TY - JOUR

T1 - Ising model for neural data

T2 - Model quality and approximate methods for extracting functional connectivity

AU - Roudi, Yasser

AU - Tyrcha, Joanna

AU - Hertz, John

N1 - Paper id:: DOI: 10.1103/PhysRevE.79.051915

PY - 2009

Y1 - 2009

N2 - (dansk abstrakt findes ikke)We study pairwise Ising models for describing the statistics ofmulti-neuron spike trains, using data from a simulated corticalnetwork. We explore efficient ways of finding the optimal couplingsin these models and examine their statistical properties. To dothis, we extract the optimal couplings for subsets of size up to$200$ neurons, essentially exactly, using Boltzmann learning. Wethen study the quality of several approximate methods for findingthe couplings by comparing their results with those found fromBoltzmann learning. Two of these methods -- inversion of the Thouless-Anderson-Palmerequations and an approximation proposed by Sessak and Monasson --are remarkably accurate. Using these approximations for largersubsets of neurons, we find that extracting couplings using datafrom a subset smaller than the full network tends systematically tooverestimate their magnitude.  This effect is describedqualitatively by infinite-range spin glass theory for the normal phase. We also show that a globally-correlatedinput to the neurons in the network lead to a small increase in theaverage coupling. However, the pair-to-pair variation of thecouplings is much larger than this and reflects intrinsic propertiesof the network. Finally, we study the quality of these models bycomparing their entropies with that of the data.  We find that theyperform well for small subsets of the neurons in the network, butthe fit quality starts to deteriorate as the subset size grows,signalling the need to include higher order correlations to describethe statistics of large networks.  Udgivelsesdato: 19 May

AB - (dansk abstrakt findes ikke)We study pairwise Ising models for describing the statistics ofmulti-neuron spike trains, using data from a simulated corticalnetwork. We explore efficient ways of finding the optimal couplingsin these models and examine their statistical properties. To dothis, we extract the optimal couplings for subsets of size up to$200$ neurons, essentially exactly, using Boltzmann learning. Wethen study the quality of several approximate methods for findingthe couplings by comparing their results with those found fromBoltzmann learning. Two of these methods -- inversion of the Thouless-Anderson-Palmerequations and an approximation proposed by Sessak and Monasson --are remarkably accurate. Using these approximations for largersubsets of neurons, we find that extracting couplings using datafrom a subset smaller than the full network tends systematically tooverestimate their magnitude.  This effect is describedqualitatively by infinite-range spin glass theory for the normal phase. We also show that a globally-correlatedinput to the neurons in the network lead to a small increase in theaverage coupling. However, the pair-to-pair variation of thecouplings is much larger than this and reflects intrinsic propertiesof the network. Finally, we study the quality of these models bycomparing their entropies with that of the data.  We find that theyperform well for small subsets of the neurons in the network, butthe fit quality starts to deteriorate as the subset size grows,signalling the need to include higher order correlations to describethe statistics of large networks.  Udgivelsesdato: 19 May

U2 - 10.1103/PhysRevE.79.051915

DO - 10.1103/PhysRevE.79.051915

M3 - Journal article

C2 - 19518488

VL - 79

SP - 051915

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5

ER -