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?

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

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

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

F. Gregory Ashby, Statistical Analysis of fMRI Data

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