Comment by vitus
5 days ago
> If you think estimating 1e-1000 is a problem, then estimating 1e+1000 shouldn't be.
They're both problems. If you want to estimate 1e1000 via sampling individual points, then you need at least that order of magnitude of samples. If all of your data points fall in one class, then it doesn't matter what you're trying to calculate from that.
As I said: "If you're inverting the ratio we're estimating, then instead of estimating the value at 0, we're estimating it at infinity (or, okay, if you want to use Laplace smoothing, then a million, which is far too low)."
> If you want to estimate 1e1000 via sampling individual points, then you need at least that order of magnitude of samples.
Ok so if the ratio is 1/2 how many samples do you need?
I mean, yes, you can estimate this for low dimension. It's a bad idea given how slow the convergence is, but you can do it.
My entire point is that this becomes infeasible very quickly for numbers that are not all that big.
First off, you didn't answer my question which to restate is: if the ratio is 1/2, how many samples do you need.
Second, your claim that it depends on dimension is wrong, given the ratio of sets, dimension doesn't matter. If the ratio is 1/2 then you'll reject one half of the times regardless of dimension, and so by your own argument it's "very efficient"
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