Inference algorithms

An inference algorithm is a procedure that takes as its inputs an arbitrary probabilistic model, a query variable (or a set of those) and an observation . Its output is the probability distribution .

In symfer, this works a little differently. Instead of directly outputting probabilities, the inference algorithm outputs a factor algebra expression. No actual multiplications or additions are made yet; this is done at the moment that we choose to evaluate this expression.

Each expression in factor algebra can be read as a script. For example, the expression (or in Python: SumProd(['A'],[SumProd([],[SumProd([],[f,g]),h])])) tells the evaluator to perform these steps:

1. multiply with
2. multiply the result of (1) with
3. sum out variable from the result of (2)

These steps are performed when we execute

>>> s.evaluate(expr)

However, first it is the task of an inference algorithm to cleverly construct expr. The most basic inference algorithm is defined as follows:

def naive(facs,query,obs):
    return I().product(*facs).index(obs).sumto(query)

It simply multiplies all factors to construct the joint, then selects only those values consistent with the assignment obs, and from these sums out all variables except those in query. Note that this calculates the distribution . It is easy to derive the sought for conditional probabilities from this by normalizing; however, symfer does not do this for you (as of yet). This is the case for all the inference algorithms.

More about the other algorithms in the future, for now take a look at symfer.inference.