Bayesian inference and belief propagation in cortical networks

Sophie Deneve1 and Alexandre Pouget2

1Gatsby computational neuroscience unit
2University of Rochester

To infer the properties of the environment or the most appropriate action from multiple noisy sensory sources, the brain must represent and manipulate the joint uncertainties over many variables. It has been proposed that population codes represent uncertainties by encoding distributions of probability of sensory variables. However, it is still unclear how these representations could be used to perform inference on multiple uncertain sources, and how statistical dependencies between these sources could be represented and learned.

In particular, Bayesian inference on large numbers of jointly dependant variables is generally intractable. Bayesian networks are a convenient graphical representation of statistical structures through which one can render inference and learning tractable. They represent groups of dependant variables as nodes, and conditional independencies as links (or lack thereof) between these nodes.

In this presentation, we will show how propagation of activity in interconnected cortical networks with population codes can be interpreted as a propagation of belief in an equivalent bayesian network. From this observation we will propose a new theory for the correspondence between cortical connectivity and modularity, neural response curves in multi-modal brain areas, statistical dependencies in the natural environment and cognitive modularity. As an example we will consider a minimal version of belief propagation were only means and covariance of input variables are propagated and show that it predicts some neural response properties in multi-sensory and sensorimotor areas.