Abstract
Current approaches to the problem of inferring network connectivity from spike data [1,2] make a stationarity assumption, which is often not valid. Here we describe a method for inferring both the connectivity of a network in the presence of nonstationarity state and the timedependent external drive that causes it. Consider an experiment in which the network is subjected repeatedly to a potentially unknown external input (such as would arise from sensory stimulation). We assume the spikes to be binned in time and represented by a binary array: Si(t,r) = ±1, according to whether neuron i fires or not in time bin t of repetition r of the measurement. We fit these data to the simplest kind of binary stochastic model: At time step t of repetition r, each formal neuron receives a net input, Hi(t,r) = hi(t) + ∑jJijSj(t,r), and it takes the value +1 at the next step with a probability given by a logistic sigmoidal function 1/[1+exp(-2Hi(t,r))] of Hi(t,r). Maximizing the likelihood of the data leads to learning rules
Highlights
Current approaches to the problem of inferring network connectivity from spike data [1,2] make a stationarity assumption, which is often not valid
We assume the spikes to be binned in time and represented by a binary array: Si(t,r) = ±1, according to whether neuron i fires or not in time bin t of repetition r of the measurement
We fit these data to the simplest kind of binary stochastic model: At time step t of repetition r, each formal neuron receives a net input, Hi(t,r) = hi(t) + ∑jJijSj(t,r), and it takes the value +1 at the step with a probability given by a logistic sigmoidal function 1/[1+exp(-2Hi(t,r))] of Hi(t,r)
Summary
Current approaches to the problem of inferring network connectivity from spike data [1,2] make a stationarity assumption, which is often not valid. Consider an experiment in which the network is subjected repeatedly to a potentially unknown external input (such as would arise from sensory stimulation). We assume the spikes to be binned in time and represented by a binary array: Si(t,r) = ±1, according to whether neuron i fires or not in time bin t of repetition r of the measurement.
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