The graded HW1 submissions can be found in mail box #263 (Daniel Carmon) at Schreiber.

Those who sent me online have a printed version of their HW there.

Also, please check if you forgot to add an ID to your submission, and if so please mail it to me at:

li.ca.uat.liam|adnomrac#li.ca.uat.liam|adnomrac

so that I can type in your grade.

Thanks,

Daniel.

I'm confused about the definition of Id-sep(G).

If we take s={i}, than xi_x[n]\{i}|xi ( and so Xi_X{not s}|Xs) in Idsep, since Xi is in s, contained in any path from it, and does not in v-structure.

If so, it also looked like a minimal MB, which I guess it's notâ€¦.

I guess the definition of d-separating is missing:

X,Y are d-separated by Z in V\{X,Y}. (As written in some articles)

Moreover, I think there is a mistake at the notes page 5:

X_Y|Z in IdsepG if every path is not active regard to Z, which means it either has a node in Z that is not in a v structure or it has a node outside of Z that is in v-structure and *all its descendants are out of Z*

(The negation of the active path definition)

Q1:

About Iq CI- which r basically 3 groups of variables X,Y,Z.

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 optionsâ€¦

(Maybe 256 if we consider there is no order between the 2 independent subset)

Should we ignore cases like X1_X2|X1,X3….? How many options should we check?

]]>and if so, can we use it without proof?

In the scribe it is said that except for a set of measure zero all BN on G will satisfy I_d-sep(G)=I(p), is that enough to prove the above?

Thanks!

]]>1. When Xi and Xj are conditionally independent given any other variable Xk

or

2. When Xi and Xj are conditionally independent given the intersection of all other variables

thanks!

]]>there are multiple options:

x1->x2->x3->x4->x1

x4->x3->x2->x1->x4

…

We've seen this definition: (1)

\begin{align} I_{sep}(G) = \{X \perp Y | Z : Z \ separates \ X \ and \ Y\} \end{align}

Does this definition rely on some probability? Or is it that given a graph G we construct the set of **all** X,Y,Z where Z separates X and Y and then, given a probability p we say that:

\begin{align} I_{sep}(G) \subseteq I(p) \end{align}

If p satisfies all these properties?

]]>I can create a DAG s.t the BN distribution on this graph equals the distribution q but the LM(G) can't be the same as I(q) because the the directed graph has asymmetric structure by definition ("is parent" ratio) and in the distribution there is symmetric structure of independent.

So I have a DAG that gives me the

What should I answer in this case? ]]>

Am I missing anything?

Just to be sure, the i in ij in E is the same i as in the first Pie_i=1?

Thanks!

]]>Should we show that I(p) contains I_{seq}(G) instead? ]]>

Or only to those of the form 'X independent of Y given Z'? ]]>

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?

I don't understand if we need to really solve the problem or just represent it in a form that we can calculate, i.e i can represent the problem formally, but in order to solve it i need to describe an algorithm, which i think i can do but not sure if i were asked for it.

Do we need to describe the algorithm solving the problem or not?

was my question clear enough?