Using WAPS for custom application #1
Description
Hi,
We want to use WAPS to sample for one of our applications. Currently, we used WAPS and it stalls indefinitely. I have a couple of questions. It would be very helpful if you (or your team members) can guide us.
If F is a CNF formula with variables X = {x_1, x_2,…, x_n} and S is the set of satisfying assignments of F. Our understanding is that WAPS makes it possible to specify any subset V of X, so that the samples returned will take the form of strings of length n such as the following: 11*1000011**1
where the variables with * are the variables not in our set of interest V. Given enough samples of the above type we can compute the joint probability distribution of the variables in V (induced by selecting uniformly from S).
In our case we don’t really care about the joint distribution of the variables in the set of interest V. The only thing we care about is whether some of the variables in V are “highly polarized.” This means that, in principle, our set V (of variables of interest) could even be as small as a single variable. That is, we run the sampler with V consisting of a single variable x, get 1000 samples (in each of which the only thing we learn is the value of x), and if x takes the same value in, say, 950 of the samples or more, we record x.
Also, we believe that asking the sampler for only one variable at a time, may make its life much easier. Is it possible to do this? If so, can we modify WAPS to achieve this?