## Neural Coding

*01 Jun 2018 10:51*

And the statistics of neural spike trains more generally.

Since I've written about the neural coding problem, at great length, in my review of Spikes (see below), I won't repeat myself here.

*Things to try to understand:* Distributed and population codes.
How much can be understood about coding without also understanding computation?

*Things to do:* Causal-state reconstruction on real neural spike
data. (Done; see below.) Transducer state reconstruction; states of the
inferred transducer = classes of stimuli (+ internal histories) which make a
difference to the cell. The information coherence measure should indicate the
quantity of distributed information in spike-trains. Calculate for actual
neuronal circuits; does this interpretation make sense?

See also: Information Theory; Neural Modeling and Data Analysis; Stochastic Processes; Synchronization; Synchronization in Neural Systems; Time Series

- Recommended, big picture:
- Larry Abbott and Terry Sejnowski (eds.), Neural Codes and Distributed Representations
- Chris Eliasmith and Charles Anderson, Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems
- Jerome Y. Lettvin, H. R. Maturana, Warren S. McCulloch and
W. H. Pitts, "What the Frog's Eye Tells the Frog's Brain", Proceedings of
the IRE,
**47**(1959): 1940--1951 [Reprinted in McCulloch's Embodiments of Mind, among other places, and available online, e.g., here] - Liam Paninski, Jonathan Pillow, and Jeremy Lewi, "Statistical models for neural encoding, decoding, and optimal stimulus design", to appear in P. Cisek, T. Drew and J. Kalaska (eds.), Computational Neuroscience: Progress in Brain Research [PDF preprint]
- Alexandre Pouget, Peter Dayan and Richard S. Zemel, "Inference and
Computation with Population Codes", Annual
Review of Neuroscience
**26**(2003): 381--401 - Fred Rieke, David Warland, Rob de Ruyter van Steveninck and William
Bialek, Spikes: Exploring the Neural Code
[Review: Cells That Go
*ping,*or, the Value of the Three-Bit Spike]

- Recommended, close-ups:
- Jose M. Amigo, Janusz Szczepanski, Elek Wajnryb and Maria
V. Sanchez-Vives, "Estimating the Entropy Rate of Spike Trains via Lempel-Ziv
Complexity",
Neural
Computation
**16**(2004): 717--736 [Normally, I have strong views on using Lempel-Ziv to measure entropy rates, but here they are using the 1976 Lempel-Ziv definitions, not the 1978 ones. The difference is subtle, but important; 1978 leads to gzip and practical compression algorithms, but very bad entropy estimates; 1976 leads, as they show numerically, to quite good entropy rate estimates, at least for some processes. Thanks to Dr. Szczepanski for correspondence about this paper.] - Riccardo Barbieri, Loren M. Frank, David P. Nguyen, Michael
C. Quirk, Victor Solo, Matthew A. Wilson and Emery N. Brown, "Dynamic Analyses
of Information Encoding in Neural
Ensembles", Neural
Computation
**16**(2004): 277--307 - M. J. Barber, J. W. Clark and C. H. Anderson, "Neural
Representation of Probabilistic Information," Neural Computation
**15**(2003): 1843--1864, cond-mat/0108425 - David Brillinger
- "Nerve Cell Spike Train Data Analysis: A Progression of
Technique," Journal of the American Statistical Association
**87**(1992): 260--270 - and Allessandro E. P. Villa, "Assessing Connections in Networks of Biological Neurons", pp. 77--92 in D. R. Brillinger, L. T. Fernholz and S. Morgenthaler (eds.), The Practice of Data Analysis: Essays in Honor of John W. TukeyPS]

`<li>A. E. Brockwell, A. L. Rojas and R. E. Kass, "Recursive`

Bayesian Decoding of Motor Cortical Signals by Particle Filtering", Journal of Neurophysiology

**91**(2004): 1899--1907 [Very nice, especially since they've combining data from multiple experiments. It is a*little*disappointing that they set up a state-space model, but then only use the state to enforce a kind of weak continuity constraint on the decoding, rather than trying to capture the actual computations going on. But I should talk to them about that... Appendix A gives a very clear and compact explanation of particle filtering.] - "Nerve Cell Spike Train Data Analysis: A Progression of
Technique," Journal of the American Statistical Association
- Uri T. Eden, Loren M. Frank, Riccardo Barbieri, Victor Solo and
Emery N. Brown, "Dynamic Analysis of Neural Encoding by Point Process Adaptive
Filtering", Neural
Computation
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coding of an auditory spatial cue", Nature
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"Model-Based Decoding, Information Estimation, and Change-Point Detection Techniques for Multineuron Spike Trains", Neural Computation
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"Invariant visual representation by single neurons in the human brain", Nature
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neural responses to natural signals: maximally informative dimensions", Neural Computation
**16**(2004): 223--250, physics/0212110 - S. P. Strong, Roland Koberle, Rob de Ruyter van Steveninck and
William Bialek, "Entropy and Information in Neural Spike Trains,"
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**80**(1998): 197--201 - Eric E. Thomson and William B. Kristan, "Quantifying Stimulus
Discriminability: A Comparison of Information Theory and Ideal Observer
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Neural
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**17**(2005): 741--778 [A useful warning against a too-common abuse of information theory. Thanks to Eric for providing me with a pre-print.] - Shreejoy J. Tripathy, Krishnan Padmanabhan, Richard C. Gerkin, and Nathaniel N. Urban, "Intermediate intrinsic diversity enhances neural population coding", Proceedings of the National Academy of Sciences (USA)
**110**(2013): 8248--8253 - Jonathan D. Victor and Keith P. Purpura, "Metric-Space Analysis of
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**8**(1997): 127--164 - Vincent Q. Vu, Bin Yu, Robert E. Kass, "Information In The Non-Stationary Case", arxiv:0806.3978

- Modesty forbids me to recommend:
- Rob Haslinger, Kristina Klinkner and CRS, "The Computational Structure of Spike Trains", Neural Computation
**22**(2010): 121--157, arxiv:1001.0036

- To read:
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- Blaise Aguera y Arcas and Adrienne Fairhall, "What causes a neuron to spike?" physics/0301014
- Blaise Aguera y Arcas, Adrienne L. Fairhall and William Bialek, "Computation in a single neuron: Hodgkin and Huxley revisited," physics/0212113
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interevent intervals of synchronous firing," Physical Review
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Nature
Neuroscience
**9**(2006): 1412--1420 [This sounds cool, and of course I shouldn't comment before reading more than just the abstract, but of course I will anyway. "This optimal decoder consistently outperformed the monkey in the detection task, demonstrating the sensitivity of our techniques": yes, but doesn't that by the same token inidcate their irrelevance to understanding the*monkey's*neural code?] - Marshall Crumiller, Bruce Knight, Yunguo Yu and Ehud Kaplan, "Estimating the amount of information conveyed by a population of neurons" [PDF preprint via Dr. Kaplan]
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coding of sound level adapts to stimulus
statistics", Nature
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**8**(2005): 1684--1689 - Coralie de Hemptinne, Sylvie Nozaradan, Quentin Duvivier, Philippe
Lefevre, and Marcus Missal, "How Do Primates Anticipate Uncertain Future
Events?",
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**27**(2007): 4334--4341 - Valeria Del Prete, "A replica free evaluation of the neuronal population information with mixed continuous and discrete stimuli: from the linear to the asymptotic regime," cond-mat/0301457
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Sequential Context in Rat Medial Prefrontal Cortex Is Accounted for by
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**26**(2006): 13143--13155 - Hugo G. Eyherabide, Ariel Rokem, Andreas V. M. Herz, Ines Samengo, "Burst firing is a neural code in an insect auditory system", arxiv:0807.2550
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R. de Ruyter van Steveninck, "Efficiency and Ambiguity in an Adaptive Neural
Code," Nature
**412**(2001): 787--792 - Michael Famulare and Adrienne Fairhall, "Feature Selection in Simple Neurons: How Coding Depends on Spiking Dynamics", Neural Computation
**22**(2010): 581--598 - F. Gabbiani
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`<li>Surya Ganguli, Dongsung Huh, and Haim Sompolinsky, "Memory traces in dynamical systems", <a href="http://dx.doi.org/10.1073/pnas.0804451105"><cite>Proceedings of the National Academy of Sciences</cite> (USA) <strong>105</strong> (2008): 18970--18975</a> <li>Yun Gao, Ioannis Kontoyiannis, Elie Bienenstock, "From the entropy`

to the statistical structure of spike trains", arxiv:0710.4117

- Ralf M. Haefner and Matthias Bethge, "Evaluating neuronal codes for inference using Fisher information", NIPS 23 (2010) [PDF]
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**436**(2005): 71--77 - Wentao Huang and Kechen Zhang, "Information-Theoretic Bounds and Approximations in Neural Population Coding", Neural Computation
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**19**(2007): 404--441 - Ole Jensen, "Information Transfer Between Rhythmically Coupled Networks: Reading the Hippocampal Phase Code," Neural Computation vol. 13 no. 12 (December 2001)
- Christof Koch, Biophysics of Computation: Information Processing in Single Neuron
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**25**(2005): 11003--11013 ["We show that the stimulus selectivity, reliability, and timing precision of primate retinal ganglion cell (RGC) light responses can be reproduced accurately with a simple model consisting of a leaky integrate-and-fire spike generator driven by a linearly filtered stimulus, a postspike current, and a Gaussian noise current. We fit model parameters for individual RGCs by maximizing the likelihood of observed spike responses to a stochastic visual stimulus. Although compact, the fitted model predicts the detailed time structure of responses to novel stimuli, accurately capturing the interaction between the spiking history and sensory stimulus selectivity. The model also accounts for the variability in responses to repeated stimuli, even when fit to data from a single (nonrepeating) stimulus sequence. Finally, the model can be used to derive an explicit, maximum-likelihood decoding rule for neural spike trains, thus providing a tool for assessing the limitations that spiking variability imposes on sensory performance."] - Jonathan W. Pillow, Jonathon Shlens, Liam Paninski, Alexander Sher,
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