Mathematical Biosciences and Engineering (MBE)

Network inference with hidden units
Pages: 149 - 165, Issue 1, February 2014

doi:10.3934/mbe.2014.11.149      Abstract        References        Full text (630.3K)           Related Articles

Joanna Tyrcha - Department of Mathematics, Stockholm University, Kräftriket, S-106 91 Stockholm, Sweden (email)
John Hertz - Nordita, Stockholm University and KTH, Roslagstullsbacken 23, S-106 91 Stockholm, Sweden (email)

1 D. Ackley, G. E. Hinton and T. J. Sejnowski, A learning algorithm for Boltzmann machines, Cogn. Sci., 9 (1985), 147-169.
2 H. Akaike, A new look at the statistical model identification. System identification and time-series analysis, IEE Transactions on Automatic Control, AC-19 (1974), 716-723.       
3 D. Barber, "Bayesian Reasoning and Machine Learning," chapter 11, Cambridge Univ. Press, 2012.
4 A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm. With discussion, J. Roy. Stat. Soc. B, 39 (1977), 1-38.       
5 B. Dunn and Y. Roudi, Learning and inference in a nonequilibrium Ising model with hidden nodes, Phys. Rev. E, 87 (2013), 022127.
6 R. J. Glauber, Time-dependent statistics of the Ising model, J. Math. Phys., 4 (1963), 294-307.       
7 J. Hertz, Y. Roudi and J. Tyrcha, Ising models for inferring network structure from spike data, in "Principles of Neural Coding" (eds. S. Panzeri and R. R. Quiroga), CRC Press, (2013), 527-546.
8 M. Mézard, G. Parisi and M. Virasoro, "Spin Glass Theory and Beyond," chapter 2, World Scientific Lecture Notes in Physics, 9, World Scientific Publishing Co., Inc., Teaneck, NJ, 1987.       
9 B. A. Pearlmutter, Learning state space trajectories in recurrent neural networks, Neural Computation, 1 (1989), 263-269.
10 P. Peretto, Collective properties of neural networks: A statistical physics approach, Biol. Cybern., 50 (1984), 51-62.
11 F. J. Pineda, Generalization of back-propagation to recurrent neural networks, Phys. Rev. Lett., 59 (1987), 2229-2232.       
12 Y. Roudi and J. Hertz, Mean-field theory for nonequilibrium network reconstruction, Phys. Rev. Lett., 106 (2011), 048702.
13 Y. Roudi, J. Tyrcha and J. Hertz, The Ising model for neural data: Model quality and approximate methods for extracting functional connectivity, Phys. Rev. E, 79 (2009), 051915.
14 D. E. Rumelhart, G. E. Hinton and R. J. Williams, Learning Internal Representations by Error Propagation, in "Parallel Distributed Processing" (eds. D. E. Rumelhart and J. L. McClelland), Vol. 1, Chapter 8, MIT Press, 1986.
15 L. K. Saul, T. Jaakkola and M. I. Jordan, Mean field theory for sigmoid belief networks, J. Art. Intel. Res., 4 (1996), 61-76.
16 E. Schneidman, M. J. Berry, R. Segev and W. Bialek, Weak pairwise correlations imply strongly correlated network states in a neural population, Nature, 440 (2006), 1007-1012.
17 G. E. Schwarz, Estimating the dimension of a model, Annals of Statistics, 6 (1978), 461-464.       
18 R. Sundberg, Maximum likelihood theory for incomplete data from an exponential family, Scand. J. Statistics, 1 (1974), 49-58.       
19 D. Sherrington and S. Kirkpatrick, Solvable model of a spin-glass, Phys. Rev. Lett., 35 (1975), 1792-1796.
20 D. J. Thouless, P. W. Anderson and R. G. Palmer, Solution of "soluble model of a spin glass,'' Philos. Mag., 92 (1974), 272-279.
21 R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent networks, Neural Comp., 1 (1989), 270-280.

Go to top