TY - JOUR
T1 - Directed Information between Connected Leaky Integrate-and-Fire Neurons
AU - Soltani, Nima
AU - Goldsmith, Andrea J.
N1 - Funding Information:
Manuscript received October 4, 2015; revised November 10, 2016; accepted March 20, 2017. Date of publication May 18, 2017; date of current version August 16, 2017. This work was supported by the NSF Center for Science of Information under Grant NSF-CCF-0939370. This paper was presented at the 2014 ISIT conference. (Corresponding author: Nima Soltani.) The authors are with the Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA (e-mail: nsoltani@alumni.stanford.edu; andrea@wsl.stanford.edu).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2017/9
Y1 - 2017/9
N2 - The connectivity structure between neurons is useful for determining how groups of neurons perform tasks. Directed information is a measure that can be used to infer connectivity between neurons using their recorded time series. In this paper, we develop a method of calculating the directed information rate from one neuron to another neuron it is connected to, given a particular neuronal topology. We assume a leaky integrate-and-fire (LIF) neuron model with independent and identically distributed random spike train inputs, which governs how the membrane potential of the output neuron evolves. We use this neuron model to find the dynamics of the resulting output spike train from its membrane potential dynamics, both for when the past of the input neuron is observed and when it is not. We show that an action potential in the LIF model causes a conditional independence of the activity before and after it, and we capture this conditional independence via a Markov model. We use these spike train dynamics to then calculate the directed information between the spike train of the input neuron to the spike train generated by the LIF model. In addition, we show how changing the refractory period of the LIF model affects the directed information, and also how the spike train dynamics are affected by memory constraints, which are commonly imposed in estimators of directed information.
AB - The connectivity structure between neurons is useful for determining how groups of neurons perform tasks. Directed information is a measure that can be used to infer connectivity between neurons using their recorded time series. In this paper, we develop a method of calculating the directed information rate from one neuron to another neuron it is connected to, given a particular neuronal topology. We assume a leaky integrate-and-fire (LIF) neuron model with independent and identically distributed random spike train inputs, which governs how the membrane potential of the output neuron evolves. We use this neuron model to find the dynamics of the resulting output spike train from its membrane potential dynamics, both for when the past of the input neuron is observed and when it is not. We show that an action potential in the LIF model causes a conditional independence of the activity before and after it, and we capture this conditional independence via a Markov model. We use these spike train dynamics to then calculate the directed information between the spike train of the input neuron to the spike train generated by the LIF model. In addition, we show how changing the refractory period of the LIF model affects the directed information, and also how the spike train dynamics are affected by memory constraints, which are commonly imposed in estimators of directed information.
KW - Analytical models
KW - Markov processes
KW - biological neural networks
KW - biological system modeling
KW - stochastic processes
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U2 - 10.1109/TIT.2017.2700464
DO - 10.1109/TIT.2017.2700464
M3 - Article
AN - SCOPUS:85029489184
SN - 0018-9448
VL - 63
SP - 5954
EP - 5967
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 9
M1 - 7931602
ER -