marginal values

[elton]

Hi keki,

I am trying to understand your works and currently reading your
thesis. When I read your chapter 3, you mentioned about marginal
values that when 0 happens at locus A and locus B, there is 0.2 value.
What does the 0.2 (or -0.2 in another case) mean? Is the value
arbitrary? How do you define Marginal Value? It seems Marginal Values
is important to identify some characteristic. Is it possible to
measure or identify it for problem solving, i.e. some combinatorial
problem.

Thanks,
Elton

[Keki Burjorjee]

Hi Elton,

0.2 is the multi-variable marginal value of the variable assignment
(A=0,B=0). The 0.0's are the marginal value of single variable
assignments.

The marginal value of a single variable assignment is defined as
follows: Consider some set of variables S={Y_1, ..., Y_m}, and some
(stochastic or deterministic) objective function f:Y_1 x .... x Y_m ->
R, where "x" denotes the cross-product. Suppose each variable can take
values in {y_1, ..., y_n}. Then, for any i in {1,...,m}, and any j in
{1, ..., n}, the marginal value of Y_i=y_j is the expected value of
f(z_1, ..., z_i-1, y_j, z_i+1, ..., z_m), where, for any k in
{1,...,i-1, i+1, ..., m}, the value of z_k is drawn from the uniform
distribution over {y_1, ..., y_n}.

The definition of the marginal value of a multi-variable assignment is
a straightforward extension of the definition given above.

Since a marginal value, as defined here, is just an expected value, it
can be estimated by sampling appropriately.

Hope this helps!

Keki