Figure 4
From: Introducing a Bayesian model of selective attention based on active inference
ABC of generative model. This figure shows the likelihood, transition and prior preference matrices used in the colour/shape task. (A) The colour category of the scenes shown on the left is determined purely by the colour in location 4 (top right quadrant). The panels on the right show the likelihood (A) matrices for location k = 4. The likelihood matrices encode the probability of outcomes (ot) given the hidden states (st). The first likelihood matrix A1 (Rule) signals what the rule is, either categorise colour or shape. The second likelihood matrix A2 (Where) signals the sampled location on the scene, one of eight locations. The third likelihood matrix A3 (What: colours) encode the probability of colours red, green and blue under different colour categories red, green and blue. The final likelihood matrix A4 (What: shapes) encode the probability of shapes square, circle and triangle under different shape categories square, circle and triangle. Because the colour and shape are separate modalities, the probability of colour and shape objects are encoded by separate likelihood matrices A3 and A4. The likelihood matrix under the colour modality for location 4 A3(k = 4) shows that the colour category of a scene is purely determined by the colours in this location; however, under the shape modality A4(k = 4) the object in this location does not provide any information about the shape category, i.e. null. (B) This panel shows the transition matrices. All the transition matrices are identity matrices except for the action dependent transition matrix B2, which encodes the most likely location to be sampled as a function of action, e.g. B2(k = 4) shows that under action 4, the top right quadrant is the most likely location to be sampled at the next time step. The identity transition matrices B1 (Rule), B3 (Category: colours) and B4 (Category: shapes) express the fact that the rule and the colour and shape objects do not change in the course of a trial. C) The prior preference matrices are shown in this panel. The prior preference matrices encode how much one outcome is preferred relative to other outcomes as a function of time. The only definitive preferences are defined over the columns of C3 (What: colours) and C4 (What: shapes). Under both C3 and C4 the utility of making a right categorisation and wrong categorisation is +2 and −4 natural units, respectively. With these utilities (i.e. log odds) the agent expects to categorise a scene correctly, while avoiding an incorrect categorisation.
