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Encoding and Decoding Neural Population Signals for Two-Dimensional Stimulus

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Abstract

Stimulus is encoded by neuronal populations and then the brain can decide what happens in the practical situations from the population patterns of neural spiking. It is meaningful to implement computations by making use of the response of population of neurons to determine a certain stimulus or to obtain the values of related parameters. Neural populations can not only encode a single attribute of a stimulus but also can encode multi-dimensional stimulus (or various properties of a stimulus) simultaneously. For example, by looking at a moving object we can estimate the direction and speed of it, which shows that the response of a population of optic neurons contain information about both the direction and speed. However, we do not find any models in literature for encoding and decoding neuronal population signals for multi-dimensional stimulus. In this paper we present a simple model for reading neural population signals for the two attributes of a stimulus (or two-dimensional stimulus). We use Poisson distribution to describe the encoding process of neural populations and then to extract the values of the stimulus by Bayesian methods. We demonstrate that the nervous population can encode two properties of a stimulus and extract the two kinds of estimated values of the stimulus at the same time. The results show that we can obtain perfect estimates of two attributes of a stimulus from our simple model. Finally, we use Fisher information matrix to examine the influence of the tuning widths on the encoding efficiency.

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References

  1. Dayan P, Abbott LF (2001) Theoretical neuroscience. MIT Press, Cambridge, pp 1–7

    MATH  Google Scholar 

  2. Berthouze L, Tijsseling A (2006) A neural model for context-dependent sequence learning. Neural Process Lett 23:27–45

    Article  Google Scholar 

  3. Chen M, Han JW, Hu XT, Jiang X, Guo L, Liu T (2014) Survey of encoding and decoding of visual stimulus via FMRI: an image analysis perspective. Brain Imaging Behav 8:7–23

    Article  Google Scholar 

  4. Nelken I, Chechik G (2005) Encoding stimulus information by spike numbers and mean response time in primary auditory cortex. Comput Neurosci 19:199–221

    Article  MATH  Google Scholar 

  5. Lippert J, Wagner H (2002) Visual depth encoding in populations of neurons with localized receptive fields. Biol Cybern 87:224–261

    Article  MATH  Google Scholar 

  6. Stuart GJ, Sakmann B (1994) Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature 367:69–72

    Article  Google Scholar 

  7. Pouget A, Dayan P, Zemel RS (2003) Inference and computation with population codes. Annu Rev Neurosci 26:381–410

    Article  Google Scholar 

  8. Kim D, Lee J (2011) Path integration mechanism with coarse coding of neurons. Neural Process Lett 34:277–291

    Article  Google Scholar 

  9. Zemel R, Dayan P, Pouget A (1998) Probabilistic interpretation of population code. Neural Comput 10:403–430

    Article  Google Scholar 

  10. Series P, Latham P, Pouget A (2004) Tuning curve sharpening for orientation selectivity: coding efficiency and the impact of correlations. Nat Neurosci 7:1129–1135

    Article  Google Scholar 

  11. Ma WJ, Beck JM, Latham PE, Pouget A (2006) Bayesian inference with probabilistic population codes. Nat Neurosci 9:1432–1438

    Article  Google Scholar 

  12. Josic K, Shea-Brown E, Doiron B, De la Rocha J (2009) Stimulus-dependent correlations and population codes. Neural Comput 21:2774–2804

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang K, Sejnowski TJ (1999) Neuronal tuning: to sharpen or broaden? Neural Comput 11:75–84

    Article  Google Scholar 

  14. Eurich CW, Wilke SD (2000) Multidimensional encoding strategy of spiking neurons. Neural Comput 12:1519–1529

    Article  Google Scholar 

  15. Beck JM, Ma WJ, Kiani R, Hanks TD, Churchland AK (2008) Bayesian decision-making with probabilistic population codes. Neuron 60:1142–1152

    Article  Google Scholar 

  16. Averbeck BB, Lee D (2006) Effects of noise correlations on information encoding and decoding. J Neurophys 95:3633–3644

    Article  Google Scholar 

  17. Wei XX, Stocker AA (2012) Bayesian inference with efficient neural population codes (ICANN lecture notes in computer science artificial neural networks and machine learning), vol 7552, pp 523–530

  18. Pouget A, Beck JM, Ma WJ, Latham PE (2013) Probabilistic brains: knowns and unknowns. Nature Neurosci 16:1170–1178

    Article  Google Scholar 

  19. Shi Z, Church RM, Meck WH (2013) Bayesian optimization of time perception. Trends Cogn Sci 17:556–564

    Article  Google Scholar 

  20. Ma WJ, Jazayeri M (2014) Neural coding of uncertainty and probability. Annu Rev Neuosci 37:205–220

    Article  Google Scholar 

  21. Kira S, Yang T, Shadlen MN (2015) A neural implementation of Wald’s sequential probability ratio test. Neuron 85:861–873

    Article  Google Scholar 

  22. Haefner RM, Berkes P, Fiser J (2016) Perceptual decision-making as probabilistic inference by neural sampling. Neuron 90:1–12

    Article  Google Scholar 

  23. Kolossa A, Kopp B, Fingscheidt T (2015) A computational analysis of the neural bases of Bayesian inference. Neuroimage 106:222–237

    Article  Google Scholar 

  24. Meyniel F, Sigman M, Mainen ZF (2015) Confidence as bayesian probability: from neural origins to behavior. Neuron 88:78–92

    Article  Google Scholar 

  25. Lee D, Seo H (2016) Neural basis of strategic decision making. Trends Neurosci 39:40–48

    Article  Google Scholar 

  26. Schneidman E (2016) Towards the design principles of neural population codes. Curr Opin Neurobiol 37:133–140

    Article  Google Scholar 

  27. Rich D, Cazettes F, Wang Y, Peña JL, Brian J, Fischer BJ (2015) Neural representation of probabilities for Bayesian inference. J Comput Neurosci 38:315–323

    Article  Google Scholar 

  28. Quiroga RQ, Panzeri S (2009) Extracting information from neuronal populations: information theory and decoding approaches. Nat Rev Neurosci 10:173–185

    Article  Google Scholar 

  29. Kay SM (1993) Fundamentals of statistical signal processing: estimation theory. Prentice Hall, Upper Saddle River, pp 45–49

    MATH  Google Scholar 

  30. Brunel N, Nadal JP (1998) Mutual information, Fisher information, and population coding. Neural Comput 10:1731–1757

    Article  Google Scholar 

  31. Jazayeri M, Movshon JA (2006) Optimal representation of sensory information by neural populations. Nature Neurosci 9:690–696

    Article  Google Scholar 

Download references

Acknowledgements

We thank the reviewers for helpful comments and suggestions. This work is supported by National NSF (61374183, 10971097, 51535005) of China, and 973 Program (2013CB932604, 2012CB933403), and a project funded by the priority academic program development of Jiangsu higher education institutions.

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Correspondence to Xinsheng Liu.

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Liu, X., Xing, Z. & Guo, W. Encoding and Decoding Neural Population Signals for Two-Dimensional Stimulus. Neural Process Lett 46, 549–559 (2017). https://doi.org/10.1007/s11063-017-9602-x

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