RISE with multi-interactions

[marc-vuffray]

The branch multi-interactions now contains the method multiRISE() that reconstruct binary models with arbitrary interactions. The ouptut is a dictionary of reconstructed interactions from each node perspective e.g. (1,2,3), (2,1,3), (3,1,2) are the reconstruction of the 3 body interaction between 1,2,3 from the perspective of node 1, 2 and 3 respectively.

The option for symmetrizing the output is still not implemented.

[ccoffrin]

Great!

[ccoffrin]

Preliminary tests on the current datasets are looking good.

[ccoffrin]

Regarding the symmetrizing option. I was thinking the way to generalize this would be to treat each tuple as an un-ordered set and then take the average of the values in that set?

[marc-vuffray]

I never manipulated an un-ordered set in julia. I guess what you propose should work.
What is needed is a comparison function that returns true iff the elements of two tuples are identical. Then we just have to do the average over compared tuples and eventually remove tuples that are not in increasing order.

[marc-vuffray]

I have tested multi-RISE on synthetic models of 5 nodes with interactions of order up to 4. It passed all the reconstruction tests on these models. It seems that the routine is correct.

[ccoffrin]

See #16.

[ccoffrin]

Also, once you have confirmed your tests (e.g. the 5 node example) are working, then archiving those tests in test/runtests.jl makes sure that future changes will not break the model. I added a few tests in there that the ising version and the 2-body version produced the same results.

[ccoffrin]

addressed in #15, #16, #18.