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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References

AlaisD.BurrD. (2004). The ventriloquist effect results from near-optimal bimodal integrationCurr. Biol. 14257262.

AnastasioT. J.PattonP. E.Belkacem-BoussaidK. (2000). Using Bayes’ rule to model multisensory enhancement in the superior colliculusNeural Comput. 1211651187.

AndersenR.EssickG.SiegelR. (1985). Encoding of spatial location by posterior parietal neuronsScience 230456458.

AndersonC. (1994). Neurobiological computational systems in: Computational Intelligence Imitating Life pp.  213222. IEEE PressNew York, USA.

BanksM. S. (2004). What you see and hear is what you getCurr. Biol. 14R236R238.

BarlowH. B. (1969). Pattern recognition and the responses of sensory neuronsAnn. N. Y. Acad. Sci. 156872881.

BeckJ. M.MaW. J.KianiR.HanksT. D.ChurchlandA. K.RoitmanJ. D.ShadlenM. N.LathamP. E.PougetA. (2008). Bayesian decision-making with probabilistic population codesNeuron 6011421145.

BeckJ. M.LathamP. E.PougetA. (2011). Marginalization in neural circuits with divisive normalizationJ. Neurosci. 311531015319.

Ben HamedS.PageG.DuffyC.PougetA. (2003). MSTd neuronal basis functions for the population encoding of heading directionJ. Neurophysiol. 90549558.

BerkesP.OrbanG.LengyelM.FiserJ. (2011). Spontaneous cortical activity reveals hallmarks of an optimal internel model of the environmentScience 3318387.

BishopC. M. (2006). Pattern Recognition and Machine Learning. SpringerCambridge, UK.

BoussaoudD.BarthT.WiseS. (1993). Effects of gaze on apparent visual responses of frontal cortex neuronsExper. Brain Res. 93423434.

BregmanA. S. (1990). Auditory Scene Analysis: The Perceptual Organization of Sound. MIT PressCambridge, MA, USA.

BremmerF.IlgU.ThieleA.DistlerC.HoffmanK. (1997). Eye position effects in monkey cortex. I: Visual and pursuit-related activity in extrastriate areas MT and MSTJ. Neurophysiol. 77944961.

CarandiniM.HeegerD. J. (2011). Normalization as a canonical neural computationNat. Rev. Neurosci. 135162.

ClarkJ.YuilleA. L. (1990). Data Fusion for Sensory Information Processing Systems. KluwerNorwell, MA, USA.

CoverT. M.ThomasJ. A. (1991). Elements of Information Theory. John Wiley and SonsNew York, USA.

DeneveS. (2008). Bayesian spiking neurons I: InferenceNeural Comput. 2091117.

ErnstM. O.BanksM. S. (2002). Humans integrate visual and haptic information in a statistically optimal fashionNature 415429433.

FiserJ.BerkesP.OrbanG.LengyelM. (2010). Statistically optimal perception and learning: from behavior to neural representationsTrends Cognit. Sci. 14119130.

GrohJ. M.TrauseA. S.UnderhillA. M.ClarkK. R.InatiS. (2001). Eye position influences auditory responses in primate inferior colliculusNeuron 29509518.

HeegerD. J. (1992). Normalization of cell responses in cat striate cortexVis. Neurosci. 9181197.

HowardI. P.TempletonW. B. (1966). Human Spatial Orientation. John Wiley and SonsNew York, USA.

HoyerP. O.HyvarinenA. (2003). Interpreting neural response variability as Monte Carlo sampling of the posterior in: Neural Information Processing SystemsVol. 15. MIT PressCambridge, MA, USA.

JazayeriM.MovshonJ. A. (2006). Optimal representation of sensory information by neural populationsNat. Neurosci. 9690696.

KordingK. P.BeierholmU.MaW. J.QuartzS.TenenbaumJ. B.ShamsL. (2007). Causal inference in multisensory perceptionPLoS ONE 2e943.

LandyM. S.KojimaH. (2001). Ideal cue combination for localizing texture-defined edgesJ. Optic. Soc. Amer. A 1823072320.

MaW. J. (2010). Signal detection theory, uncertainty, and Poisson-like population codesVision Research 5023082319.

MaW. J.BeckJ. M.LathamP. E.PougetA. (2006). Bayesian inference with probabilistic population codesNat. Neurosci. 914321438.

MaW. J.NavalpakkamV.BeckJ. M.Van den BergR.PougetA. (2011). Behavior and neural basis of near-optimal visual searchNat. Neurosci. 14783790.

PougetA.DayanP.ZemelR. S. (2003). Inference and computation with population codesAnn. Rev. Neurosci. 26381410.

RaoR. P. (2004). Bayesian computation in recurrent neural circuitsNeural Comput. 16138.

SatoY.ToyoizumiT.AiharaK. (2007). Bayesian inference explains perception of unity and ventriloquism aftereffect: identification of common sources of audiovisual stimuliNeural Comput. 1933353355.

ShamsL.BeierholmU. (2010). Causal inference in perceptionTrends Cognit. Sci. 14425432.

ShiL.GriffithsT. L.FeldmanN. H.SanbornA. N. (2010). Exemplar models as a mechanism for performing Bayesian inferencePsychon. Bull. Rev. 17443464.

SlutskyD. A.RecanzoneG. H. (2001). Temporal and spatial dependency of the ventriloquism effectNeuroreport 12710.

TrommershauserJ.KordingK.LandyM. S. (Eds) (2011). Sensory Cue Integration. Oxford University PressNew York, USA.

TrotterY.CelebriniS.StricanneB.ThorpeS.ImbertM. (1996). Neural processing of stereopsis as a function of viewing distance in primate visual cortical area V1J. Neurophysiol. 7628722885.

Van den BergR.VogelM.JosicK.MaW. J. (2011). Optimal inference of samenessProc. Nat. Acad. Sci. USA 10931783183.

VilaresI.KordingK. P. (2011). Bayesian models: the structure of the world, uncertainty, behavior, and the brainAnn. New York Acad. Sci. 12242239.

WallaceM. T.RobersonG. E.HairstonW. D.SteinB. E.VaughanJ. W.SchirilloJ. A. (2004). Unifying multisensory signals across time and spaceExper. Brain Res. 158252258.

WoznyD.BeierholmU.ShamsL. (2008). Human trimodal perception follows optimal statistical inferenceJ. Vision 8(3) 111.

ZemelR.DayanP.PougetA. (1998). Probabilistic interpretation of population codeNeural Computat. 10403430.

Figures

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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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