MathWorks, but I think the issue is that finite difference Hessians are only relevant to the trust-region algorithm, since the quasi-newton algorithm does not use Hessian computations. But in the trust-region algorithm, the user is required to provide an analytical gradient computation via SpecifyObjectiveGradient=true. It seems a rather narrow use case that an analytical gradient calculation would be tractable, but not an analytical Hessian computation, assuming the memory footprint of such a matrix is not prohibitive. If the memory footprint of the Hessian is prohibitive, the user is meant to be use the HessianMultiplyFcn or HessPattern options.

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Bruno Luong 2022-10-4

And furthermore the Hessian returned by minimization algorithms are usuallt NOT suitable to compute error standard deviations.

Jonne Guyt 2022-10-4

If you need the Hessian for the purposes of computing standard errors (and not iterative optimization), then I agree it may make sense to have a parallelized finite differencer for that. However, it is not clear why that belongs in fminunc/fmincon. Because the Hessian is not being recomputed iteratively, you would use a standalone Hessian computing routine for that.

Yes - this is exactly the use case. I think you inferred it was optimization, but I never mentioned this. If you request the hessian to be returned at the end (to compute SE's), it is approximated with finite differences, so it is 'built-in', but it might as well be standalone (hence my workaround). I hope it makes more sense now...

@Bruno Luong exact and approximated SE's may differ a small amount, but can you show me to where I can find that these are not suitable for discrete choice models with non-obvious gradients?

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