Neural Coding

25 Oct 2007 13:38

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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. States of the inferred transducer = classes of stimuli 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
• 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]
• 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.]
• 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 16 (2005): 971-988
• Nicol S. Harper and David McAlpine, "Optimal neural population coding of an auditory spatial cue", Nature 430 (2004): 682--686
• R. Quian Quiroga, L. Reddy, G. Kreiman, C. Koch and I. Fried, "Invariant visual representation by single neurons in the human brain", Nature 435 (2005): 1102--1107
• Tatyana Sharpee, Nicole C. Rust and William Bialek, "Analyzing neural responses to natural signals: maximally informative dimensions," physics/0212110 = Neural Computation 16 (2004): 223--250
• S. P. Strong, Roland Koberle, Rob de Ruyter van Steveninck and William Bialek, "Entropy and Information in Neural Spike Trains," Physical Review Letters 80 (1998): 197--201
• Eric E. Thomson and William B. Kristan, "Quantifying Stimulus Discriminability: A Comparison of Information Theory and Ideal Observer Analysis", Neural Computation 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.]
• Jonathan D. Victor and Keith P. Purpura, "Metric-Space Analysis of Spike Trains: Theory, Algorithms and Application," Network: Computation in Neural Systems 8 (1997): 127--164

To read:
• E. D. Adrian, Physical Background of Perception [Adrian was one of the first --- maybe the first? --- to record spike trains from neurons, and realize they were how neurons communicate]
• 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
• Kazuyuki Aihara and Isao Tokuda, "Possible neural coding with interevent intervals of synchronous firing," Physical Review E 66 (2002): 026212
• Vijay Balasubramanian and Michael J. Berry, "Metabolically Efficient Codes in The Retina," cond-mat/0105128
• Vijay Balasubramanian, Don Kimber and Michael J. Berry, "Metabolically Efficient Information Processing," cond-mat/0105127
• Michele Bezzi, Mathew E. Diamond and Alessandro Treves, "Redundency and synergy arising from correlations in large ensembles," cond-mat/0012119
• Michele Bezzi, Ines Samengo, Stefan Leutgeb and Sheri Mizumori, "Measuring information spatial densities," cond-mat/0111150
• William Bialek and Rob R. de Ruyter van Steveninck, "Features and dimensions: Motion estimation in fly vision", q-bio.NC/0505003
• Naama Brenner, Steven P. Strong, Roland Koberle, William Bialek and Rob R. de Ruter van Steveninck, "Synergy in a Neural Code," Neural Computation, 12 (2000): 1531--1552
• Daniel A. Butts, Chong Weng, Jianzhong Jin, Chun-I Yeh, Nicholas A. Lesica, Jose-Manuel Alonso and Garrett B. Stanley, "Temporal precision in the neural code and the timescales of natural vision", Nature 449 (2007): 92--95
• C. E. Carr and M. A. Friedman, "Evolution of Time Coding Systems," Neural Computation 11 (1999): 1--20
• Guillermo A. Cecchi, Mariano Sigman, Josée-Manuel Alonso, Luis Martínez, Dante r. Chialvo and Marcelo O. Magnasco, "Noise in Neurons is Message-Dependent," cond-mat/0004492
• Yuzhi Chen, Wilson S. Geisler and Eyal Seidemann, "Optimal decoding of correlated neural population responses in the primate visual cortex", 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?]
• Isabel Dean, Nicol S Harper and David McAlpine, "Neural population coding of sound level adapts to stimulus statistics", Nature Neuroscience 8 (2005): 1684--1689
• Coralie de Hemptinne, Sylvie Nozaradan, Quentin Duvivier, Philippe Lefevre, and Marcus Missal, "How Do Primates Anticipate Uncertain Future Events?", Journal of Neuroscience 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
• David R. Euston and Bruce L. McNaughton, "Apparent Encoding of Sequential Context in Rat Medial Prefrontal Cortex Is Accounted for by Behavioral Variability", The Journal of Neuroscience 26 (2006): 13143--13155
• Adrienne L. Fairhall, Geofrrey D. Lewen, William Bialek and Robert R. de Ruyter van Steveninck, "Efficiency and Ambiguity in an Adaptive Neural Code," Nature 412 (2001): 787--792
• F. Gabbiani
  • "Rate Coding and Signal Processing" [Reprint]
  • and J. Midtgaard, "Neural Information Processing" [Reprint]
• Yun Gao, Ioannis Kontoyiannis, Elie Bienenstock, "From the entropy to the statistical structure of spike trains", arxiv:0710.4117
• Kenneth D. Harris, "Neural Signatures of Cell Assembly Organization", Nature Reviews Neuroscience 6 (2005): 399--407
• V. Hok, E. Save, P. P. Lenck-Santini and B. Poucet, "Coding for spatial goals in the prelimbic/inframlimbic area of the rat frontal cortex", PNAS 102 (2005): 4602--4607
• Toshihiko Hosoya, Stephen A. Baccus and Markus Meister, "Dynamic predictive coding by the retina", Nature 436 (2005): 71--77
• Quentin J. M. Huys, Richard S. Zemel, Rama Natarajan, and Peter Dayan , "Fast Population Coding", Neural Computation 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 [Blurb]
• Philipp Knüsel, Reto Wyss, Peter König and Paul F.M.J. Verschure, "Decoding a Temporal Population Code", Neural Computation 16 (2004): 2079--2100
• R. Krahe, G. Kreiman, F. Gabbiani, C. Koch, W. Metzner, "Stimulus encoding and feature extraction by multiple sensory neurons" [Reprint]
• Petr Lansky and Priscilla E. Greenwood, "Optimal Signal Estimation in Neuronal Models", Neural Computation 17 (2005): 2240--2257
• G. D. Lewen, W. Bialek and R. R. de Ruyter van Steveninck, "Neural coding of naturalistic motion stimuli," physics/0103088
• Longnian Lin, Remus Osan, Shy Shoham, Wenjun Jin, Wenqi Zuo, and Joe Z. Tsien, "Identification of network-level coding units for real-time representation of episodic experiences in the hippocampus", PNAS 102 (2005): 6125--6130
• Christian K. Machens, "Adaptive sampling by information maximization," physics/0112070
• Gary Marsat and Gerald S. Pollack, "A Behavioral Role for Feature Detection by Sensory Bursts", The Journal of Neuroscience 26 (2006): 10542--10547
• Laura Martignon, Gustavo Deco, Kathryn Laskey, Mathew Diamond, Winrich Freiwald and Eilon Vaadia, "Neural Coding: Higher-Order Temporal Patterns in the Neurostatistics of Cell Assemblies," Neural Computation 12 (2000): 2621--2653
• Mark D. McDonnell, Nigel G. Stocks, Charles E. M. Pearce and Derek Abbott, "Point singularities and suprathreshold stochastic resonance in optimal coding", cond-mat/0409528
• Panzeri and Schultz, "A Unified Approach to the Study of Temporal, Correlational, and Rate Coding," Neural Computation 13 (2001): 1311--1349
• Phillips and Singer, In Search of Common Foundations for Cortical Computation
• Jonathan W. Pillow, Liam Paninski, Valerie J. Uzzell, Eero P. Simoncelli, and E. J. Chichilnisky, "Prediction and Decoding of Retinal Ganglion Cell Responses with a Probabilistic Spiking Model", The Journal of Neuroscience 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."]
• K. Prank, F. Gabbiani and G. Brabant, "Coding efficiency and information rates in transmembrane signaling" [Abstract]
• D. S. Reich, F. Mechler and J. D. Victor, "Independent and Redundant Information in Nearby Cortical Neurons", Science 294 (2001): 2566--2568
• Hugh P. C. Robinson and Annette Harsch, "Stages of spike time variability during neuronal responses to transient inputs," Physical Review E 66 (2002): 061902
• Enrico Rossoni and Jianfeng Feng, "Decoding spike train ensembles: tracking a moving stimulus", Biological Cybernetics 96 (2007): 99--112 [Improvements for some non-stationary situations through censored maximum likelihood estimation]
• Rob de Ruyter van Steveninck and William Bialek, "Timing and Counting Precision in the Blowfly Visual System," physics/0202014
• Ines Samengo, "Information loss in an optimal maximum likelihood decoding," physics/0110074
• Elad Schneidman, William Bialek and Michael J. Berry, II, "An information theoretic approach to the functional classification of neurons," physics/0212114
• Maoz Shamir and Haim Sompolinsky, "Nonlinear Population Codes", Neural Computation 16 (2004): 1105--1136
• Tatyana Sharpee and William Bialek, "Neural Decision Boundaries for Maximal Information Transmission", q-bio.NC/0703046
• Richard B. Stein, E. Roderich Gossen and Kelvin E. Jones, "Neuronal Variability: Noise or Part of the Signal?", Nature Reviews Neuroscience 6 (2005): 389--397
• Michael Stiber, "Spike timing precision and neural error correction: local behavior", q-bio.NC/0501021
• Giulio Tononi and Olaf Sporns, "Measuring information integration", Biomedcentral Neuroscience 4 (2003): 31 [Really more neural information theory than neural coding as such]
• Brian D. Wright, Kamal Sen, William Bialek and Allison J. Doupe, "Spike timing and the coding of naturalistic sounds in a central auditory area of songbirds," physics/0201027
• Si Wu and Shun-ichi Amari, "Computing with Continuous Attractors: Stability and Online Aspects", Neural Computation 17 (2005); 2215--2239

To write:
• Rob Haslinger, CRS, Kristina Lisa Klinkner and Greg Gage, "Nonlinear State-Space Models and Population Codes in vivio"