Towards a Neural Implementation of Causal Inference in Cue Combination

in Multisensory Research
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Causal inference in sensory cue combination is the process of determining whether multiple sensory cues have the same cause or different causes. Psychophysical evidence indicates that humans closely follow the predictions of a Bayesian causal inference model. Here, we explore how Bayesian causal inference could be implemented using probabilistic population coding and plausible neural operations, but conclude that the resulting architecture is unrealistic.

Towards a Neural Implementation of Causal Inference in Cue Combination

in Multisensory Research



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    Generative model of causal inference. Nodes represent variables, arrows conditional dependencies. The common-cause variable C is of interest to the observer. When C=1 (common cause), s1 equals s2. When C=2 (different causes), s1 and s2 are independent. Independent Gaussian noise corrupts the scalar measurements x1 and x2. In the neural version of this model, the measurements are replaced by population patterns of activity, r1 and r2.

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    (a) The strength of the evidence in favor of a common cause, as expressed by the log likelihood ratio, as a function of the measurements x1 and x2. The d=0 contour lines are shown in black. Two aspects of interest are the band around the diagonal and the structure within this band. Parameters were σ1=3, σ2=10, and σs=10. (b) Proportion reports of a common cause as a function of stimulus disparity (s2 minus s1). This figure is published in colour in the online version.

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    A population pattern of activity r encodes, on a single trial, a neural likelihood function of the stimulus. Note that although both plots have a roughly Gaussian shape, their interpretations are completely different and their widths will in general not be equal. This figure is published in colour in the online version.

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    (a) Example set of tuning curves in an input population of sensory neurons used in the simulation. (b) Contribution of each of the four terms of the log likelihood ratio in equation (11). The fourth term has a much lower variance than the first three and we approximate it by its trial average. (c) Comparison of the posterior probability of a common cause estimated by an approximate network and the optimal posterior probability. Red lines indicate the decision criteria. Points in off-diagonal quadrants indicate deviations from the optimal observer. (d) Comparison of the proportion reports of a common cause as a function of stimulus disparity between the approximate network and the optimal observer.

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    Circuit diagram of a network that can approximate the posterior probability of a common cause using linear combinations, quadratic operations, and divisive normalization. Input is assumed Poisson-like.


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