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
SN - 1539-3755
VL - 79
SP - 051915
JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
IS - 5
ER -