If you have a distribution, with density p, that you don't know how to sample from, you can still estimate integrals like ∫f(x)p(x)dx by sampling:. Sample from a different distribution, with density q, then weight your samples by p(x) / q(x). This is called importance sampling

I'm speaking at @developconf in July with @vTimeNet about using AI to aid the development of a top rated game on a modest budget, using our recent game Border Bots VR as a case study. Details of the session here: #ImASpeaker #developconf

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RT @EchoStatements: New blog post: Visualising the Legendre Transform. In which, I show how the Legendre transform can be derived in a visu….

I hope either somebody finds this useful or there's an easier way that somebody can share with me. Explanation of the problem and the solution on the other site. Hope that's legal.

It seems (?) like there isn't an easy way to use PyTorch's transformer implementations autoregressively at prediction time efficiently; in each iteration of the loop the whole sequence attends to the whole sequence. Here's a solution I came up with:

In NumPy/PyTorch if I have some arrays (that may share some axes) that I want to make jointly broadcastable, I use this 'make_broadcastable' function, using einops underneath and the same pattern syntax. Anyone know of an easier/built-in way?.

Bonus points to Jan Zacharias for the only publication I could find exposing the 'alleged prime number' as a fraud!.

A fun example of a falsehood spreading through citation: according to (most of) these 47 papers, 19,349,663 is prime

RT @AndrewM_Webb: Let's ride a Martian space elevator—from Pavonis Mons to areostationary orbit!. The left hand side looks down on the nort….

Happy Halloween! I decided to get in the spirit and dress as the walking dead. (I've no idea if non-British followers will know who this is)

I'm doing a night-time trek up mount Snowdon with friends and we're raising money for Mind, a charity in England & Wales that helps people with mental health problems and raises awareness of mental health. I'd really appreciate any donations or retweets.

RT @AndrewM_Webb: A simple visual aid to see why the area of a circle is half the circumference times the radius. Based on a section of @st….

You can get super efficient estimates of ∫f(x)p(x)dx by, rather than picking a q similar to p, pick one similar to |f(x)|p(x) (suitably normalized). I.e., pick something that has a high density in regions that have a large effect on the integral.

How efficient this is, in terms of number of samples required, depends on how similar the two distributions are. You usually want the distribution you sample from to have heavier tails than the target distribution: it's better to oversample the tails than not sample them at all.

For clarity: for each sample xᵢ you'd compute the weight wᵢ = p(xᵢ) / q(xᵢ), then your monte carlo estimate of the integral would be Σwᵢ⋅f(xᵢ).

(Tweeting at 3 am because I was having coding nightmares).

It results in not-very-restful sleep and I first experienced this with learning programming, so I still call them 'coding nightmares'.

If I spend a few hours in a day learning something new and abstract, that night I'll often have non-visual dreams: the 'dream' is just repetitive, nonsensical thoughts. It feels like repeatedly trying out new ideas but on nonsense data. Anyone else experience this?.

re: Dawkins' science tweet. It's hard to have useful discussions when we use "science" to mean at least three distinct things:. - objective reality.- the process people use to understand reality.- the collection of facts we've come to accept as true by using that process.