Figure 2.

Partition functions and free energy. This schematic illustrates a useful operation known as “closing the box” or taking a partition function of part of a graph. By summing (or integrating) over all variables on edges within the dashed box, we can reduce this portion of the graph to a single factor that plays the part of a (marginal) likelihood. While it is not always feasible to perform the summation explicitly, we can approximate the marginal likelihood with a negative free energy. This affords an efficient method for evaluating subregions of the graph. Taking the partition function, or computing the free energy, for the whole graph allows us to evaluate the evidence sensory data affords the generative model.