[pmiller2]

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

[contravariant]

If 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]

This 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]

That'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.

[contravariant]

It 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.

[pvitz]

Just 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.