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Estimation of the number of spikes, possibly equal, in the high-dimensional case

Damien Passemier, Jianfeng Yao
2014 Journal of Multivariate Analysis  
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]

Ross S. Williamson, Maneesh Sahani, Jonathan W. Pillow
2015 arXiv   pre-print
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

Ross S. Williamson, Maneesh Sahani, Jonathan W. Pillow, Matthias Bethge
2015 PLoS Computational Biology  
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]

Tatyana Sharpee, Nicole C. Rust, William Bialek
2002 arXiv   pre-print
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

Carlos Vargas-Irwin, John P. Donoghue
2007 Journal of Neuroscience Methods  
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]

Tatyana Sharpee, Nicole C. Rust, William Bialek
2003 arXiv   pre-print
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

Odelia Schwartz, Jonathan W. Pillow, Nicole C. Rust, Eero P. Simoncelli
2006 Journal of Vision  
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

Konstantinos Karantzalos
2009 2009 16th International Conference on Digital Signal Processing  
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

Rounak Dey, Seunggeun Lee
2019 Journal of Multivariate Analysis  
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]

Nanyi Cui, Jiaying Tang, Simon R. Schultz
2012 Lecture Notes in Computer Science  
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

Israel Nelken, Gal Chechik, Thomas D. Mrsic-Flogel, Andrew J. King, Jan W. H. Schnupp
2005 Journal of Computational Neuroscience  
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

Luca Mazzucato, Alfredo Fontanini, Giancarlo La Camera
2016 Frontiers in Systems Neuroscience  
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

Jonathan W. Pillow, Eero P. Simoncelli
2006 Journal of Vision  
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

Sara Mahallati, James C. Bezdek, Milos R. Popovic, Taufik A. Valiante, Gennady Cymbalyuk
2019 PLoS ONE  
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

Ryan J. Rowekamp, Tatyana O. Sharpee
2011 Network  
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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