Proof of semi-graphoid symmetry axiom
I have some trouble understanding why this proof is a proof:
Lemma:
 \iff I_p(Y, Z, X))
Proof:
 \iff P(C_x | C_y \land C_z) = P(C_x | C_z))
Ok, this is just conditional independence, x independent of y given z.
}{P(C_y \land C_z)} = \frac{P(C_x \land C_z)}{P(C_z)})
This is rewritten according to the rule of conditional independence P(A|B) = P(A & B) / P(B).
Bottom up the same is done for the right hand side of the lemma, but I don't get how the following and previous step are equal.. Why does this prove anything?
}{P(C_x \land C_z)} = \frac{P(C_y \land C_z)}{P(C_z)})
 = P(C_y | C_z))
)
Re: Proof of semi-graphoid symmetry axiom
Hey Lepzed.
Is the random variable X independent to Z?
Re: Proof of semi-graphoid symmetry axiom
The independence relation )
expresses that in the context of information about Z, information about Y is irrelevant with respect to Y or put differently: X is condtionally independent of Y given Z.
