Q1- I(q)

Q1- I(q)

std (guest) 26 Mar 2017 16:10

About I(q) definition- can a variable appear more than once at a CI (for example, x1_x2,x3|x3 or x1,x3_x2,x3|x1,x3)? or its just of the form x1_x2|x3? What about the regular pairwise independent (x1_x2|<nothing>)?
In other words, what is the maximal size of I(q) over n variables?

Moreover, are we expected to give an elegant way to prove such independents without enumerate over the options-table?
If so, may I get a clue?

Last edited on 26 Mar 2017 16:12 by Anonymous (188.120.154.x) Show more

Re: Q1- I(q)

Amir Globerson 28 Mar 2017 02:42

The set I(q) can contain any expression of the form W independent of V given Z where W,V,Z are arbitrary subsets of X1,..,Xn.
It also includes the case where Z is an empty set, meaning unconditional expectation.

If you are referring to question 1 then there are just three variables and there aren't too may possibilities and some of these are symmetric.

Amir

student (guest) 31 Mar 2017 20:21

Any of them can be empty? (Or just the condition part?)
Can them contain the same variables?

If so, there r 8 subsets of {1,2,3}, Wich means 8 options of each subset at the CI triple => 512 options…
(Maybe 256 if we consider there is no order between the 2 independent subset)