Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks

Biological Cybernetics

Volumn 106, Issue 4-5, 2012, Pages 201-217

  Bitzer, Sebastian ^a   Kiebel, Stefan J ^a  

^a MAX PLANCK INSTITUTE FOR HUMAN COGNITIVE AND BRAIN SCIENCES   (Germany)

Author keywords

Bayesian inference; Human motion; Nonlinear dynamics; Recurrent neural networks

Indexed keywords

BAYESIAN INFERENCE; BAYESIAN INVERSION; BRAIN FUNCTIONS; BRAIN PROCESSING; COMPUTATIONAL NEUROSCIENCE; DYNAMIC STIMULI; FAST DECODING; GENERATIVE MODEL; HUMAN KINEMATICS; HUMAN MOTIONS; INITIAL CONDITIONS; MACHINE LEARNING APPLICATIONS; NEURONAL NETWORKS; NONLINEAR FUNCTIONS; PREDICTIVE CODING;

BAYESIAN NETWORKS; BRAIN MODELS; DECODING; DYNAMICS; INFERENCE ENGINES; KINEMATICS; LEARNING SYSTEMS; NEURONS; NONLINEAR DYNAMICAL SYSTEMS;

RECURRENT NEURAL NETWORKS;

ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; BAYES THEOREM; BIOLOGICAL MODEL; BIOMECHANICS; CYBERNETICS; HUMAN; NERVE CELL NETWORK; NONLINEAR SYSTEM; PHYSIOLOGY; WALKING;

ARTIFICIAL INTELLIGENCE; BAYES THEOREM; BIOMECHANICS; CYBERNETICS; HUMANS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; WALKING;

EID: 84864538788     PISSN: 03401200     EISSN: 14320770     Source Type: Journal    
DOI: 10.1007/s00422-012-0490-x     Document Type: Article

References (71)

1. Archambeau C, Opper M, Shen Y, Cornford D, Shawe-Taylor J (2008) Variational inference for diffusion processes. In: Platt J, Koller D, Singer Y, Roweis SAdvances in neural information processing systems. MIT Press, Cambridge, pp 17-24
2. Bar M (2009) The proactive brain: memory for predictions. Philos Trans R Soc Lond B 364(1521): 1235-1243. Doi:10.1098/rstb. 2008.0310
3. Blake R, Shiffrar M (2007) Perception of human motion. Annu Rev Psychol 58: 47-73. Doi:10.1146/annurev.psych.57.102904. 190152
4. BoerlinM, Denève S (2011) Spike-based population coding and working memory. PLoS Comput Biol 7(2):e1001-080. Doi:10.1371/ journal.pcbi.1001080
5. Buonomano DV, MaassW (2009) State-dependent computations: spatiotemporal processing in cortical networks. Nat Rev Neurosci 10(2): 113-125. Doi:10.1038/nrn2558
6. Cessac B, Samuelides M (2007) From neuron to neural networks dynamics. Eur Phys J 142: 7-88. Doi:10.1140/epjst/ e2007-00058-2
7. Connor JT,Martin RD, Atlas LE (1994) Recurrent neural networks and robust time series prediction. IEEE Trans Neural Netw 5(2): 240-254. Doi:10.1109/72.279188
8. Daunizeau J, Friston K, Kiebel S (2009) Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models. Physica D 238(21): 2089-2118. Doi:10.1016/j.physd.2009. 08.002
9. Debanne D, Campanac E, Bialowas A, Carlier E, Alcaraz G (2011) Axon physiology. Physiol Rev 91(2): 555-602. Doi:0. 1152/physrev.00048.2009
10. Denève S (2008) Bayesian spiking neurons i inference. Neural Comput 20(1): 91-117. Doi:10.1162/neco.2008.20.1.91
11. To see how these standard covariance matrices are translated into generalized coordinates, we refer the reader to Friston et al. (2008, p. 860).
12. Denève S, Duhamel JR, Pouget A (2007) Optimal sensorimotor integration in recurrent cortical networks a neural implementation of Kalman filters. J Neurosci 27(21): 5744-5756. Doi:10.1523/ JNEUROSCI.3985-06.2007
13. Doucet A, Tadić V (2003) Parameter estimation in general state-space models using particle methods. Ann Inst Stat Math 55: 409-422. Doi:10.1007/BF02530508
14. Doucet A, de Freitas N, Gordon N (eds) (2001) Sequential Monte Carlo Methods in Practice. Springer, Berlin
15. Elman JL (1990) Finding structure in time. Cogn Sci 14(2): 179-211. Doi:10.1207/s15516709cog1402-1
16. Friston KJ (2002) Bayesian estimation of dynamical systems an application to fMRI. NeuroImage 16(2): 513-530. Doi:10.1006/nimg. 2001.1044
17. FristonK,Kiebel S (2009) Predictive coding under the free-energy principle. Philos Trans R Soc Lond B 364(1521): 1211-1221. Doi:10. 1098/rstb.2008.0300
18. Friston KJ, Penny W, Phillips C, Kiebel S, Hinton G, Ashburner J (2002) Classical and bayesian inference in neuroimaging theory. NeuroImage 16(2): 465-483. Doi:10.1006/nimg.2002.1090
19. Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. NeuroImage 19(4):1273-1302
20. Friston K, Trujillo-Barreto N, Daunizeau J (2008) DEM A variational treatment of dynamic systems. NeuroImage 41(3): 849-885. Doi:10.1016/j. neuroimage.2008.02.054
21. Friston K, Stephan K, Li B, Daunizeau J (2010) Generalised filtering. Math Probl Eng. Article ID 621, 670. Doi:10.1155/2010/621670
22. Ghahramani Z, Beal MJ (2001) Propagation algorithms for variational bayesian learning. In:LeenT, DietterichT,TrespV(eds)Advances in neural information processing systems, vol 13, MIT Press, Cambridge, pp 507-513
23. Hamker FH (2005) The reentry hypothesis the putative interaction of the frontal eye field ventrolateral prefrontal cortex and areas v4 it for attention and eye movement. Cereb Cortex 15(4): 431-447. Doi:10.1093/cercor/bhh146
24. Hammer B, Steil JJ (2002) Tutorial Perspectives on learning with rnns. In: Proceedings of European symposium on artificial neural networks (ESANN) d-side publi, pp 357-368
25. Hinton GE, Salakhutdinov RR (2006) Reducing the dimensionality of data with neural networks. Science 313(5786): 504-507. Doi:10. 1126/science.1127647
26. Jaeger H (2001) The "echo state" approach to analysing and training recurrent neural networks. GMD Report 148, German National Research Center for Information Technology
27. Jaeger H, Lukosevicius M, Popovici D, Siewert U (2007) Optimization and applications of echo state networks with leaky-integrator neurons. Neural Netw 20(3): 335-352. Doi:10.1016/j.neunet.2007. 04.016
28. Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, New York
29. Jirsa VK, Kelso JAS (2005) The excitator as a minimal model for the coordination dynamics of discrete and rhythmic movement generation. J Mot Behav 37(1): 35-51. Doi:10.3200/JMBR.37.1.35-51
30. Kantas N, Doucet A, Singh SS, Maciejowski JM (2009) Overview of sequential monte carlo methods for parameter estimation on general state space models. In: Proceedings of the 15th IFAC symposium on system identification (SYSID), Saint-Malo, France
31. Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior. MIT Press, Cambridge
32. Kiebel SJ, David O, Friston KJ (2006) Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization. NeuroImage 30(4): 1273-1284. Doi:10.1016/j.neuroimage.2005. 12.055
33. Kiebel SJ, Daunizeau J, Friston KJ (2008) A hierarchy of time-scales and the brain. PLoS Comput Biol 4(11): e1000-209. Doi:10.1371/ journal.pcbi.1000209
34. Kiebel SJ, Garrido MI, Moran R, Chen CC, Friston KJ (2009a) Dynamic causal modeling for eeg and meg. Hum Brain Mapp 30(6): 1866-1876. Doi:10.1002/hbm.20775
35. Kiebel SJ, von Kriegstein K, Daunizeau J, Friston KJ (2009b) Recognizing sequences of sequences. PLoS Comput Biol 5(8): e1000-464. Doi:10.1371/journal. pcbi.1000464
36. Lazar A, Pipa G, Triesch J (2009) Sorn a self-organizing recurrent neural network. Front Comput Neurosci 3:23. Doi:10.3389/neuro.10. 023.2009
37. Legenstein R, Maass W (2007) What makes a dynamical system computationally powerful? In: Haykin S, Principe JC, Sejnowski TJ, McWhirter JG(eds) Newdirections in statistical signal processing: from systems to brains, MIT Press, Cambridge, pp 127-154
38. MaassW,Natschlger T,MarkramH (2002) Real-time computingwithout stable states a new framework for neural computation based on perturbations. Neural Comput 14(11): 2531-2560. Doi:10.1162/ 089976602760407955
39. Mel BW (2008) Why have dendrites? a computational perspective, Chap. 16. In: Stuart G, Spruston N, Häusser M (eds) Dendrites, 2nd edn. Oxford University Press, Oxford
40. Miller EK, Cohen JD (2001) An integrative theory of prefrontal cortex function. Annu Rev Neurosci 24: 167-202. Doi:10.1146/annurev. Neuro.24.1.167
41. Mottet D, Bootsma RJ (1999) The dynamics of goal-directed rhythmical aiming. Biol Cybern 80(4): 235-245. Doi:10.1007/ s004220050521
42. Mumford D (1996) Pattern theory: a unifying perspective. In: Knill DC Richards W (eds) Perception as Bayesian inference. Cambridge University Press, Cambridge
43. Narendra K, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1(1): 4-27. Doi:10.1109/72.80202
44. Natarajan R, Huys QJM, Dayan P, Zemel RS (2008) Encoding and decoding spikes for dynamic stimuli. Neural Comput 20(9): http://www.mitpressjournals. org/doi/pdf/10.1162/neco.2008. 01-07-436 2325-2360. Doi:10.1162/neco.2008.01-07- 436
45. Parlos A, Menon S, Atiya A (2001) An algorithmic approach to adaptive state filtering using recurrent neural networks. IEEE Trans Neural Netw 12(6): 1411-1432. Doi:10.1109/72.963777
46. Pearlmutter BA (1989) Learning state space trajectories in recurrent neural networks. Neural Comput 1(2): http://www. Mitpressjournals.org/doi/pdf/ 10.1162/neco.1989.1.2.263 263-269. Doi:10.1162/neco.1989.1.2.263
47. Perdikis D, Huys R, Jirsa V (2011a) Complex processes from dynamical architectures with time-scale hierarchy. PLoS One 6(2): e10-589. Doi:10.1371/journal.pone.0016589
48. Perdikis D, Huys R, Jirsa VK (2011b) Time scale hierarchies in the functional organization of complex behaviors. PLoS Comput Biol 7(9): e1002-198. Doi:10.1371/journal.pcbi.1002198
49. Pissadaki EK, Sidiropoulou K, Reczko M, Poirazi P (2010) Encoding of spatio-temporal input characteristics by a ca1 pyramidal neuron model. PLoS Comput Biol 6(12): e1001-038. Doi:10.1371/ journal.pcbi.1001038
50. Poirazi P, Brannon T, Mel BW (2003) Pyramidal neuron as two-layer neural network. Neuron 37(6): http://dx.doi.org 989-999. Doi:10. 1016/S0896-6273(03) 00149-1
51. Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI (2006) Dynamical principles in neuroscience. Rev Mod Phys 78(4): 1213-1265. Doi:10.1103/ RevModPhys.78.1213
52. Rao RPN (2004) Bayesian computation in recurrent neural circuits. Neural Comput 16(1): 1-38. Doi:10.1162/08997660460733976
53. Rao RP, Ballard DH (1997) Dynamic model of visual recognition predicts neural response properties in the visual cortex. Neural Comput 9(4):721-763
54. Rao RP, Ballard DH (1999) Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nat Neurosci 2(1): 79-87. Doi:10.1038/4580
55. Rodrigues S, Chizhov AV, Marten F, Terry JR (2010) Mappings between a macroscopic neural-mass model and a reduced conductance-based model. Biol Cybern 102(5): 361-371. Doi:10.1007/ s00422-010-0372-z
56. Roweis S, Ghahramani Z (2001) Learning nonlinear dynamical systems using the expectation-maximization algorithm. In Haykin S (ed) Kalman filtering and neural networks. Wiley, New York. Doi:10. 1002/0471221546
57. Schön TB, Wills A, Ninness B (2011) System identification of nonlinear state-space models. Automatica 47(1): 39-49. Doi:10.1016/j. Automatica.2010.10.013
58. Schöner G (1990) A dynamic theory of coordination of discrete movement. Biol Cybern 63(4): 257-270. Doi:10.1007/BF00203449
59. Sidiropoulou K, Pissadaki EK, Poirazi P (2006) Inside the brain of a neuron. EMBO Rep 7(9): 886-892. Doi:10.1038/sj.embor. 7400789
60. Sotero RC, Trujillo-Barreto NJ, Iturria-MedinaY,Carbonell F, Jimenez JC (2007) Realistically coupled neural mass models can generate eeg rhythms. Neural Comput 19(2): 478-512. Doi:10.1162/neco. 2007.19.2.478
61. Spruston N (2008) Pyramidal neurons: dendritic structure and synaptic integration. Nat Rev Neurosci 9(3): 206-221. Doi:10.1038/ nrn2286
62. Summerfield C, Egner T, Greene M, Koechlin E, Mangels J, Hirsch J (2006) Predictive codes for forthcoming perception in the frontal cortex. Science 314(5803): 1311-1314. Doi:10.1126/science. 1132028
63. Taylor GW, Hinton GE (2009) Factored conditional restricted boltzmann machines for modeling motion style. In: Proceedings of the 26th international conference on machine learning (ICML).
64. Ting-Ho Lo J (1994) Synthetic approach to optimal filtering. IEEE Trans Neural Netw 5(5): 803-811. Doi:10.1109/72.317731
65. Valpola H, Karhunen J (2002) An unsupervised ensemble learning method for nonlinear dynamic state-space models. Neural Comput 14(11): http://www.mitpressjournals.org/doi/ pdf/10.1162/089976602760408017 2647-2692. Doi:10.1162/ 089976602760408017
66. vanWassenhove V, Grant KW, Poeppel D (2005) Visual speech speeds up the neural processing of auditory speech. Proc Natl Acad Sci USA 102(4): 1181-1186. Doi:10.1073/pnas.0408949102
67. Verstraeten D, Schrauwen B, D'Haene M, Stroobandt D (2007) An experimental unification of reservoir computing methods. Neural Netw 20(3): 391-403. Doi:10.1016/j.neunet.2007.04.003
68. Wan EA, van der Merwe R (2001) The unscented Kalman filter. In Haykin S (ed) Kalman Filtering and Neural Networks.Wiley, New York. Doi:10.1002/ 0471221546
69. Wan EA, Nelson AT (2001) Dual extended Kalman filter methods. In Haykin S (ed) Kalman Filtering and Neural Networks.Wiley, New York. Doi:10.1002/ 0471221546
70. Williams RJ, Zipser D (1989) A learning algorithm for continually running fully recurrent neural networks. Neural Comput 1(2): http://www. mitpressjournals.org/doi/pdf/10.1162/neco. 1989.1.2.270 270-280. Doi:10.1162/neco.1989.1.2.270
71. Wilson R, Finkel L (2009)Aneural implementation of the Kalman filter. In: Bengio Y, Schuurmans D, Lafferty J,Williams CKI, Culotta A (eds) Advances in neural information processing systems, vol 22. MIT Press, Cambridge, pp 2062-2070