Skip to main content
SpringerLink
Log in
Book cover

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits pp 81–112Cite as

A New Approach to the Identification of Sensory Processing Circuits Based on Spiking Neuron Data

  • Chapter
  • First Online:

  • 591 Accesses

Part of the book series: Springer Theses ((Springer Theses))

Abstract

The cascade model, comprising a filter in series with a spiking neuron, have been widely used as representation for spiking neural circuits. Although the state-of-the-art identification methods for cascade models can accommodate a wide range of filters and spiking neurons, the assumptions proposed can in some cases be considered restrictive. Specifically, for [Filter]-[IF] circuits, it is assumed that the IF model is known, or that the filter output is available for measurement. In this chapter, two new identification methodologies are proposed for neural circuits comprising a linear or nonlinear filter in cascade with a spiking neuron. A [Nonlinear Filter]-[Ideal IF] circuit is reformulated as a scaled nonlinear filter in series with a modified ideal IF neuron. The identification is subsequently carried out by employing the NARMAX nonlinear system identification methodology to infer the structure and parameters of a discrete-time representation for the scaled nonlinear filter. An equivalent [Linear Filter]-[Leaky IF] circuit is identified, assuming that input-output measurements of the spiking neuron are not available and that all parameters are unknown. The leaky IF model is identified by solving an equation whose solution is proven to be unique. An algorithm is provided that computes the solution with arbitrary precision. Subsequently, the structure and parameters of the filter are inferred using the NARMAX identification methodology. Numerical simulations are given to test the performance of the new methods.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Stat Math 21(1):243–247

    Article  MathSciNet  MATH  Google Scholar 

  • Akaike H (1970) Statistical predictor identification. Ann Inst Stat Math 22(1):203–217

    Article  MathSciNet  MATH  Google Scholar 

  • Bartolini P, Carcano EC, Piroddi L, Valdes JB (2008) Forecasting daily streamflows using narmax models: How disturbances may affect model performance. In: World environmental and water resources congress 2008. ASCE, pp 1–13

    Google Scholar 

  • Billings SA (2013) Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. Wiley

    Google Scholar 

  • Billings SA, Coca D (2002) Identification of narmax and related models. In: Control systems, robotics and automation VI

    Google Scholar 

  • Billings S, Korenberg M, Chen S (1988) Identification of non-linear output-affine systems using an orthogonal least-squares algorithm. Int J Syst Sci 19(8):1559–1568

    Article  MATH  Google Scholar 

  • Billings S, Chen S, Korenberg M (1989) Identification of mimo non-linear systems using a forward-regression orthogonal estimator. Int J Control 49(6):2157–2189

    Article  MATH  Google Scholar 

  • Billings S, Tsang K, Tomlinson G (1990) Spectral analysis for non-linear systems, part iii: case study examples. Mech Syst Signal Process 4(1):3–21

    Article  MATH  Google Scholar 

  • Billings S, Chen S (1989) Extended model set, global data and threshold model identification of severely non-linear systems. Int J Control 50(5):1897–1923

    Article  MATH  Google Scholar 

  • Billings S, Fadzil M (1984) The practical identification of systems with nonlinearities. University of Sheffield, Technical report, Department of Automatic Control and System Engineering

    Google Scholar 

  • Billings S, Leontaritis I (1982) Parameter estimation techniques for nonlinear systems. In: 6th IFAC symposium identification and system parameter estimation, pp 427–433

    Google Scholar 

  • Billings S, Tsang K (1989a) Spectral analysis for non-linear systems, part i: parametric non-linear spectral analysis. Mech Syst Signal Process 3(4):319–339

    Article  MATH  Google Scholar 

  • Billings S, Tsang K (1989b) Spectral analysis for non-linear systems, part ii: interpretation of non-linear frequency response functions. Mech Syst Signal Process 3(4):341–359

    Article  MATH  Google Scholar 

  • Boyd S, Chua LO (1985) Fading memory and the problem of approximating nonlinear operators with volterra series. IEEE Trans Circuits Syst 32(11):1150–1161

    Article  MathSciNet  MATH  Google Scholar 

  • Chen S, Billings SA, Luo W (1989) Orthogonal least squares methods and their application to non-linear system identification. Int J Control 50(5):1873–1896

    Article  MATH  Google Scholar 

  • Chen S (2006) Local regularization assisted orthogonal least squares regression. Neurocomputing 69(4):559–585

    Article  MathSciNet  Google Scholar 

  • Chen S, Billings S (1989) Representations of non-linear systems: the narmax model. Int J Control 49(3):1013–1032

    Article  MATH  Google Scholar 

  • Chua LO, Ng C (1979a) Frequency-domain analysis of nonlinear systems: formulation of transfer functions. IEE J Electron Circuits Syst 3(6):257–269

    Article  Google Scholar 

  • Chua LO, Ng CY (1979b) Frequency domain analysis of nonlinear systems: general theory. IEE J Electron Circuits Syst 3(4):165–185

    Article  Google Scholar 

  • Coca D, Balikhin M, Billings S, Alleyne H, Dunlop M, Luhr H (2000) Time-domain identification of nonlinear processes in space plasma turbulence using multi-point measurements. In: Cluster-II workshop multiscale/multipoint plasma measurements, vol 449, p 111

    Google Scholar 

  • Diaz H, Desrochers AA (1988) Modeling of nonlinear discrete-time systems from input-output data. Automatica 24(5):629–641

    Article  MathSciNet  MATH  Google Scholar 

  • Friederich U, Coca D, Billings S, Juusola M (2009a) Data modelling for analysis of adaptive changes in fly photoreceptors. In: Neural information processing, Springer, pp 34–48

    Google Scholar 

  • Friederich U, Coca D, Billings S, Juusola M (2009b) Nonlinear identification for modeling and analysis of adaptive neuronal systems. Front Syst Neurosci. (Conference abstract: computational and systems neuroscience)

    Google Scholar 

  • Friederich U, Coca D, Billings S, Juusola M (2010) Invariant contrast coding in photoreceptors. In: Front neuroscience conference abstract: computational and systems neuroscience

    Google Scholar 

  • Fung EH, Wong Y, Ho H, Mignolet MP (2003) Modelling and prediction of machining errors using armax and narmax structures. Appl Math Model 27(8):611–627

    Article  MATH  Google Scholar 

  • Geffen MN, Broome BM, Laurent G, Meister M (2009) Neural encoding of rapidly fluctuating odors. Neuron 61(4):570–586

    Article  Google Scholar 

  • George DA (1959) Continuous nonlinear systems. Technical report, DTIC Document

    Google Scholar 

  • Gu Y, Lucas P, Rospars JP (2009) Computational model of the insect pheromone transduction cascade. PLoS Comput Biol 5(3):e1000321

    Article  Google Scholar 

  • Guo L, Billings S (2007) A modified orthogonal forward regression least-squares algorithm for system modelling from noisy regressors. Int J Control 80(3):340–348

    Article  MathSciNet  MATH  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544

    Article  Google Scholar 

  • Hong X, Chen S, Harris CJ (2008a) A-optimality orthogonal forward regression algorithm using branch and bound. IEEE Trans Neural Netw 19(11):1961–1967

    Article  Google Scholar 

  • Hong X, Mitchell RJ, Chen S, Harris CJ, Li K, Irwin GW (2008b) Model selection approaches for non-linear system identification: a review. Int J Syst Sci 39(10):925–946

    Article  MathSciNet  MATH  Google Scholar 

  • Jones JP (2007) Simplified computation of the volterra frequency response functions of non-linear systems. Mech Syst Signal Process 21(3):1452–1468

    Article  Google Scholar 

  • Kim AJ, Lazar AA, Slutskiy YB (2011) System identification of drosophila olfactory sensory neurons. J Comput Neurosci 30(1):143–161

    Article  Google Scholar 

  • Korenberg M, Billings S, Liu Y, McIlroy P (1988) Orthogonal parameter estimation algorithm for non-linear stochastic systems. Int J Control 48(1):193–210

    Article  MATH  Google Scholar 

  • Korenberg MJ, Hunter IW (1996) The identification of nonlinear biological systems: Volterra kernel approaches. Ann Biomed Eng 24(2):250–268

    Article  Google Scholar 

  • Lang ZQ, Billings S (1996) Output frequency characteristics of nonlinear systems. Int J Control 64(6):1049–1067

    Article  MathSciNet  MATH  Google Scholar 

  • Lazar AA (2005) Multichannel time encoding with integrate-and-fire neurons. Neurocomputing 65:401–407

    Article  Google Scholar 

  • Lazar AA, Pnevmatikakis EA (2008) Faithful representation of stimuli with a population of integrate-and-fire neurons. Neural Comput 20(11):2715–2744

    Google Scholar 

  • Lazar AA, Pnevmatikakis EA (2011) Video time encoding machines. IEEE Trans Neural Netw 22(3):461–473

    Article  Google Scholar 

  • Lazar AA, Slutskiy YB (2010) Identifying dendritic processing. In: Lafferty J, Williams CKI, Shawe-Taylor J, Zemel R, Culotta A (eds) Advances in neural information processing systems 23, pp 1261–1269. (spotlight presentation)

    Google Scholar 

  • Lazar AA, Slutskiy YB (2012) Channel identification machines. J Comput Intell Neurosci 2012:1–20

    Article  Google Scholar 

  • Lazar AA, Slutskiy Y (2013) Multisensory encoding, decoding, and identification. In: Advances in neural information processing systems, pp 3183–3191

    Google Scholar 

  • Lazar AA, Slutskiy YB (2014a) Channel identification machines for multidimensional receptive fields. Front Comput Neurosci 8

    Google Scholar 

  • Lazar AA, Slutskiy YB (2014b) Functional identification of spike-processing neural circuits. Neural Comput 26(2):264–305

    Google Scholar 

  • Lazar AA, Slutskiy YB (2015) Spiking neural circuits with dendritic stimulus processors. J Comput Neurosci 38(1):1–24

    Article  Google Scholar 

  • Lazar AA, Slutskiy YB, Zhou Y (2015) Massively parallel neural circuits for stereoscopic color vision: encoding, decoding and identification. Neural Netw 63:254–271

    Article  MATH  Google Scholar 

  • Lee YW, Chang TL (2009) Application of narx neural networks in thermal dynamics identification of a pulsating heat pipe. Energy Convers Manag 50(4):1069–1078

    Article  Google Scholar 

  • Leontaritis I, Billings SA (1985a) Input-output parametric models for non-linear systems part i: deterministic non-linear systems. Int J Control 41(2):303–328

    Article  MATH  Google Scholar 

  • Leontaritis I, Billings SA (1985b) Input-output parametric models for non-linear systems part ii: stochastic non-linear systems. Int J Control 41(2):329–344

    Article  MATH  Google Scholar 

  • Leontaritis I, Billings S, SUD of Control Engineering (1981) Identification of non-linear systems using parameter estimation techniques. In: Proceedings of IEEE conference of control and applications, pp 183–190

    Google Scholar 

  • Li L, Billings S (2011) Estimation of generalized frequency response functions for quadratically and cubically nonlinear systems. J Sound Vib 330(3):461–470

    Article  Google Scholar 

  • Linkens D, Khelfa M (1992) Control strategies for nonlinear dynamics of muscle relaxant anaesthesia. Comput Methods Programs Biomed 37(1):1–30

    Article  Google Scholar 

  • Nirenberg S, Pandarinath C (2012) Retinal prosthetic strategy with the capacity to restore normal vision. Proc Natl Acad Sci 109(37):15,012–15,017

    Google Scholar 

  • Paninski L, Pillow JW, Simoncelli EP (2004) Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model. Neural Comput 16(12):2533–2561

    Article  MATH  Google Scholar 

  • Pearson RK (1995) Nonlinear input/output modelling. J Process. Control 5(4):197–211

    Google Scholar 

  • Pearson RK (1999) Discrete-time dynamic models. Oxford University Press

    Google Scholar 

  • Pillow JW, Simoncelli EP (2006) Dimensionality reduction in neural models: an information-theoretic generalization of spike-triggered average and covariance analysis. J Vis 6(4):9

    Article  Google Scholar 

  • Pisoni E, Farina M, Carnevale C, Piroddi L (2009) Forecasting peak air pollution levels using narx models. Eng Appl Artif Intell 22(4):593–602

    Article  Google Scholar 

  • Santos AAP, da Costa NCA, dos Santos Coelho L (2007) Computational intelligence approaches and linear models in case studies of forecasting exchange rates. Expert Syst Appl 33(4):816–823

    Article  Google Scholar 

  • Slee SJ, Higgs MH, Fairhall AL, Spain WJ (2005) Two-dimensional time coding in the auditory brainstem. J Neurosci 25(43):9978–9988

    Article  Google Scholar 

  • Smith C (2008) Biology of sensory systems. Wiley

    Google Scholar 

  • Song Z, Postma M, Billings SA, Coca D, Hardie RC, Juusola M (2012) Stochastic, adaptive sampling of information by microvilli in fly photoreceptors. Curr Biol 22(15):1371–1380

    Article  Google Scholar 

  • Song Z, Coca D, Billings S, Postma M, Hardie RC, Juusola M (2009) Biophysical modeling of a drosophila photoreceptor. In: International conference on neural information processing. Springer, pp 57–71

    Google Scholar 

  • Thomson M, Schooling S, Soufian M (1996) The practical application of a nonlinear identification methodology. Control Eng Pract 4(3):295–306

    Article  Google Scholar 

  • Trefethen LN, Bau III D (1997) Numerical linear algebra, vol 50. Siam

    Google Scholar 

  • Volterra V (2005) Theory of functionals and of integral and integro-differential equations. Courier Corporation

    Google Scholar 

  • Wei HL, Zheng Y, Pan Y, Coca D, Li LM, Mayhew JE, Billings S et al (2009) Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach. IEEE Trans Biomed Eng 56(6):1606–1616

    Article  Google Scholar 

  • Wu MCK, David SV, Gallant JL (2006) Complete functional characterization of sensory neurons by system identification. Annu Rev Neurosci 29:477–505

    Article  Google Scholar 

  • Zhang H, Billings S (1993) Analysing non-linear systems in the frequency domain-i. the transfer function. Mech Syst Signal Process 7(6):531–550

    Article  Google Scholar 

  • Zhu D, Balikhin M, Gedalin M, Alleyne H, Billings S, Hobara Y, Krasnosel’Skikh V, Dunlop M, Ruderman M (2008) Nonlinear dynamics of foreshock structures: application of nonlinear autoregressive moving average with exogenous inputs model to cluster data. J Geophys Res Space Phys (1978–2012) 113(A4)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, UK

    Dorian Florescu

Authors
  1. Dorian Florescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dorian Florescu .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Florescu, D. (2017). A New Approach to the Identification of Sensory Processing Circuits Based on Spiking Neuron Data. In: Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-57081-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-57081-5_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57080-8

  • Online ISBN: 978-3-319-57081-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation