Figure 3.

The same generative model in active inference, represented as a Forney factor graph. Left panel: Expressions for the belief updates enabling approximate Bayesian inference and action selection. In this figure, boldface denotes the expectations or sufficient statistics of hidden states in the previous figures. The brackets that figure in the action selection panel are Iverson brackets; if the condition in square brackets is obtained, these return the value 1, and return 0 otherwise. Right panel: Forney or normal style factor graphs are equivalent to Bayesian networks, with some important difference. In this kind of graph, nodes (the square boxes) correspond not to variables, as in a Bayesian network, but to factors; and edges represent unknown variables that must be inferred. Filled squares, echoing the above, denote observable outcomes. Edges are labelled in terms of the sufficient statistics of their marginal posteriors. Factors are labelled according to the parameters that encode the associated probability distributions. Circled numbers denote the implicit message passing in the belief updates – as messages are passed from nodes (factors) to edges (variables). Figure re-used from REF under the CC license.

Source: From Friston, Parr, and de Vries (2017).