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Inferring network connectivity using kinetic Ising models

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One approach that has been explored recently for analyzing functional connectivity involves parametrizing the spike pattern distribution by an Ising model with symmetric connectivity... However, the connections found using this procedure do not generally agree well with the true synaptic connectivity... Here we try, instead, a kinetic Ising network with asymmetric connections, updated either asynchronously or synchronously... For these models, it is possible to derive an iterative algorithm for the optimal connection strengths by formally maximizing the log-likelihood of the measured history... We have tested the iterative algorithm on data generated by randomly-connected, synchronously-updated Ising networks for a range of sizes, firing rates, noise levels and concentration of nonzero connections... In all cases, the rms reconstruction error falls off approximately like a -1/3 power of the length of the run used to generate the correlations statistics... The approximate formula gives qualitatively good results, enabling us to identify the strongest connection reliably, though the magnitudes obtained tend to be off by a scaling factor that depends on noise level and mean firing rate... These conclusions hold for the asynchronous model as well... We applied the approximate formula to data from a realistic cortical network model... Fig. 1 shows histograms of the connection strengths found in 30 randomly chosen sets of n = 50 inhibitory neurons, separated according to whether there actually was a synapse connecting the pair in question (blue) or not (green)... If the cn(n-1) pairs with the most negative inferred couplings are identified as connected, with c the connection probability in the population, we find average false-positive and false-negative rates of 5.6% and 7.2%, respectively... To illustrate the point visually, Fig. 2 shows the actual connections in the original simulated network and Fig. 3 shows those identified by this procedure for a set of 25 neurons.

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Inferred connections.
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Figure 3: Inferred connections.

Mentions: We applied the approximate formula to data from a realistic cortical network model [3]. Fig. 1 shows histograms of the connection strengths found in 30 randomly chosen sets of n = 50 inhibitory neurons, separated according to whether there actually was a synapse connecting the pair in question (blue) or not (green). If the cn(n-1) pairs with the most negative inferred couplings are identified as connected, with c the connection probability in the population, we find average false-positive and false-negative rates of 5.6% and 7.2%, respectively. To illustrate the point visually, Fig. 2 shows the actual connections in the original simulated network and Fig. 3 shows those identified by this procedure for a set of 25 neurons.


Inferring network connectivity using kinetic Ising models
Inferred connections.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3090939&req=5

Figure 3: Inferred connections.
Mentions: We applied the approximate formula to data from a realistic cortical network model [3]. Fig. 1 shows histograms of the connection strengths found in 30 randomly chosen sets of n = 50 inhibitory neurons, separated according to whether there actually was a synapse connecting the pair in question (blue) or not (green). If the cn(n-1) pairs with the most negative inferred couplings are identified as connected, with c the connection probability in the population, we find average false-positive and false-negative rates of 5.6% and 7.2%, respectively. To illustrate the point visually, Fig. 2 shows the actual connections in the original simulated network and Fig. 3 shows those identified by this procedure for a set of 25 neurons.

View Article: PubMed Central - HTML

AUTOMATICALLY GENERATED EXCERPT
Please rate it.

One approach that has been explored recently for analyzing functional connectivity involves parametrizing the spike pattern distribution by an Ising model with symmetric connectivity... However, the connections found using this procedure do not generally agree well with the true synaptic connectivity... Here we try, instead, a kinetic Ising network with asymmetric connections, updated either asynchronously or synchronously... For these models, it is possible to derive an iterative algorithm for the optimal connection strengths by formally maximizing the log-likelihood of the measured history... We have tested the iterative algorithm on data generated by randomly-connected, synchronously-updated Ising networks for a range of sizes, firing rates, noise levels and concentration of nonzero connections... In all cases, the rms reconstruction error falls off approximately like a -1/3 power of the length of the run used to generate the correlations statistics... The approximate formula gives qualitatively good results, enabling us to identify the strongest connection reliably, though the magnitudes obtained tend to be off by a scaling factor that depends on noise level and mean firing rate... These conclusions hold for the asynchronous model as well... We applied the approximate formula to data from a realistic cortical network model... Fig. 1 shows histograms of the connection strengths found in 30 randomly chosen sets of n = 50 inhibitory neurons, separated according to whether there actually was a synapse connecting the pair in question (blue) or not (green)... If the cn(n-1) pairs with the most negative inferred couplings are identified as connected, with c the connection probability in the population, we find average false-positive and false-negative rates of 5.6% and 7.2%, respectively... To illustrate the point visually, Fig. 2 shows the actual connections in the original simulated network and Fig. 3 shows those identified by this procedure for a set of 25 neurons.

No MeSH data available.