Probabilistic Inference in General Graphical Models through Sampling in Stochastic Networks of Spiking Neurons
The visual perception experiment of  that demonstrates “explaining away” and its corresponding Bayesian network model.
A) Two visual stimuli, each exhibiting the same luminance profile in the horizontal direction, differ only with regard to their contours, which suggest different 3D shapes (flat versus cylindrical). This in turn influences our perception of the reflectance of the two halves of each stimulus (a step in the reflectance at the middle line, versus uniform reflectance): the cylindrical 3D shape “explains away”the reflectance step. B) The Bayesian network that models this effect represents the probability distribution . The relative reflectance () of the two halves is either different ( = 1) or the same ( = 0). The perceived 3D shape can be cylindrical ( = 1) or flat ( = 0). The relative reflectance and the 3D shape are direct causes of the shading (luminance change) of the surfaces (), which can have the profile like in panel A ( = 1) or a different one ( = 0). The 3D shape of the surfaces causes different perceived contours, flat ( = 0) or cylindrical ( = 1). The observed variables (evidence) are the contour () and the shading (). Subjects infer the marginal posterior probability distributions of the relative reflectance and the 3D shape based on the evidence. C) The RVs are represented in our neural implementations by principal neurons . Each spike of sets the RV to 1 for a time period of length . D) The structure of a network of spiking neurons that performs probabilistic inference for the Bayesian network of panel B through sampling from conditionals of the underlying distribution. Each principal neuron employs preprocessing to satisfy the NCC, either by dendritic processing or by a preprocessing circuit.