Bernal S D_2010.pdf - University of Plymouth

3.4. EXISTING MODELS
is on models that use Bayesian belief propagation or similar inference algorithms in the context
of hierarchical generative models. In particular. Section 3.4.1 describes several implementa­
tions of belief propagation using spiking neurons; Section 3.4.2 describes implementations of
belief propagation at a higher level of abstraction, specilically those attempting to model object
perception In the visual system; and Section 3.4,3 compares diftcrcni speculative mappings of
the algorithm over the cortical laminar circuitry.
3.4.1 Biological models with spiking neurons
There have been several proposals for how spiking neurons can implement belief propagation
in graphical models such as Bayesian networks. Three of these models are described in this
subsection.
3.4.1.1 Single layer hidden Markov model
The first one. by Rao (2()04, 2()0.'i. 2U06). describes a single-layered recurrent network that is
able to perform a simple visual motion detection task. The input lo the model is a I -dimensional
30 pixel image, with a moving pixel. The model contains 30 neurons, each one coding the 30
different states of a hidden Markov model. The stales code a specific spatial location (15 lo­
cations with 2 pixel intervals), and the direction of motion (leftward or rightward). The firing
rate of each neuron encodes the log of the posterior probability (belicO of being in a specific
state, such that the neuron with the highest hring rate indicates the state of the world. To model
the likelihood function, equivalent to the bottom-up messages, the input image was filtered by
a set of feedforward weights (Gaussian functions), which represent the conditional probabil­
ity function. The prior, or lop-down message, was approximated by multiplying the posterior
probability at the previous time-step by a set of recurrent weights which represent the transition
pnibabilities between states.
The model was later extended by adding a second layer of Bayesian decision-making neurons
that calculated a log-posterior ratio lo perform the random-dot motion detection task. A similar
implementation using a simple two-level hierarchical network with two interconnected path­
ways for features and locations, modelling the ventral and dorsal paths, was used to simulate
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