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  • Review Article
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Extracting information from neuronal populations: information theory and decoding approaches

Nature Reviews Neuroscience volume 10, pages 173–185 (2009)Cite this article

Key Points

  • To understand complex brain processes, there is a clear need to shift from traditional single-cell studies of trial-averaged responses to single-trial analyses of multiple neurons. In this respect, the decoding and information-theory formalisms offer a powerful framework to study how the brain computes information from the single-trial activity of neuronal populations.

  • Compared with single-cell studies, population analysis with decoding and information theory has several advantages: the information of the neuronal population is considered as a whole; information is extracted from single-trial occurrences; it is possible to discover which stimulus features are encoded by the neural responses; it is possible to evaluate which features of the neural responses carry relevant information; and it is possible to combine information from different types of neural signals.

  • Several studies have shown how much more knowledge can be extracted using the decoding and information-theory methodologies and how, in some cases, information that it is ambiguous at the single-cell level can be clearly interpreted when considering the whole population.

  • Decoding has the advantage of being similar to real behavioural calculations, but it may lose information contained in the neural responses. Information theory considers all the information in the neural response, but it is more difficult to compute for large populations and its values may not be biologically relevant.

  • The complementary knowledge offered by decoding and information theory has not been exploited enough in neuroscience. A joint application of both approaches may offer additional insights into how neuronal populations encode information.

Abstract

To a large extent, progress in neuroscience has been driven by the study of single-cell responses averaged over several repetitions of stimuli or behaviours. However,the brain typically makes decisions based on single events by evaluating the activity of large neuronal populations. Therefore, to further understand how the brain processes information, it is important to shift from a single-neuron, multiple-trial framework to multiple-neuron, single-trial methodologies. Two related approaches — decoding and information theory — can be used to extract single-trial information from the activity of neuronal populations. Such population analysis can give us more information about how neurons encode stimulus features than traditional single-cell studies.

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Figure 1: Three main steps for the population analysis of neural recordings.
Figure 2: Decoding analysis.
Figure 3: Sources of information loss.
Figure 4: Decoding arm reaches and saccades to eight different directions.
Figure 5: Encoding of information by the local field potential phase.

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References

  1. Hubel, D. Tungsten microelectrode for recording from single units. Science 125, 549–550 (1957).

    Article  CAS  PubMed  Google Scholar 

  2. Kandel, E. R., Schwartz, J. H. & Jessell, T. M. Principles of Neural Science (McGraw Hill, New York, 2000).

    Google Scholar 

  3. Schwartz, A. B. Cortical neural prosthetics. Annu. Rev. Neurosci. 27, 487–507 (2004).

    Article  CAS  PubMed  Google Scholar 

  4. Buzsaki, G. Large-scale recording of neuronal ensembles. Nature Neurosci. 7, 446–451 (2004).

    Article  CAS  PubMed  Google Scholar 

  5. Csicsvari, J. et al. Massively parallel recording of unit and local field potentials with silicon-based electrodes. J. Neurophysiol. 90, 1314–1323 (2003).

    Article  PubMed  Google Scholar 

  6. Kelly, R. C. et al. Comparison of recordings from microelectrode arrays and single electrodes in the visual cortex. J. Neurosci. 27, 261–264 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Rousche, P. J. & Normann, R. A. Chronic recording capability of the Utah intracortical electrode in cat sensory cortex. J. Neurosci. Methods 82, 1–15 (1998).

    Article  CAS  PubMed  Google Scholar 

  8. Blanche, T. J., Spacek, M. A., Hetke, J. F. & Swindale, N. V. Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording. J. Neurophysiol. 93, 2987–3000 (2005).

    Article  PubMed  Google Scholar 

  9. Brown, E. N., Kass, R. E. & Mitra, P. P. Multiple neural spike train data analysis: state-of-the-art and future challenges. Nature Neurosci. 7, 456–461 (2004).

    Article  CAS  PubMed  Google Scholar 

  10. Abbott, L. F. Decoding neuronal firing and modelling neural networks. Q. Rev. Biophys. 27, 291–331 (1994).

    Article  CAS  PubMed  Google Scholar 

  11. Pouget, A., Dayan, P. & Zemel, R. Information processing with population codes. Nature Rev. Neurosci. 1, 125–132 (2000).

    Article  CAS  Google Scholar 

  12. Rieke, F., Warland, D., de Ruyter van Steveninck, R. R. & Bialek, W. Spikes: Exploring the Neural Code (MIT Press, Cambridge, Massachusetts, 1997).

    Google Scholar 

  13. Oram, M. W., Foldiak, P., Perrett, D. I. & Sengpiel, F. The 'ideal homunculus': decoding neural population signals. Trends Neurosci. 21, 259–265 (1998).

    Article  CAS  PubMed  Google Scholar 

  14. Dayan, P. & Abbott, L. F. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, Cambridge, Massachusetts, 2001).

    Google Scholar 

  15. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 & 623–656 (1948).

    Article  Google Scholar 

  16. Deco, G. & Obradovic, D. An Information-Theoretic Approach to Neural Computing (Springer, Berlin, 1997).

    Google Scholar 

  17. Borst, A. & Theunissen, F. E. Information theory and neural coding. Nature Neurosci. 2, 947–957 (1999).

    Article  CAS  PubMed  Google Scholar 

  18. Quian Quiroga, R. Spike sorting. Scholarpedia 2, 3583 (2007). A short review describing the steps for processing neural data, basically focused on spike detection and sorting.

    Article  Google Scholar 

  19. Quian Quiroga, R., Nadasdy, Z. & Ben-Shaul, Y. Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering. Neural Comput. 16, 1661–1687 (2004).

    Article  PubMed  Google Scholar 

  20. Lewicki, M. A review of methods for spike sorting: the detection and classification of neural action potentials. Network 9, R53–R78 (1998).

    Article  CAS  PubMed  Google Scholar 

  21. Harris, K. D., Henze, D. A., Csicsvari, J., Hirase, H. & Buzsaki, G. Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements. J. Neurophysiol. 84, 401–414 (2000).

    Article  CAS  PubMed  Google Scholar 

  22. Singer, W. & Gray, C. M. Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci. 18, 555–586 (1995).

    Article  CAS  PubMed  Google Scholar 

  23. Engel, A. K. & Singer, W. Temporal binding and the neural correlates of sensory awareness. Trends Cogn. Sci. 5, 16–25 (2001).

    Article  PubMed  Google Scholar 

  24. Quian Quiroga, R., Reddy, L., Kreiman, G., Koch, C. & Fried, I. Invariant visual representation by single neurons in the human brain. Nature 435, 1102–1107 (2005).

    Article  CAS  PubMed  Google Scholar 

  25. Reich, D. S., Mechler, F. & Victor, J. D. Independent and redundant information in nearby cortical neurons. Science 294, 2566–2568 (2001).

    Article  CAS  PubMed  Google Scholar 

  26. Barlow, H. B., Hill, R. M. & Levick, W. R. Retinal ganglion cells responding selectively to direction and speed of image motion in the rabbit. J. Physiol. (Lond.) 173, 377–407 (1964).

    Article  CAS  PubMed Central  Google Scholar 

  27. MacKay, D. M. Information Theory, Inference, and Learning Algorithms (Cambridge Univ. Press, Cambridge, 2003).

    Google Scholar 

  28. Foldiak, P. in Computation and Neural Systems (eds Eeckman, F. H. & Bower, J.) 55–60 (Kluwer, Norwell, Massachusetts, 1993).

    Book  Google Scholar 

  29. Sanger, T. D. Probability density estimation for the interpretation of neural population codes. J. Neurophysiol. 76, 2790–2793 (1996).

    Article  CAS  PubMed  Google Scholar 

  30. Paradiso, M. A. A theory for the use of visual orientation information which exploits the columnar structure of striate cortex. Biol. Cybern. 58, 35–49 (1988).

    Article  CAS  PubMed  Google Scholar 

  31. Duda, O. H., Hart, P. E. & Stork, D. G. Pattern Classification (Wiley & sons, New York, 2001).

    Google Scholar 

  32. Kjaer, T. W., Hertz, J. A. & Richmond, B. J. Decoding cortical neuronal signals: network models, information estimation and spatial tuning. J. Comp. Neurosci. 1, 109–139 (1994).

    Article  CAS  Google Scholar 

  33. Averbeck, B. B. in Coherent Behavior in Neuronal Networks (ed. Rubin, J., Matias, M. and Romo, R.) (Springer, New York, in the press).

  34. Cover, T. M. & Thomas, J. A. Elements of Information Theory. (Wiley & sons, Hoboken, New Jersey, 2006).

    Google Scholar 

  35. Victor, J. D. Approaches to information-theoretic analysis of neural activity. Biol. Theory 1, 302–316 (2006).

    Article  PubMed  PubMed Central  Google Scholar 

  36. Panzeri, S., Senatore, R., Montemurro, M. A. & Petersen, R. S. Correcting for the sampling bias problem in spike train information measures. J. Neurophysiol. 98, 1064–1072 (2007).

    Article  PubMed  Google Scholar 

  37. Samengo, I. Information loss in an optimal maximum likelihood decoding. Neural Comput. 14, 771–779 (2002).

    Article  PubMed  Google Scholar 

  38. Treves, A. On the perceptual structure of face space. Biosystems 40, 189–196 (1997). One of the first papers to analyse the information given by the confusion matrix, showing that the distribution of incorrect stimulus predictions is important for understanding neural representations. This work was later extended to the study of how incorrect stimulus predictions relate to the mutual information between stimuli and responses in reference 47.

    Article  CAS  PubMed  Google Scholar 

  39. Panzeri, S., Treves, A., Schultz, S. & Rolls, E. T. On decoding the responses of a population of neurons from short time windows. Neural Comput. 11, 1553–1577 (1999).

    Article  CAS  PubMed  Google Scholar 

  40. Robertson, R. G., Rolls, E. T., Georges-Francois, P. & Panzeri, S. Head direction cells in the primate pre-subiculum. Hippocampus 9, 206–219 (1999).

    Article  CAS  PubMed  Google Scholar 

  41. Georgopoulos, A. P., Schwartz, A. B. & Kettner, R. E. Neuronal population coding of movement direction. Science 233, 1416–1419 (1986). The first study to implement a population analysis of neuronal responses by using a population vector.

    Article  CAS  PubMed  Google Scholar 

  42. Zhang, K., Ginzburg, I., McNaughton, B. L. & Sejnowski, T. J. Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. J. Neurophysiol. 79, 1017–1044 (1998).

    Article  CAS  PubMed  Google Scholar 

  43. Knill, D. C. & Pouget, A. The bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci. 27, 712–719 (2004).

    Article  CAS  PubMed  Google Scholar 

  44. Quian Quiroga, R., Reddy, L., Koch, C. & Fried, I. Decoding visual inputs from multiple neurons in the human temporal lobe. J. Neurophysiol. 98, 1997–2007 (2007). This paper showed that it is possible to correctly predict picture presentations from the firing of neurons in the human medial temporal lobe far above chance. The authors also showed that more information can be extracted from a population analysis than from a single-cell study.

    Article  PubMed  Google Scholar 

  45. Victor, J. D. & Purpura, K. P. Nature and precision of temporal coding in visual cortex: a metric-space analysis. J. Neurophysiol. 76, 1310–1326 (1996).

    Article  CAS  PubMed  Google Scholar 

  46. Schnupp, J. W. H., Hall, T. M., Kokelaar, R. F. & Ahmed, B. Plasticity of temporal pattern codes for vocalization stimuli in primary auditory cortex. J. Neurosci. 26, 4785–4795 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Thomson, E. E. & Kristan, W. B. Quantifying stimulus discriminability: a comparison of information theory and ideal observer analysis. Neural Comput. 17, 741–778 (2005).

    Article  PubMed  Google Scholar 

  48. Ma, W. J., Beck, J. M., Latham, P. E. & Pouget, A. Bayesian inference with probabilistic population codes. Nature Neurosci. 9, 1432–1438 (2006).

    Article  CAS  PubMed  Google Scholar 

  49. Beck, J. M. et al. Probabilistic population codes for Bayesian decision making. Neuron 60, 1142–1152 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Averbeck, B. B., Sohn, J.-W. & Lee, D. Activity in prefrontal cortex during dynamic selection of action sequences. Nature Neurosci. 9, 276–282 (2006).

    Article  CAS  PubMed  Google Scholar 

  51. Pouget, A., Zhang, K., Deneve, S. & Latham, P. E. Statistically efficient estimation using population coding. Neural Comput. 10, 373–401 (1998).

    Article  CAS  PubMed  Google Scholar 

  52. Sahani, M. & Dayan, P. Doubly distributional population codes: simultaneous representation of uncertainty and multiplicity. Neural Comput. 15, 2255–2279 (2003).

    Article  PubMed  Google Scholar 

  53. Pouget, A., Zemel, R. & Dayan, P. Inference and computation with population code. Annu. Rev. Neurosci. 26, 381–410 (2003).

    Article  CAS  PubMed  Google Scholar 

  54. Victor, J. D. & Nirenberg, S. Indices for testing neural codes. Neural Comput. 20, 2895–2936 (2008). The authors analysed in detail the relative strengths and weaknesses of information theory and Bayesian decoders when they are used to rule out neural codes. They also introduced a set of measures that varied smoothly between information theory and Bayesian decoders.

    Article  PubMed  PubMed Central  Google Scholar 

  55. Andersen, R. A. & Buneo, C. A. Intentional maps in the posterior parietal cortex. Annu. Rev. Neurosci. 25, 189–220 (2002).

    Article  CAS  PubMed  Google Scholar 

  56. Mountcastle, V. B., Lynch, J. C., Georgopoulos, A., Sakata, H. & Acuna, C. Posterior parietal association cortex of the monkey: command functions for operations within extrapersonal space. J. Neurophysiol. 38, 871–908 (1975).

    Article  CAS  PubMed  Google Scholar 

  57. Andersen, R. A., Essick, G. K. & Siegel, R. M. Neurons of area 7 activated by both visual stimuli and oculomotor behavior. Exp. Brain Res. 67, 316–322 (1987).

    Article  CAS  PubMed  Google Scholar 

  58. Snyder, L. H., Batista, A. P. & Andersen, R. A. Coding of intention in the posterior parietal cortex. Nature 386, 167–170 (1997).

    Article  CAS  PubMed  Google Scholar 

  59. Bisley, J. W. & Goldberg, M. E. Neuronal activity in the lateral intraparietal area and spatial attention. Science 299, 81–81 (2003).

    Article  CAS  PubMed  Google Scholar 

  60. Robinson, D. L., Goldberg, M. E. & Stanton, G. B. Parietal association cortex in the primate: sensory mechanisms and behavioral modulations. J. Neurophysiol. 41, 910–932 (1978).

    Article  CAS  PubMed  Google Scholar 

  61. Quian Quiroga, R., Snyder, L. H., Batista, A. P., Cui, H. & Andersen, R. A. Movement intention is better predicted than attention in the posterior parietal cortex. J. Neurosci. 26, 3615–3620 (2006). Using a decoding population analysis, the authors showed that neurons in the posterior parietal cortex encode different movement plans and not just attention to target location.

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  62. Musallam, S., Corneil, B., Greger, B., Scherberger, H. & Andersen, R. A. Cognitive control signals for neural prosthetics. Science 305, 258–262 (2004).

    Article  CAS  PubMed  Google Scholar 

  63. Pesaran, B., Pezaris, J., Sahani, M., Mitra, P. M. & Andersen, R. A. Temporal structure in neuronal activity during working memory in macaque parietal cortex. Nature Neurosci. 5, 805–811 (2002).

    Article  CAS  PubMed  Google Scholar 

  64. Scherberger, H., Jarvis, M. & Andersen, R. A. Cortical local field potential encodes movement intentions in the posterior parietal cortex. Neuron 46, 347–354 (2005).

    Article  CAS  PubMed  Google Scholar 

  65. Wessberg, J. et al. Real-time prediction of hand trajectory by ensembles of cortical neurons in primates. Nature 408, 361–365 (2000).

    Article  CAS  PubMed  Google Scholar 

  66. Andersen, R. A., Burdick, J. W., Musallam, S., Pesaran, B. & Cham, J. G. Cognitive neural prosthetics. Trends Cogn. Sci. 8, 486–493 (2004).

    Article  CAS  PubMed  Google Scholar 

  67. Nicolelis, M. A. Actions from thoughts. Nature 409, 403–407 (2001).

    Article  CAS  PubMed  Google Scholar 

  68. Stopfer, M., Jayaraman, V. & Laurent, G. Intensity versus identity coding in an olfactory system. Neuron 39, 991–1004 (2003).

    Article  CAS  PubMed  Google Scholar 

  69. Arabzadeh, E., Panzeri, S. & Diamond, M. E. Whisker vibration information carried by rat barrel cortex neurons. J. Neurosci. 24, 6011–6020 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Adrian, E. D. The Basis of Sensations (Norton, New York, 1928).

    Google Scholar 

  71. Optican, L. M. & Richmond, B. J. Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III. Information theoretic analysis. J. Neurophysiol. 57, 162–178 (1987). The first study to demonstrate that the time profile of cortical spike trains encodes much more information about static visual features than spike counts.

    Article  CAS  PubMed  Google Scholar 

  72. de Ruyter van Steveninck, R. R., Lewen, G. D., Strong, S. P. & Koberle, R. Reproducibility and variability in neural spike trains. Science 275, 1805–1808 (1997).

    Article  CAS  PubMed  Google Scholar 

  73. Hopfield, J. J. Pattern recognition computation using action potential timing for stimulus representation. Nature 376, 33–36 (1995).

    Article  CAS  PubMed  Google Scholar 

  74. Theunissen, F. & Miller, J. P. Temporal encoding in nervous systems: a rigorous definition. J. Comp. Neurosci. 2, 149–162 (1995).

    Article  CAS  Google Scholar 

  75. Victor, J. D. Temporal aspects of neural coding in the retina and lateral geniculate. Network 10, R1–R66 (1999).

    Article  CAS  PubMed  Google Scholar 

  76. Panzeri, S., Petersen, R. S., Schultz, S. R., Lebedev, M. & Diamond, M. E. The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron 29, 769–777 (2001).

    Article  CAS  PubMed  Google Scholar 

  77. Reinagel, P. & Clay Reid, R. Temporal coding of visual information in the thalamus. J. Neurosci. 20, 5392–5400 (2000).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Berry, M. J., Warland, D. K. & Meister, M. The structure and precision of retinal spike trains. Proc. Natl Acad. Sci. USA 94, 5411–5416 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Engineer, C. T. et al. Cortical activity patterns predict speech discrimination ability. Nature Neurosci. 11, 603–608 (2008).

    Article  CAS  PubMed  Google Scholar 

  80. Shadlen, M. N. & Movshon, J. A. Synchrony unbound: a critical evaluation of the temporal binding hypothesis. Neuron 24, 67–77; 111–125 (1999).

    Article  CAS  PubMed  Google Scholar 

  81. Huxter, J. R., Senior, T. J., Allen, K. & Csicsvari, J. Theta phase–specific codes for two-dimensional position, trajectory and heading in the hippocampus. Nature Neurosci. 11, 587–594 (2008). The authors recorded spiking activity and local field oscillations in the hippocampus of rats moving through a two-dimensional environment. Using a decoding analysis, they demonstrated that spikes emitted at different oscillation phases represent complementary aspects of the animal's trajectory.

    Article  CAS  PubMed  Google Scholar 

  82. Huxter, J. R., Burgess, N. & O'Keefe, J. Independent rate and temporal coding in hippocampal pyramidal cells. Nature 425, 828–832 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Buracas, G. T., Zador, A., DeWeese, M. & Albright, T. Efficient encoding of rapidly varying stimuli by motion-sensitive neurons in MT of alert monkeys. Neuron 20, 959–969 (1998).

    Article  CAS  PubMed  Google Scholar 

  84. Kara, P., Reinagel, P. & Clay Reid, R. Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron 27, 635–646 (2000).

    Article  CAS  PubMed  Google Scholar 

  85. Theunissen, F. E. From synchrony to sparseness. Trends Neurosci. 26, 61–64 (2003).

    Article  CAS  PubMed  Google Scholar 

  86. Perez-Orive, J. et al. Oscillations and sparsening of odor representations in the mushroom body. Science 297, 359–365 (2002).

    Article  CAS  PubMed  Google Scholar 

  87. Hahnloser, R. H. R., Kozhevnikov, A. A. & Fee, M. S. An ultra-sparse code underlies the generation of neural sequences in a songbird. Nature 419, 65–70 (2002).

    Article  CAS  PubMed  Google Scholar 

  88. Salinas, E., Hernandez, A., Zainos, A. & Romo, R. Periodicity and firing rate as candidate neural codes for the frequency of vibrotactile stimuli. J. Neurosci. 20, 5503–5515 (2000).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Arabzadeh, E., Panzeri, S. & Diamond, M. E. Deciphering the spike train of a sensory neuron: counts and temporal patterns in the rat whisker pathway. J. Neurosci. 26, 9216–9226 (2006). This paper developed an analytical formalism that quantifies how much sensory information can be extracted from the spike times when the stimulus time is not known precisely.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  90. Reich, D. S., Mechler, F. & Victor, J. D. Temporal coding of contrast in primary visual cortex: when, what, and why. J. Neurophysiol. 85, 1039–1050 (2001).

    Article  CAS  PubMed  Google Scholar 

  91. Gawne, T. J., Kjaer, T. W. & Richmond, B. J. Latency: another potential code for feature binding in striate cortex. J. Neurophysiol. 76, 1356–1360 (1996).

    Article  CAS  PubMed  Google Scholar 

  92. Muller, J. R., Metha, A. B., Krauskopf, J. & Lennie, P. Information conveyed by onset transients in responses of striate cortical neurons. J. Neurosci. 21, 6978–6990 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Ahrens, K. F. & Kleinfeld, D. Current flow in vibrissa motor cortex can phase-lock with exploratory rhythmic whisking in rat. J. Neurophysiol. 92, 1700–1707 (2004).

    Article  PubMed  Google Scholar 

  94. Abbott, L. F. & Dayan, P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11, 91–101 (1999).

    Article  CAS  PubMed  Google Scholar 

  95. Averbeck, B. B., Latham, P. E. & Pouget, A. Neural correlations, population coding and computation. Nature Rev. Neurosci. 7, 358–366 (2006). An up-to-date and comprehensive review of the role of noise correlations in population coding.

    Article  CAS  Google Scholar 

  96. Nirenberg, S. & Latham, P. E. Decoding neuronal spike trains: how important are correlations? Proc. Natl Acad. Sci. USA 100, 7348–7353 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Salinas, E. & Sejnowski, T. J. Correlated neuronal activity and the flow of neural information. Nature Rev. Neurosci. 2, 539–550 (2001).

    Article  CAS  Google Scholar 

  98. Zohary, E., Shadlen, M. & Newsome, W. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370, 140–143 (1994).

    Article  CAS  PubMed  Google Scholar 

  99. Panzeri, S., Schultz, S., Treves, A. & Rolls, E. T. Correlations and the encoding of information in the nervous system. Proc. R. Soc. Lond. B Biol. Sci. 266, 1001–1012 (1999).

    Article  CAS  Google Scholar 

  100. Petersen, R. S., Panzeri, S. & Diamond, M. E. Population coding of stimulus location in rat somatosensory cortex. Neuron 32, 503–514 (2001).

    Article  CAS  PubMed  Google Scholar 

  101. Montani, F., Kohn, A., Smith, M. A. & Schultz, S. R. The role of correlations in direction and contrast coding in the primary visual cortex. J. Neurosci. 27, 2338–2348 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. Nirenberg, S., Carcieri, S. M., Jacobs, A. L. & Latham, P. E. Retinal ganglion cells act largely as independent encoders. Nature 411, 698–701 (2001).

    Article  CAS  PubMed  Google Scholar 

  103. Dan, Y., Alonso, J. M., Usrey, W. M. & Clay Reid, R. Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus. Nature Neurosci. 1, 501–507 (1998).

    Article  CAS  PubMed  Google Scholar 

  104. Mitzdorf, U. Properties of the evoked potential generators: current source-density analysis of visually evoked potentials in the cat cortex. Int. J. Neurosci. 33, 33–59 (1987).

    Article  CAS  PubMed  Google Scholar 

  105. Juergens, E., Guettler, A. & Eckhorn, R. Visual stimulation elicits locked and induced gamma oscillations in monkey intracortical and EEG-potentials, but not in human EEG. Exp. Brain Res. 129, 247–259 (1999).

    Article  CAS  PubMed  Google Scholar 

  106. Harada, Y. & Takahashi, T. The calcium component of the action potential in spinal motoneurones of the rat. J. Physiol. 335, 89–100 (1983).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Kamondi, A., Acsady, L., Wang, X. J. & Buzsaki, G. Theta oscillations in somata and dendrites of hippocampal pyramidal cells in vivo: activity-dependent phase-precession of action potentials. Hippocampus 8, 244–261 (1998).

    Article  CAS  PubMed  Google Scholar 

  108. Montemurro, M., Rasch, M. J., Murayama, Y., Logothetis, N. K. & Panzeri, S. Phase-of-firing coding of natural visual stimuli in primary visual cortex. Curr. Biol. 18, 375–380 (2008). This study used information theory to demonstrate that, in the macaque primary visual cortex, the phase of slow (<12 Hz) local field fluctuations encodes information about natural visual scenes that cannot be obtained from spike counts.

    Article  CAS  PubMed  Google Scholar 

  109. Belitski, A. et al. Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information. J. Neurosci. 28, 5696–5709 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  110. Mehta, M. R., Lee, A. K. & Wilson, M. A. Role of experience and oscillations in transforming a rate code into a temporal code. Nature 417, 741–746 (2002).

    Article  CAS  PubMed  Google Scholar 

  111. Harris, K. D. et al. Spike train dynamics predicts theta-related phase precession in hippocampal pyramidal cells. Nature 417, 738–741 (2002).

    Article  CAS  PubMed  Google Scholar 

  112. Harris, K. D. Neural signatures of cell assembly organization. Nature Rev. Neurosci. 6, 399–407 (2005).

    Article  CAS  Google Scholar 

  113. Kraskov, A., Quian Quiroga, R., Reddy, L., Fried, I. & Koch, C. Local field potentials and spikes in the human medial temporal lobe are selective to image category. J. Cogn. Neurosci. 19, 479–492 (2007).

    Article  PubMed  Google Scholar 

  114. Kreiman, G. et al. Object selectivity of local field potentials and spikes in the macaque inferior temporal cortex. Neuron 49, 433–445 (2006).

    Article  CAS  PubMed  Google Scholar 

  115. Andersen, R. A., Musallam, S. & Pesaran, B. Selecting the signals for a brain-machine interface. Curr. Opin. Neurobiol. 14, 720–726 (2004).

    Article  CAS  PubMed  Google Scholar 

  116. Schneiman, E., Berry, M. J., Segev, R. & Bialek, W. Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440, 1007–1012 (2006).

    Article  CAS  Google Scholar 

  117. Logothetis, N. K. What we can do and what we cannot do with fMRI. Nature 453, 869–878 (2008).

    Article  CAS  PubMed  Google Scholar 

  118. Haxby, J. V. et al. Distributed and overlapping representations of faces and objects in ventral temporal cortex. Science 293, 2425–2430 (2001).

    Article  CAS  PubMed  Google Scholar 

  119. Haynes, J.-D. & Rees, G. Decoding mental states from brain activity in humans. Nature Rev. Neurosci. 7, 523–534 (2006).

    Article  CAS  Google Scholar 

  120. Eichele, T. et al. Assessing the spatiotemporal evolution of neuronal activation with single-trial event-related potentials and functional MRI. Proc. Natl Acad. Sci. USA 102, 17798–17803 (2005). First study using a single-trial analysis to combine the temporal and spatial resolutions of electroencephalogram and functional MRI recordings.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  121. Debener, S., Ullsperger, M., Siegel, M. & Engel, A. K. Single-trial EEG-fMRI reveals the dynamics of cognitive function. Trends Cogn. Sci. 10, 558–563 (2006).

    Article  PubMed  Google Scholar 

  122. Gerstein, G. L. & Clark, W. A. Simultaneous studies of firing patterns in several neurons. Science 143, 1325–1327 (1964).

    Article  PubMed  Google Scholar 

  123. Vapnik, R. J. Statistical Learning Theory (Wiley & sons, New York, 1998).

    Google Scholar 

  124. Soong, T. T. Fundamentals of Probability and Statistics for Engineers (Wiley, Sussex, 2004).

    Google Scholar 

  125. Latham, P. E. & Nirenberg, S. Synergy, redundancy, and independence in population codes, revisited. J. Neurosci. 25, 5195–5206 (2005). This study derived a rigorous measure of the information that is lost when using algorithms that make incorrect assumptions about the probabilities of neural responses to stimuli. It provides a useful tool for understanding which features of the stimulus–response relationship are important for information transmission.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

We are very thankful to F. Montani, K. Whittingstall, J. Csicsvari, A. Mazzoni and G. Kreiman for comments, to P. Dayan for interesting discussions about uncertainty and decoding, and to all our brilliant colleagues that collaborated with us on these topics: R. Andersen, M. Diamond, I. Fried, C. Koch, N. Logothetis, C. Kayser, M. Montemurro, R. Petersen and A. Treves. We acknowledge support from the Engineering and Physical Sciences Research Council, the Medical Research Council, the Royal Society and the Italian Institute of Technology.

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Authors and Affiliations

  1. Department of Engineering, University of Leicester, Leicester, LE1 7RH, UK

    Rodrigo Quian Quiroga

  2. Department of Robotics, Italian Institute of Technology, Brain and Cognitive Sciences, Genoa, 16163, Italy

    Stefano Panzeri

  3. Faculty of Life Sciences, University of Manchester, Manchester, M13 9PL, UK

    Stefano Panzeri

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  1. Rodrigo Quian Quiroga
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  2. Stefano Panzeri
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Correspondence to Rodrigo Quian Quiroga.

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Glossary

Spike sorting

The grouping of spikes into clusters based on the similarity of their shapes. Given that, in principle, each neuron tends to fire spikes of a particular shape, the resulting clusters correspond to the activity of different putative neurons. The end result of spike sorting is determining which spike corresponds to which of these neurons.

Decoding

Predicting the most likely stimulus or behaviour eliciting an observed neural response.

Information theory

A mathematical theory that deals with measures of information and their application to the study of communication systems. In neuroscience it is used to establish the amount of information about a stimulus or behaviour that is contained in the neural responses.

Local field potential

(LFP). A neurophysiological signal that is obtained by low-pass filtering extracellular recordings. It represents the mean field potential generated by the slow components of synaptic and neural events in the vicinity of the recording electrode.

Posterior probability

The posterior probability of a random variable is the conditional probability assigned to the variable given some event. For example, the posterior probability P(s|r) is the conditional probability that stimulus s was presented, given that a response r was observed.

Shannon entropy

A measure of the uncertainty about the value that might be taken by a random variable.

Bit

The unit used to measure reduction of uncertainty. One bit corresponds to a reduction of uncertainty by a factor of two (for example, a correct answer to a yes/no question).

Unbiased decoder

A decoder is said to be unbiased if the expected value of its decoding error (the difference between the true and the estimated stimulus values) is zero.

Brain–machine interface

A direct communication link between a brain (human or animal) and an external device, such as a prosthetic limb or a sensing device.

Principal-component analysis

A linear transformation that projects the data on to an orthogonal base, in which the greatest variance of the data lies on the first coordinate (the first principal component), the second greatest variance on the second coordinate, and so on. It is usually used to reduce the dimensionality of complex data.

Spike afterpotential

A transient hyperpolarization of a neuron following the firing of an action potential. It is caused by K+ channels, which open during the spike and close a few milliseconds after the neural membrane potential goes back to its resting value.

Voxel

In MRI research, a voxel refers to the smallest measured volume unit, analogous to a three-dimensional pixel. In functional MRI studies these are typically of the order of 30 mm3, although much smaller voxel volumes have been achieved in more recent work.

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Quian Quiroga, R., Panzeri, S. Extracting information from neuronal populations: information theory and decoding approaches. Nat Rev Neurosci 10, 173–185 (2009). https://doi.org/10.1038/nrn2578

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