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Implicit encoding of prior probabilities in optimal neural populations
 Advances in Neural Information Processing Systems (NIPS
, 2010
"... Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of neurons and spikes in a population. We model the spikes ..."
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Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of neurons and spikes in a population. We model the spikes of each cell as samples from an independent Poisson process with rate governed by an associated tuning curve. For this response model, we approximate the Fisher information in terms of the density and amplitude of the tuning curves, under the assumption that tuning width varies inversely with cell density. We consider a family of objective functions based on the expected value, over the sensory prior, of a functional of the Fisher information. This family includes lower bounds on mutual information and perceptual discriminability as special cases. In all cases, we find a closed form expression for the optimum, in which the density and gain of the cells in the population are power law functions of the stimulus prior. This also implies a power law relationship between the prior and perceptual discriminability. We show preliminary evidence that the theory successfully predicts the relationship between empirically measured stimulus priors, physiologically measured neural response properties (cell density, tuning widths, and firing rates), and psychophysically measured discrimination thresholds. 1
Optimal inference explains the perceptual coherence of visual motion stimuli
 Journal of Vision
"... The local spatiotemporal pattern of light on the retina is often consistent with a single translational velocity which may also be interpreted as a superposition of spatial patterns translating with different velocities. Human perception reflects such interpretations, as can be demonstrated using st ..."
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The local spatiotemporal pattern of light on the retina is often consistent with a single translational velocity which may also be interpreted as a superposition of spatial patterns translating with different velocities. Human perception reflects such interpretations, as can be demonstrated using stimuli constructed from a superposition of two drifting gratings. Depending on a variety of parameters, these stimuli may be perceived as a coherently moving plaid pattern or as two transparent gratings moving in different directions. Here, we propose a quantitative model that explains how and why such interpretations are selected. An observer’s percept corresponds to the most probable interpretation of noisy measurements of local image motion, based on separate prior beliefs about the speed and singularity of visual motion. This model accounts for human perceptual interpretations across a broad range of angles and speeds. With optimized parameters, its components are consistent with previous results in motion perception.
Eero P. SimoncelliDedication To my parents, Sham and Karobi Ganguli. iii Acknowledgements
, 2012
"... encouragement, and inspiration he has given me throughout the course of this research. It still amazes me how quickly he can arrive at solutions to my math problems (which mostly consist of symbols scribbled nervously on a chalkboard) by drawing simple pictures. I have learned so much from him. I am ..."
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encouragement, and inspiration he has given me throughout the course of this research. It still amazes me how quickly he can arrive at solutions to my math problems (which mostly consist of symbols scribbled nervously on a chalkboard) by drawing simple pictures. I have learned so much from him. I am grateful to members of the Simoncelli lab: Umesh Rajaeshekar, for teaching me everything I know about image processing and Matlab’s implementation of the Fast Fourier Transform; Josh McDermott, for always answering my audio signal processing questions; Chaitue Ekhanadham, for being my resident calculus guru; Brett Vintch, for teaching me how to rock climb, learning how to snowboard with me, and always being down to ride bikes and chill at Le Basket; and Rob Young, for fixing my computer every time it broke and not being too mad when it was my fault. I am especially grateful to Jeremy Freeman, who in many ways was my second advisor. His contributions include thoroughly reading and editing drafts of my papers, helping me put together talks, teaching me Adobe Illustrator and aspects
Optimal inference explains the perceptual coherence
"... The local spatiotemporal pattern of light on the retina is often consistent with a single translational velocity which may also be interpreted as a superposition of spatial patterns translating with different velocities. Human perception reflects such interpretations, as can be demonstrated using st ..."
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The local spatiotemporal pattern of light on the retina is often consistent with a single translational velocity which may also be interpreted as a superposition of spatial patterns translating with different velocities. Human perception reflects such interpretations, as can be demonstrated using stimuli constructed from a superposition of two drifting gratings. Depending on a variety of parameters, these stimuli may be perceived as a coherently moving plaid pattern or as two transparent gratings moving in different directions. Here, we propose a quantitative model that explains how and why such interpretations are selected. An observer’s percept corresponds to the most probable interpretation of noisy measurements of local image motion, based on separate prior beliefs about the speed and singularity of visual motion. This model accounts for human perceptual interpretations across a broad range of angles and speeds. With optimized parameters, its components are consistent with previous results in motion perception.
Preprint To appear in the British Journal for the Philosophy of Science Bayes in the Brain. On Bayesian Modelling in Neuroscience
"... Abstract According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this paper is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some o ..."
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Abstract According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this paper is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some of their epistemological challenges, and some of their implications. We address two questions: i) How are Bayesian models used in theoretical neuroscience? ii) From the use of Bayesian models in theoretical neuroscience, have we learned or can we hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine? From actual practice in theoretical neuroscience, we argue for three claims. First, currently Bayesian models do not provide mechanistic explanations; instead they are useful devices for predicting and systematizing observational statements about people’s performances in a variety of perceptual tasks. That is, currently we should have an instrumentalist attitude towards Bayesian models in neuroscience. Second, the inference typically drawn from Bayesian behavioural performance in a variety of perceptual tasks to underlying Bayesian mechanisms should be understood within the threelevel framework laid out by David Marr ([1982]). Third, we can hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine to the extent that Bayesian models will prove successful in yielding secure and informative predictions of both subjects ’ perceptual performance and features of the underlying neural mechanisms.
unknown title
, 2012
"... Implicit embedding of prior probabilities in optimally efficient neural populations ..."
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Implicit embedding of prior probabilities in optimally efficient neural populations