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Why would you use the Monte Carlo method when the quasi-Monte Carlo method converges so much more quickly? I admit, I am a little biased, because I worked on s
by pmiller2 6y ago
Why would you use the Monte Carlo method when the quasi-Monte Carlo method converges so much more quickly? I admit, I am a little biased, because I worked on some QMC stuff in grad school, but it works really, really well in practice.
https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method
- pvitz 6y agoJust a guess, but if you think about Sobol sequences, maybe the available dimensions get exhausted in this use case and then QMC doesn't perform well anymore.
- contravariant 6y agoIf the number of dimensions is high enough then pretty much all points are far away from each other so there's no real need to worry about points clustering. You're at a much greater risk of simply missing interesting parts of your space than you are of oversampling any part of it.
- blake1 6y agoThis can be especially bad if one corner hides a catastrophe. Any automatic method is likely to have an exponential struggle to sample appropriately. At a certain point, you just need to apply your own understanding of the problem you are trying to solve, and resort to an ad hoc method to do the “right” thing.
- pmiller2 6y agoThat's exactly the problem QMC methods solve. By choosing a sequence of sample points of low discrepancy, you make sure to sample the entire space as evenly as possible.
- deleted 6y ago[deleted]
- contravariant 6y agoIt does but if you've got 100s of dimensions then you have no hope of ever sampling anything close to the entire space. Even if you just pick 2 points per dimension you've got no way of trying every combination.