Generating general and specific lattice of structures

[venkatachalapathy]

• Generate general and specific lattice of structures for small number of variables

I think this was raised by Marty during the 1st March meeting. This might be a good thing overall when we compare similarly enumerated model spaces for other graphical models.

[gdcutting]

Maybe we could improve on the format used in the Overview and Wholes and Parts papers? Thoughts on that?

[venkatachalapathy]

I think Marty wanted this in some connection to some BDD related project. So, this might satisfy his criteria of occam enhancement. Also, It might give us an excuse to explore the use of set theoretic structures from STL. Once we have a brute force implementation model generation, we might be able to first, show a first pass version to Bart; then, use his expertise to develop better heuristics, going beyond the beam search currently in use; and third, explore newer smarter ways to hop around the lattice of structures.

[gdcutting]

That makes sense. I would like to discuss this more because I still want to clarify, in my mind and in the docs, what exactly the lattice of structures is in formal terms. There are some informal statements in existing material but I think we could use a more formal mathematical definition, or at least a more precise statement.