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No Statistical-Computational Gap in Spiked Matrix Models with Generative Network Priors

Jorio Cocola, Paul Hand, Vladislav Voroninski
2021 Entropy  
In stark contrast to such cases, we show that there is no statistical-computational gap under a generative network prior, in which the spike lies on the range of a generative neural network.  ...  We provide a non-asymptotic analysis of the spiked Wishart and Wigner matrix models with a generative neural network prior.  ...  Figure 2 . 2 Reconstruction error for the recovery of a spike y = G(x ) in the Wishart and Wigner models with random generative network priors.  ... 
doi:10.3390/e23010115 pmid:33467175 pmcid:PMC7830301 fatcat:w2cevf2j7rdalmmsdq2bgafaaa

Nonasymptotic Guarantees for Spiked Matrix Recovery with Generative Priors [article]

Jorio Cocola, Paul Hand, Vladislav Voroninski
2020 arXiv   pre-print
This result suggests that generative priors have no computational-to-statistical gap for structured rank-one matrix recovery in the finite data, nonasymptotic regime.  ...  We present this analysis in the case of both the Wishart and Wigner spiked matrix models.  ...  Generative priors have been shown to close a computational-to-statistical gap in the Compressive Phase Retrieval problem.  ... 
arXiv:2006.07953v2 fatcat:bj2chmc5uvhk5kgn3wdfymbaiy

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

Mark D. Humphries, Ric Wood, Kevin Gurney
2009 Neural Networks  
A new model of gap junctions between the FSIs is introduced and tuned to experimental data.  ...  We construct a new three-dimensional model of the striatal microcircuit's connectivity, and instantiate this with our dopamine-modulated neuron models of the MSNs and FSIs.  ...  In addition, we use the same N, r in the spike-event generators for the FSIs, as there is no data on cortical input to these neurons.  ... 
doi:10.1016/j.neunet.2009.07.018 pmid:19646846 fatcat:kbpqaxu4xfcsxnk2o3n7ev6i6e

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

Gurney Kevin
2010 Frontiers in Neuroscience  
A new model of gap junctions between the FSIs is introduced and tuned to experimental data.  ...  We construct a new three-dimensional model of the striatal microcircuit's connectivity, and instantiate this with our dopamine-modulated neuron models of the MSNs and FSIs.  ...  In addition, we use the same N, r in the spike-event generators for the FSIs, as there is no data on cortical input to these neurons.  ... 
doi:10.3389/conf.fnins.2010.03.00238 fatcat:cvtpbha62zat3noxjnukt6v4gq

Optimal Population Coding for Dynamic Input by Nonequilibrium Networks

Kevin S. Chen
2022 Entropy  
Theoretical studies focus on optimal response in single neuron and population code in networks with weak pairwise interactions.  ...  Here, we study the collective response in a kinetic Ising model that encodes the dynamic input.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e24050598 pmid:35626482 pmcid:PMC9140425 fatcat:schvzei5lfb75lveuht7p3br4e

Connectivity Inference from Neural Recording Data: Challenges, Mathematical Bases and Research Directions [article]

Ildefons Magrans de Abril, Junichiro Yoshimoto, Kenji Doya
2017 arXiv   pre-print
We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches.  ...  This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging.  ...  Validation In order to validate the connectivity inference method itself, the use of synthetic data from a network model with a known connection matrix is the first step.  ... 
arXiv:1708.01888v2 fatcat:fezbmzuzenac7mqcnqhq5sveye

Training deep neural density estimators to identify mechanistic models of neural dynamics [article]

Pedro J. Gonçalves, Jan-Matthis Lueckmann, Michael Deistler, Marcel Nonnenmacher, Kaan Öcal, Giacomo Bassetto, Chaitanya Chintaluri, William F. Podlaski, Sara A. Haddad, Tim P. Vogels, David S. Greenberg, Jakob H. Macke
2019 bioRxiv   pre-print
Our tool identifies all parameters consistent with data, is scalable both in the number of parameters and data features, and does not require writing new code when the underlying model is changed.  ...  The approach presented here will help close the gap between data-driven and theory-driven models of neural dynamics.  ...  The other 80% were computed from the remaining 1681 summary 462 statistics given by spike-triggered averages.  ... 
doi:10.1101/838383 fatcat:nqmbrp6zbzfyln3sihz3x2oqde

Modeling the impact of common noise inputs on the network activity of retinal ganglion cells

Michael Vidne, Yashar Ahmadian, Jonathon Shlens, Jonathan W. Pillow, Jayant Kulkarni, Alan M. Litke, E. J. Chichilnisky, Eero Simoncelli, Liam Paninski
2011 Journal of Computational Neuroscience  
Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies.  ...  In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, Action Editor: Brent Doiron M. Vidne  ...  We also gratefully acknowledge the use of the Hotfoot shared cluster computer at Columbia University.  ... 
doi:10.1007/s10827-011-0376-2 pmid:22203465 pmcid:PMC3560841 fatcat:dhtdyn2mlbgipoq4ijzb5m4vgy

Statistical Inference for Assessing Functional Connectivity of Neuronal Ensembles With Sparse Spiking Data

Zhe Chen, David F Putrino, Soumya Ghosh, Riccardo Barbieri, Emery N Brown
2011 IEEE transactions on neural systems and rehabilitation engineering  
The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data.  ...  Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons.  ...  Hessian matrix cannot be computed).  ... 
doi:10.1109/tnsre.2010.2086079 pmid:20937583 pmcid:PMC3044782 fatcat:ycusw6o6azhnzmm2c2k6gyonoe

Identifying Functional Connectivity in Large-Scale Neural Ensemble Recordings: A Multiscale Data Mining Approach

Seif Eldawlatly, Rong Jin, Karim G. Oweiss
2009 Neural Computation  
We also demonstrate how activity-dependent plasticity can be tracked and quantified in multiple network topologies built to mimic distinct behavioral contexts.  ...  Using point process theory to model population activity, we demonstrate the robustness of the approach in tracking a broad spectrum of neuronal interaction, from synchrony to rate co-modulation, by systematically  ...  Figure 4a shows the network topology of the 16-neuron population with no across-cluster connectivity.  ... 
doi:10.1162/neco.2008.09-07-606 pmid:19431266 pmcid:PMC2808693 fatcat:n7x6w6x2inehjc3qtnr4zxxs6i

Image Completion using Spiking Neural Networks

In this paper, we are showing how spiking neural networks are applied in image repainting, and its results are outstanding compared with other machine learning techniques.  ...  The model has an effective and fast to complete the image by filling the gaps (holes).  ...  But this classification deals with high costs and consumes more time. No prior information is required in unsupervised classification since it is free from human intervention.  ... 
doi:10.35940/ijitee.a5294.119119 fatcat:j6jkc4ke2jf6roarwtuywqepem

Millimeter-scale epileptiform spike propagation patterns and their relationship to seizures

Ann C Vanleer, Justin A Blanco, Joost B Wagenaar, Jonathan Viventi, Diego Contreras, Brian Litt
2016 Journal of Neural Engineering  
Currently, clinical electrode arrays with a sparse spatial density (1 cm) are used to map the seizure onset zone (SOZ) and epileptic network in patients prior to epilepsy surgery.  ...  We found that sub-millimeter-scale ST spike wave-propagation patterns reveal network dynamics that may elucidate mechanisms underlying local circuit activity generating seizures.  ...  with seizures in order to map the putative brain networks involved prior to resective surgery [9, 19] .  ... 
doi:10.1088/1741-2560/13/2/026015 pmid:26859260 pmcid:PMC4807853 fatcat:qhm4yyvdobbezo5wwgv62gr77e

Optimality and sub-optimality of PCA I: Spiked random matrix models

Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
2018 Annals of Statistics  
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random  ...  These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences.  ...  Such computational vs. statistical gaps have received considerable recent attention (e.g. Berthet and Rigollet (2013b) ; Ma and Wu (2015) ), often in connection with sparsity.  ... 
doi:10.1214/17-aos1625 fatcat:7yrxzyhfszeudhjh4jinvnl6wq

Data-driven Perception of Neuron Point Process with Unknown Unknowns [article]

Ruochen Yang, Gaurav Gupta, Paul Bogdan
2019 arXiv   pre-print
Results suggest that the neural connection model with unknown unknowns can efficiently estimate the statistical properties of the process by increasing the network likelihood.  ...  Towards this end, the current work focuses on statistical neuron system model with multi-covariates and unknown inputs.  ...  In this paper, we propose a neural system model with more general unknown inputs, i.e., we remove restrictive dynamical assumption on the unknowns and put mild assumptions on its prior statistics.  ... 
arXiv:1811.00688v2 fatcat:qtkd3sw24fh6ppuiphyjtmraoe

Learning Multisensory Integration and Coordinate Transformation via Density Estimation

Joseph G. Makin, Matthew R. Fellows, Philip N. Sabes, Gunnar Blohm
2013 PLoS Computational Biology  
In particular, we train a restricted Boltzmann machine with the biologically plausible contrastive-divergence rule to learn a range of neural computations not previously demonstrated under a single approach  ...  data is modeled in terms of a set of fixed parameters and a set of latent variables.  ...  Acknowledgments Base code for training a deep belief network with contrastive divergence was taken from Salukhutdinov and Hinton [67] .  ... 
doi:10.1371/journal.pcbi.1003035 pmid:23637588 pmcid:PMC3630212 fatcat:t2vnpu5perdijkrlilzgbqqbwy
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