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Estimation of the number of spikes, possibly equal, in the high-dimensional case
2014
Journal of Multivariate Analysis
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Estimating the number of spikes in a spiked model is an important problem in many areas such as signal processing. ...
In this paper, we consider the case of high dimension, where p is large compared to n. The approach is based on recent results of random matrix theory. ...
Acknowledgment The authors are grateful to two Referees and the Associate Editor for their helpful comments that have led to many improvements of the paper. ...
doi:10.1016/j.jmva.2014.02.017
fatcat:wdvie2raxnc3hj6hof5mdaph7e
The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction
[article]
2015
arXiv
pre-print
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Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. ...
Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. ...
Latham for insightful discussions and providing scientific input during the course of this project. We thank M. Day, B. Dichter, D. Goodman, W. Guo, and L. ...
arXiv:1308.3542v2
fatcat:htnjglgdjvbezkhk247qsrxymy
The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction
2015
PLoS Computational Biology
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Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. ...
Using these insights, we propose novel dimensionality-reduction methods that incorporate non-Poisson spiking, and suggest new parametrizations that allow for tractable estimation of high-dimensional subspaces ...
Latham for insightful discussions and providing scientific input during the course of this project. We thank M. Day, B. Dichter, D. Goodman, W. Guo, and L. ...
doi:10.1371/journal.pcbi.1004141
pmid:25831448
pmcid:PMC4382343
fatcat:fzxmbwbhczgr5k5z3zfkj7dzdy
Maximally informative dimensions: Analyzing neural responses to natural signals
[article]
2002
arXiv
pre-print
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We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of the high dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear ...
Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. ...
Work at UCSF was supported in part by the Sloan and Swartz Foundations and by a training grant from the NIH. ...
arXiv:physics/0208057v1
fatcat:dmcwvdap6vablgns653lgtrdo4
Automated spike sorting using density grid contour clustering and subtractive waveform decomposition
2007
Journal of Neuroscience Methods
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Acknowledgements We thank Wilson Truccolo, John Simeral, Matthew Fellows and Juliana Dushanova for their valuable feedback during the development of the algorithm and the drafting of this paper. ...
This work is partially supported by NIH-NINDS NS-25074, the VA, and by the Office of Naval Research, NRD-386. ...
Once the templates are identified, the algorithm reverts to the original full-dimensional representation of the data (in this case vectors of 48 voltage measurements) to sort each spike. ...
doi:10.1016/j.jneumeth.2007.03.025
pmid:17512603
pmcid:PMC2104515
fatcat:r6e74fny6bbitosvobkdvnbh4q
Analyzing neural responses to natural signals: Maximally informative dimensions
[article]
2003
arXiv
pre-print
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We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of a high dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear ...
Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. ...
Work at UCSF was supported in part by the Sloan and Swartz Foundations and by a training grant from the NIH. ...
arXiv:physics/0212110v2
fatcat:jftyykynsffcddftbwfog676r4
Spike-triggered neural characterization
2006
Journal of Vision
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Spike-triggered average and covariance analyses can be used to estimate the filters and nonlinear combination rule from extracellular experimental data. ...
This description may be formalized in a model that operates with a small set of linear filters whose outputs are nonlinearly combined to determine the instantaneous firing rate. ...
The accuracy of the estimation is dependent on the dimensionality (number of filters) in the linear subspace. ...
doi:10.1167/6.4.13
pmid:16889482
fatcat:567kgwyfmjfbllwilscwzkjq2a
Intrinsic dimensionality estimation and dimensionality reduction through scale space filtering
2009
2009 16th International Conference on Digital Signal Processing
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of high dimensional datasets. ...
However, when these techniques are applied directly to the initial degraded and noisy data, the assumptions on the possible statistical separation of real world classes do not, in the general case, hold ...
The spatial g s marker acts as in the 2D case ensuring an elegant simplification in the spatial neighborhood of a pixel and the spectral g c accounts for the spike-like features by enforcing its relevant ...
doi:10.1109/icdsp.2009.5201196
fatcat:7ksgzjaq3bhrpo7he7c2io3pxm
Asymptotic properties of principal component analysis and shrinkage-bias adjustment under the generalized spiked population model
2019
Journal of Multivariate Analysis
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Most of the existing theoretical and methodological results for high-dimensional PCA are based on the spiked population model in which all the population eigenvalues are equal except for a few large ones ...
With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. ...
Acknowledgments We thank the Editor-in-Chief, Christian Genest, and referees for their helpful comments and suggestions, which lead to substantial improvements of the manuscript. ...
doi:10.1016/j.jmva.2019.02.007
pmid:32831421
pmcid:PMC7441582
fatcat:7lji3cwjybe2leeoasfzurjfjy
Differential Entropy of Multivariate Neural Spike Trains
[chapter]
2012
Lecture Notes in Computer Science
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In our framework, the unidimensional special case corresponds to estimating the differential entropy of the ISI distribution; this is generalised to multidimensional cases including patterns across successive ...
This is likely to underestimate the information carried by spike timing codes, in practice, if they involve high precision patterns of inter-spike intervals (ISIs). ...
In the current work, we adopt the approach of Victor, examining how well it can be used to estimate the differential entropy of a sequence of interspike intervals, beginning with a one-dimensional case ...
doi:10.1007/978-3-642-33269-2_36
fatcat:npvrd5woy5ezlhhlyzvpdjpdqu
Encoding Stimulus Information by Spike Numbers and Mean Response Time in Primary Auditory Cortex
2005
Journal of Computational Neuroscience
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We demonstrate that, in both cases, spike counts and mean response times jointly carry essentially all the available information about the stimuli. ...
Neurons can transmit information about sensory stimuli via their firing rate, spike latency, or by the occurrence of complex spike patterns. ...
King, by a grant from the Israeli ministry of science to G. Chechik, and by a Volkswagen grant and a GIF grant to I. Nelken. ...
doi:10.1007/s10827-005-1739-3
pmid:16133819
fatcat:7b7yojqv7zetrj77rubxj6chb4
Stimuli Reduce the Dimensionality of Cortical Activity
2016
Frontiers in Systems Neuroscience
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The empirical estimation of such bounds depends on the number and duration of trials. ...
, and pair-wise correlations in spiking network models. ...
In this case, dimensionality is minimal and equal to one. ...
doi:10.3389/fnsys.2016.00011
pmid:26924968
pmcid:PMC4756130
fatcat:bxvk3tr76rfghei6yxwv6fwc4q
Dimensionality reduction in neural models: An information-theoretic generalization of spike-triggered average and covariance analysis
2006
Journal of Vision
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rate, in the form of a ratio of Gaussians. (4) it is equivalent to maximum likelihood estimation of this default model, but also converges to the correct filter estimates whenever the conditions for the ...
and robust, allowing recovery of multiple linear filters from a data set of relatively modest size; (3) it provides an explicit "default" model of the nonlinear stage mapping the filter responses to spike ...
Movshon for helpful discussions and for providing us with the physiological data shown in this paper. Thanks also to L. Paninski for helpful comments on the manuscript. ...
doi:10.1167/6.4.9
pmid:16889478
fatcat:52eiednkira2tno2e3xj7tfe4m
Cluster tendency assessment in neuronal spike data
2019
PLoS ONE
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In data with a relatively small number of clusters, iVAT is beneficial in estimating the number of clusters to inform the initialization of clustering algorithms. ...
We also introduce a visualization technique called improved visual assessment of cluster tendency (iVAT) to estimate possible cluster structures in data without the need for dimensionality reduction. ...
Acknowledgments This research was supported by the Natural Sciences and Engineering Research Council of Canada. ...
doi:10.1371/journal.pone.0224547
pmid:31714913
pmcid:PMC6850537
fatcat:myottwvbh5hitaqicbpdxii67u
Analyzing multicomponent receptive fields from neural responses to natural stimuli
2011
Network
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to the curse of dimensionality. ...
The challenge of building increasingly better models of neural responses to natural stimuli is to accurately estimate the multiple stimulus features that may jointly affect the neural spike probability ...
Stryker, in whose laboratories the V1 data were collected. ...
doi:10.3109/0954898x.2011.566303
pmid:21780916
pmcid:PMC3251001
fatcat:v6ngkv44zrh6po7ohzxjvp6gne
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