Markov Blanket

[cscherrer]

Hi @mschauer, here you said,

I looked into making interfaces to https://github.com/mschauer/ZigZagBoomerang.jl 1 . It’s kind of the master level problem for a foreign inference interface because zigzag produces a piecewise linear trace (not just samples) and it ideally wants to know your Markov blanket. For Gen/Jaynes there is some progress, more to come: probcomp/Gen.jl#281

Can you help me understand how the Markov blanket helps? For Soss models, we can statically get turn a model into a collection of conditional models as you would need for Gibbs sampling. I'd love to find opportunities to exploit this for better performance

[mschauer]

The inner working of the ZigZag:

1.) all coordinates move independently all the time up or down with unit speed and each of them has an inner clock telling it when it might need to change direction.

2.) If a clock rings, you need to check the partial derivative of the score with respect to that coordinate to see if you actually want to change directions. The partial derivative of the score depends only on neighbours in the Markov blanket/members of the same factor... So you give me a $\partial_i \log p(x)$ computed efficiently using your internal information about the layout.

3.) If the partial derivative tells you actually want to change direction, you also need to reset some clocks, but only those of the neighbours in the Markov blanket... So you tell me the Markov blanket so I don't have to reset all the clocks, only those of neighbours.

[mschauer]

PS: The most relevant formal description is in https://arxiv.org/pdf/2001.05889.pdf in sections 4.2 and 4.3

[cscherrer]

Thanks! This explanation is very clear and helpful. I definitely want to get this hooked up, but maybe there's too much to it to start it right now. I'll make some more progress with MeasureTheory.jl and hopefully get back to this soon :)