2.1 Uniform Distribution

Now that we know the basic commands and file types used in Alchemy, we want to start with the simplest MLN one can think of: the empty MLN. Suppose we want to consider the output of a coin flip. We can state that the outcome of a flip is heads with the predicate Heads(flip), where flip ranges from, say, 1 to 20. If Heads(n) is true, then flip n was heads; otherwise it was tails. By supplying an empty MLN with Heads as the only predicate:

flip = {1,...,20}

Heads(flip)

we can perform probabilistic inference to result in a uniform distribution:

infer -i uniform.mln -r uniform.result -e empty.db -q Heads

Alchemy requires a .db file with evidence; here, empty.db is an empty file. The resulting file uniform.result shows the marginal probabilities of each grounding of Heads given no other evidence. In the limit, these should approach 0.5 (note, we can trade off accuracy for speed by varying the number of samples with the option -maxSteps).