Inference of the time-dependent maximum entropy model
This protocol is extracted from research article:
Predicting synchronous firing of large neural populations from sequential recordings
PLoS Comput Biol, Jan 28, 2021; DOI: 10.1371/journal.pcbi.1008501

The inference of the model (14) is done by log-likelihood maximization using an iterative algorithm with adaptive learning rate similar to that of [64]. Because the model belongs to the exponential family, the log-likelihood derivative with respect to any parameter θi takes the form: 〈Oidata − 〈Oimodel, where Oi is the sufficient statistics conjugated to the parameter θi. As a consequence, the model inference requires only the first two moments of ni(t) across repetitions and the value of the noise covariances (Methods section c). In our case we estimate the firsts from the marginal response of each neurons and we used the copula model to predict the second, without any other empirical information or statistics.

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