Bernal S D_2010.pdf - University of Plymouth

3.1. THE BAYESIAN BRAIN HYPOTHESIS
on a probabilistic generative model m, which captures the dependencies between causes and
sensory data, and can thus generate sensory samples from given causes, and likewise obtain a
posterior distribution of causes given the sensory input. The generative model is hypothesized
to be implicitly imprinted in the hierarchical stmclure of the brain.
The theory accomnKxJaies several aspects of brain function in terms of optimizing the differ­
ent parameters in order to minimize the free energy of the system. For example, perception is
understood as the process of minimizing free energy with respect to the neuronal activity (en­
coded as part of the internal stale, n), which entails m;Kimi/ing the posterior probability of the
recognition density. The recognition density therefore becomes an approximation of the true
posterior density. This is cquivatenl to the Baycsian inference approach described previously
in this section. Similarly, learning or plasticity in the brain is explained as the optimization of
synaptic weights, also enctxlcd by the internal state variable, ;i. These two processes minimize
free energy by changing the recognition density, which modifies the expectations about sensory
data, but without modifying sensory data itself.
On the other hand, action is understood as a process of active inference, aimed at modifying
sensory data so that it conforms to the predictions or expectations made by the recognition den­
sity. Increasing the accuracy of predictions also reduces the free energy of the system. Broadly
speaking, the prediction error (i.e. sensations minus predictions), and thus free energy, can be
minimized by either changing the sensory input through action, or changing the predictions
through perception and learning. For a comprehensive description of the mathemalieal formu­
lation of free energy minimi/alion the reader is referred lo l-rision and Kiebel (2009),
The free energy fonnulation was originally developed to deal with the problem of obtaining
exact inferences in complex systems. It tackles the problem by converting it into an easier
optimization problem. The inversion of the likthhood function (based on the Hayes theorem)
to infer the posterior distribution over causes, thus becomes an optimization problem which
consists of minimizing the difference between the recognition and the posterior densities to
suppress free energy. This technique can be described as a type of variational Bayesian method
(Beal 2003, Friston and Kiebel 2009. Winn and Bishop 2005), also called ensemble learning.
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