Bernal S D_2010.pdf - University of Plymouth

3.1. THE BAYESJAN BRAIN HYPOmESIS
These methods provide an analytical approximation to the posterior probability of intractable
Bayesian inference problems.
Tn summary, ihe free energy principle provides a unifying framework for Ihe Bayesian brain
and predictive coding approaches, which understand the brain as an inference machine trying to
oplimi/e the probabihstic representation of what caused its sensory input. As stated by Friston
(2010), the theory can be implemented by many different schemes, most of which involve some
form of hierarchical message passing or belief propagation among regions of the brain.
The model proposed in this thesis describes such a hierarchical message passing scheme, and
thus is theoretically grounded on the free energy principle and the Bayesian brain hypothe­
sis. Panicuhirly. the focus of this thesis is on Bayesian networks, a type of graphical model
which represents ihe causal dependencies present in generative models: and the Bayesian belief
propagation algorithm, which perfonn.s inference in this type of network. A more formal defi­
nition and the relevant mathematical formulation of Bayesian networks and belief propagation
is included in Section 3.3.
3.1.4 Origins
One of ihe first people to propose formulating perception in terms of a generative model was
Mumford, who based his ideas on (irenader's pattern theory and earlier suggestions by Helmholiz
(Mumford 1996). Applied to visual perception, this theory states thai what we perceive is noi
ihe true sensory signal, but a rational reconstruction of what the signal should be. The am­
biguities present in the early stages of processing an image never become conscious because
the visual system finds an explanation for every pecuHarily of the image. Pallem theory is
based on the idea ihat pattern analysis requires patlem synthesis, thereby adding to the previous
purely boliom-up or feedforward structure a top-down or feedback process in which the signal
or pattern is reconstructed.
The Helmholtz machine (Dayan el al. I99.'i) extended these ideas by implementing inferential
priors using feedback. Here, the generative and recognition models were both implemented
as slruclured networks whose parameters had to be learned. The connectivity of the system
is based on the hierarchical lop-down and botiom-up connections in the cortex. This layered
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