## Neural Modeling and Data Analysis

*04 May 2023 11:34*

Especially, but not exclusively, modeling of spike trains (which is important for neural coding, and overlaps therewith).

*Things to investigate*: How easy would it be to adapt spike-sorting
algorithms to cluster or classify other kinds of time series? Easy or not,
would there be any point?

What's up with all the papers on using Ising models (and their variants) to model neural interactions? Some very respectable people are involved, but just saying the words makes me dubious. What's been done on using graphical-model structure learning for neural data?

- See also:
- Neural Coding
- Synchronization in Neural Systems
- Neuroscience in general
- Point Processes

- Recommended, bigger pictures:
- David Brillinger, "Nerve Cell Spike Train Data Analysis: A
Progression of Technique," Journal of the American Statistical
Association
**87**(1992): 260--270 - Emery N. Brown, Robert E. Kass and Partha P. Mitra, "Multiple
Neural Spike Train Data Analysis: State-of-the-art and Future
Challanges", Nature
Neuroscience
**7**(2004): 456--461 [PDF reprint via Rob] - Chris Eliasmith and Charles Anderson, Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems
- Robert E. Kass, Valerie Ventura and Emery N. Brown, "Statistical
Issues in the Analysis of Neuronal
Data", Journal of
Neurophysiology
**94**(2005): 8--25 [PDF reprint via Rob] - Martin A. Lindquist, "The Statistical Analysis of fMRI
Data", Statistical Science
**23**(2008): 439--464, arxiv:0906.3662 - 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]
- Russell A. Poldrack, Jeanette A. Mumford and Thomas E. Nichols, Handbook of Functional MRI Data Analysis

- Recommended, close-ups:
- 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.] - Emery N. Brown Riccardo Barbieri Valérie Ventura, Robert
E. Kass and Loren M. Frank, "The Time-Rescaling Theorem and Its Applications to
Neural Spike Train Data Analysis", Neural
Computation
**14**(2002): 325--346 [PDF reprint; see also Random Time Changes for Stochastic Processes] - Sami El Boustani, Alain Destexhe, "Does brain activity stem from high-dimensional chaotic dynamics? Evidence from the human electroencephalogram, cat cerebral cortex and artificial neuronal networks", arxiv:0904.4217
- Felipe Gerhard, Robert Haslinger, and Gordon Pipa, "Applying the Multivariate Time-Rescaling Theorem to Neural Population Models", Neural Computation
**23**(2011): 1452--1483 - Stephen José Hanson and Martin Bunzl, Foundational Issues in Human Brain Mapping
- Matthew T. Harrison and Stuart Geman, "A Rate and
History-Preserving Resampling Algorithm for Neural Spike Trains",
Neural Computation
**21**(2009): 1244--1258 - Robert Haslinger, Gordon Pipa and Emery Brown,
"Discrete Time Rescaling Theorem: Determining Goodness of Fit for
Discrete Time Statistical models of Neural Spiking",
Neural Computation
**22**(2010): 2477--2506 - Yoshito Hirata, Kevin Judd and Kazuyuki Aihara, "Characterizing
chaotic response of a squid axon through generating
partitions", Physics Letters
A
**346**(2005): 141--147 [The obvious approach to symbolic dynamics for spike trains works.] - Shinsuke Koyama and Shiegeru Shinomoto, "Empirical Bayes
interpretations of random point
events", Journal
of Physics A: Mathematical and General
**38**(2005): L531--L537 - Murat Okatan, Matthew A. Wilson and Emery N. Brown,
"Analyzing Functional Connectivity Using a Network
Likelihood Model of Ensemble Neural Spiking Activity", Neural
Computation
**17**(2005): 1927--1961 - J. D. Ramsey, S. J. Hanson, C. Hanson, Y. O. Halchenko,
R. A. Poldrack and C. Glymour, "Six Problems for Causal Inference from
fMRI", NeuroImage
**49**(2010): 1545--1558 [PDF via Prof. Hanson; thanks to Prof. Glymour for having shared a preprint with me] - Sommer and Wichert (eds.), Exploratory Analysis and Data Modeling in Functional Neuroimaging

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

- Not altogether recommended:
- F. Gregory Ashby, Statistical Analysis of fMRI Data

- To read:
- Asohan Amarasingham, Stuart Geman and Matthew T. Harrison,
"Ambiguity and nonidentifiability in the statistical analysis of neural
codes", Proceedings
of the National Academy of Sciences (USA)
**112**(2015): 6455--6460 - Shun-ichi Amari, "Conditional Mixture Model for Correlated Neuronal
Spike
Trains", Neural
Computation
**22**(2010): 1718--1736 - Pierre Baldi, "Probabilistic Models of Neuronal Spike Trains," in Giles and Gori (eds.), Adaptive Processing of Sequences and Data Structures
- Peter beim Graben, J. Douglas Saddy, Matthias Schlesewsky and
Jürgen Kurths, "Symbolic Dynamics of Event-Related Brain Potentials,"
Physical Review E
**62**(2000): 5518--5541 - William Bialek, "Thinking about the brain," physics/0205030
- Hemant Bokil, Bijan Pesaran, R. A. Andersen and Partha P. Mitra, "A framework for detection and classification of events in neural activity", q-bio.NC/0507045
- Romain Brette and Wulfram Gerstner, "Adaptive Exponential
Integrate-and-Fire Model as an Effective Description of Neuronal
Activity", Journal of
Neurophysiology
**94**(2005): 3637--3642 - R. Brette, M. Rudolph, T. Carnevale, M. Hines, D. Beeman, J. M. Bower, M. Diesmann, A. Morrison, P. H. Goodman, F. C. Harris Jr., M. Zirpe, T. Natschlager, D. Pecevski, B. Ermentrout, M. Djurfeldt, A. Lansner, O. Rochel, T. Vieville, E. Muller, A. P. Davison, S. El Boustani, and A. Destexhe, "Simulation of networks of spiking neurons: A review of tools and strategies", q-bio.NC/0611089
- A. Brezger, L. Fahrmeir, A. Hennerfeind, "Adaptive Gaussian Markov random fields with applications in human brain mapping", Journal of the Royal Statistical Society C
**56**(2007): 327--345 - David Brillinger, "Some statistical methods for random process
data from seismology and neurophysiology", Annals of Statistics
**16**(1988): 1--54 - David Cai, Louis Tao and David W. McLaughlin, "An Embedded Network
Approach for Scale-Up of Fluctuation-Driven Systems with Preservation of Spike
Information", Proceedings of the
National Academy of Sciences (2004) [
*Abstract*: " address computational 'scale-up' issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network dynamics. However, because of local averaging in space and time, these methods do not contain detailed spike information and, thus, cannot be used to investigate, e.g., cortical mechanisms that are encoded through detailed spike-timing statistics. To retain high-order statistical information of spikes, we develop a hybrid theoretical framework that embeds a subnetwork of point neurons within, and fully interacting with, a coarse-grained network of dynamical background. We use a newly developed kinetic theory for the description of the coarse-grained background, in combination with a Poisson spike reconstruction procedure to ensure that our method applies to the fluctuation-driven regime as well as to the mean-driven regime. This embedded-network approach is verified to be dynamically accurate and numerically efficient. As an example, we use this embedded representation to construct 'reverse-time correlations' as spiked-triggered averages in a ring model of orientation-tuning dynamics." ] - Hock Peng Chan and Wei-Liem Loh, "Some theoretical results on neural spike train probability models", math.ST/0703829
- Yonghong Chen, Steven L. Bressler, and Mingzhou Ding, "Frequency
decomposition of conditional Granger causality and application to multivariate
neural field potential
data", q-bio.NC/0608034
= Journal of Neuroscience Methods
**150**(2006): 228--237 - Todd P. Coleman and Sridevi S. Sarma, "A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes", Neural Computation
**22**(2010): 2002--2030 - Mauro Copelli and Osame Kinouchi, "Intensity Coding in Two-Dimensional Excitable Neural Networks", q-bio.NC/0409032 [Greenberg-Hastings cellular automata as a toy model of visual response!]
- Luciano da F. Costa and Olaf Sporns, "Hierarchical Features of Large-Scale Cortical Connectivity", q-bio.NC/0508007
- J. Davidsen and H. G. Schuster, "Simple model for 1/f noise," cond-mat/0201198 [a null model]
- Peter Dayan and Larry Abbott, Theoretical Neuroscience [website]
- Matthieu Delescluse and Christophe Pouzat, "Efficient spike-sorting of multi-state neurons using inter-spike intervals information", q-bio.QM/0505053
- Mingzhou Ding, Yonghong Chen and Steve L. Bressler, "Granger Causality: Basic Theory and Application to Neuroscience", q-bio.QM/0608035 = pp. 451--474 in B. Schelter, M. Winterhalder, and J. Timmer (eds.), Handbook of Time Series Analysis
- Alexander J. Dubbs, Brad A. Seiler and Marcelo O. Magnasco,
"A Fast
*L*_{p}Spike Alignment Metric", Neural Computation**22**(2010): 2785--2808 - Jean-Pierre Eckmann, Ofer Feinerman, Leor Gruendlinger, Elisha Moses, Jordi Soriano, Tsvi Tlusty, "The Physics of Living Neural Networks", arxiv:1007.5465
- Victor M. Eguiluz, Dante R. Chialvo, Guillermo A. Cecchi, Marwan
Baliki and A. Vania Apkarian, "Scale-free brain functional networks",
Physical Review
Letters
**94**(2005): 018102 = cond-mat/0309092 - Seif Eldawlatly, Yang Zhou, Rong Jin
and Karim G. Oweiss, "On the Use of Dynamic Bayesian Networks in Reconstructing Functional Neuronal Networks from Spike Train Ensembles", Neural Computation
**22**(2010): 158--189 - Nicholas Fisher and Arunava Banerjee, "A Novel Kernel for Learning a Neuron Model from Spike Train Data", NIPS 23 (2010) [PDF]
- Michael D. Fox, Abraham Z. Snyder, Justin L. Vincent, Maurizio
Corbetta, David C. Van Essen and Marcus E. Raichle, "The human brain is
intrinsically organized into dynamic, anticorrelated functional networks", Proceedings of the National
Academy of Sciences
**102**(2005): 9673--9678 - Yun Gao, Ioannis Kontoyiannis, Elie Bienenstock, "From the entropy to the statistical structure of spike trains", arxiv:0710.4117
- Wulfram Gerstner, Spiking Neuron Models
- Gail Gilboa, Ronen Chen, and Naama Brenner, "History-Dependent
Multiple-Time-Scale Dynamics in a Single-Neuron Model", Journal of
Neuroscience
**25**(2005): 6479--6489 - Paul Glimcher, Decisions, Uncertainty, and the Brain: The Science of Neuroeconomics
- Andreas Grönlund, "The difference in directed structure of Neural and Transcriptional Regulation Networks", cond-mat/0406268
- Richard H. R. Hahnloser, "Stationary transmission distribution of
random spike trains by dynamical synapses," Physical Review E
**67**(2003) 022901 - Ronald M. Harris-Warrick, Eve Marder, Allen I. Selverston and Maurice Moulins (eds.), Dynamic Biological Networks: The Stomatogastric Nervous System
- Matthew T. Harrison, Asohan Amarasingham and Wilson Truccolo, "Spatiotemporal Conditional Inference and Hypothesis Tests for Neural Ensemble Spiking Precision", Neural Computation
**27**(2015): 104--150 - H. R. Heekeren, S. Marrett, P. A. Bandettini and L. G. Ungerleider,
"A general mechanism for perceptual decision-making in the human brain",
Nature
**431**(859--862) - Kim L. Hoke, Michael J. Ryan, and Walter Wilczynski, "Social cues
shift functional connectivity in the hypothalamus", PNAS
**102**(2005): 10712--10717 - Kazushi Ikeda, "Information Geometry of Interspike Intervals in
Spiking Neurons", Neural
Computation
**17**(2005): 2719--2735 - Eugene M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting
- Alon Keinan, Ben Sandbank, Claus C. Hilgetag, Isaac Meilijson and
Eytan Ruppin, "Fair Attribution of Functional Contribution in Artificial and
Biological Networks", Neural
Computation
**16**(2004): 1887--1915 - Alexei A. Koulakov, Dmitry Rinberg and Dmitry N. Tsigankov, "How to find decision makers in neural circuits?", q-bio.NC/0401005
- Christian Kuehn, Martin G. Riedler, "Large Deviations for Nonlocal Stochastic Neural Fields", Journal of Mathematical Neuroscience
**4**(2014): 1--33, arxiv:1302.5616 - Danial Lashkari, Ramesh Sridhara and Polina Golland, "Categories and Functional Units: An Infinite Hierarchical Model for Brain Activations" [NIPS 2010]
- Li Zhaoping, Alex Lewis and Silvia Scarpetta, "Mathematical Analysis and Simulations of the Neural Circuit for Locomotion in Lamprey", q-bio.NC/0404012
- Wolfgang Maass and Eduardo D. Sontag, "Neural Systems as Nonlinear
Filters," Neural Computation
**12**(2000): 1743--1772 - Olivier Marre, Sami El Boustani, Yves Fregnac and Alain
Destexhe, "Prediction of spatio-temporal patterns of neural activity from pairwise correlations", arxiv:0903.0127
= Physical Review Letters
**102**(2009): 138101 - Roy Mukamel, Hagar Gelbard, Amos Arieli, Uri Hasson, Itzhak Fried
and Rafael Malach, "Coupling Between Neuronal Firing, Field Potentials, and
fMRI in Human Auditory Cortex", Science
**309**(2005): 951--954 ["als in auditory cortex of two neurosurgical patients and compared them with the fMRI signals of 11 healthy subjects during presentation of an identical movie segment. The predicted fMRI signals derived from single units and the measured fMRI signals from auditory cortex showed a highly significant correlation (r = 0.75, P < 10^-47). Thus, fMRI signals can provide a reliable measure of the firing rate of human cortical neurons."] - Aatira G. Nedungadi, Govindan Rangarajan, Neeraj Jain and
Mingzhou Ding, "Analyzing multiple spike trains with nonparametric granger causality", Journal of Computational
Neuroscience
**27**(2009): 55--64 - Murat Okatan, Matthew A. Wilson and Emery N. Brown, "Analyzing
Functional Connectivity Using a Network Likelihood Model of Ensemble Neural
Spiking
Activity", Neural
Computation
**17**(2005): 1927--1961 - Liam Paninski, Jonathan W. Pillow and Eero P. Simoncelli, "Maximum
Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding
Model", Neural
Computation
**16**(2004): 2533--2561 - G. Pola, R. S. Petersen, A. Thiele, M. P. Young and S. Panzeri,
"Data-Robust Tight Lower Bounds to the Information Carried by Spike Times of a
Neuronal Population", Neural
Computation
**17**(2005): 1962--2005 - R. Quian Quiroga, Z. Nadasdy and Y. Ben-Shaul, "Unsupervised Spike
Detection and Sorting with Wavelets and Superparamagnetic
Clustering", Neural
Computation
**16**(2004): 1661--1687 - Rajesh P. N. Rao (ed.), Probabilistic Models of the Brain: Perception and Neural Function
- George N. Reeke and Allan D. Coop, "Estimating the Temporal
Interval Entropy of Neuronal
Discharge", Neural
Computation
**16**(2004): 941--970 [From the abstract, I'm skeptical. They're assuming that successive inter-spike intervals are all*independent*samples from a*fixed*distribution of*known*parametric form, and then using maximum likelihood to estimate the parameters, which of course gives them an entropy estimate and confidence intervals. But all of the italicized points seem dubious to me. Still, I need to read it.] - Hermann Riecke, Alex Roxin, Santiago Madruga and Sara A. Solla,
"Multiple attractors, long chaotic transients, and failure in small-world
networks of excitable
neurons", Chaos
**17**(2007): 026110 - P. A. Robinson, "Propagator theory of brain dynamics", Physical Review
E
**72**(2005): 011904 - Yasser Roudi, Joanna Tyrcha and John Hertz, "The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity", arxiv:0902.2885
= Physical Review E
**79**(2009): 051915 - Naoki Saito, "The Generalized Spike Process, Sparsity, and Statistical Independence," math.PR/0110103
- P. S. Sastry and K. P. Unnikrishnan, "Conditional probability based
significance tests for sequential patterns in multi-neuronal spike
trains", Neural Computation
**22**(2010): 1025--1059, arxiv:0808.3511 - Silvia Scarpetta, Zhaoping Li and John Hertz, "Hebbian imprinting and retrieval in oscillatory neural networks," cond-mat/0111034
- Margaret Euphrasia Sereno, Neural Computation of Pattern Motion
- Anil K. Seth, Gerald M. Edelman, "Distinguishing Causal
Interactions in Neural Populations", Neural
Computation
**19**(2007): 910--933 - Xilin Shen, Francois G. Meyer, "Low Dimensional Embedding of fMRI datasets", arxiv:0709.3121 ["embedding optimally preserves the local functional coupling between fMRI time series, and provides a low-dimensional coordinate system for detecting activated voxels. To compute the embedding, we build a network of functionally connected voxels and represent it with a graph. A spectral decomposition of the graph probability transition matrix produces a set of eigenvectors that are used to define the embedding"]
- Svetlana V. Shinkareva, Vladimir Gudkov, Jing Wang, "A Network Analysis Approach to fMRI Condition-Specific Functional Connectivity", arxiv:1008.0590
- Lavi Shpigelman, Yoram Singer, Rony Paz and Eilon Vaadia,
"Spikernels: Predicting Arm Movements by Embedding Population Spike Rate
Patterns in Inner-Product Spaces",
Neural
Computation
**17**(2005): 671--690 ["Inner-product operators, often referred to as kernels in statistical learning, define a mapping from some input space into a feature space. The focus of this letter is the construction of biologically motivated kernels for cortical activities. The kernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm for computing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach by comparing the Spikernel to various standard kernels in the task of predicting hand movement velocities from cortical recordings. All of the kernels that we tested in our experiments outperform the standard scalar product used in linear regression, with the Spikernel consistently achieving the best performance."] - Sean L. Simpson, Satoru Hayasaka, Paul J. Laurienti, "Selecting an exponential random graph model for complex brain networks", arxiv:1007.3230
- Terence R. Stanford, Stephan Quessy and Barry E. Stein, "Evaluating
the Operations Underlying Multisensory Integration in the Cat Superior
Colliculus", Journal of
Neuroscience
**25**(2005): 6499--6508 - Wilson Truccolo, John P. Donoghue, "Nonparametric Modeling of
Neural Point Processes via Stochastic Gradient Boosting Regression", Neural
Computation
**19**(2007): 672-705 - Arjen vanOoyen (ed.), Modeling Neural Development
- J. C. Vasquez, B. Cessac and T. Viéville, "Entropy-based parametric estimation of spike train statistics", arxiv:1003.3157 [From a first glance, here "entropy-based" just means "exponential-family distribution"]
- Valérie Ventura, "Testing for and Estimating Latency Effects
for Poisson and Non-Poisson Spike
Trains", Neural
Computation
**16**(2004): 2323--2349 - T. Verechtchaguina, L. Schimansky-Geier and I. M. Sokolov, "Spectra and waiting-time distributions in firing resonant and non-resonant neurons", q-bio.NC/0401013 [Need to see whether their ability to determine response properties from interspike-interval distributions is limited to FitzHugh-Nagumo neurons, or is more general.]
- Hugh R. Wilson, Spikes, Decisions and Actions: The Dynamical Foundations of Neuroscience
- Tor D. Wager and Tomas E. Nichols, "Optimization of experimental
design in fMRI: A general framework using a genetic
algorithm", Neuroimage
**18**(2003): 293--309 - Masahiko Yoshioka, "The spike-timing-dependent learning rule to encode spatiotemporal patterns in a network of spiking neurons," cond-mat/0110070