This is the neuron tuning modeling part of the paper "Multicentric tracking of multiple agents by anterior cingulate cortex during pursuit and evasion" by Seng Bum Michael Yoo, Jiaxin Cindy Tu and Benjamin Yost Hayden at Nature Communications (2021). This same model was also used in "The neural basis of predictive pursuit" by Seng Bum Michael Yoo, Jiaxin Cindy Tu, Steven T Piantadosi, Benjamin Yost Hayden at Nature Neuroscience (2020) and my sfn poster (2018) presentation "Neural representation of allocentric and egocentric positions in a dynamic foraging task".
The example data is excluded in ./Data, along with the code to generate it from raw spike trains and behavior in ./FormatData.
We got the inspiration from the coding properties of neurons in the mice medial entorhinal cortex and built our models using the pipeline proposed in this paper: "A Multiplexed, Heterogeneous, and Adaptive Code for Navigation in Medial Entorhinal Cortex" and the respective code. This idea was first proposed in Park et al. 2014 Nature Neuroscience with the repository for tutorial here
The details are summarized below and described in depth in the paper. The LN models estimated the spike rate (ri) of one neuron during time bin t as an exponential function of the sum of the relevant value of each variable at time t projected onto a corresponding set of parameters (wi). The Poisson log-likelihood of the observed spike train given the behavioral variables using the MATLAB function "fminunc". Model performance of each neuron is quantified by the log-likelihood of held-out data under the model.This cross-validation procedure was repeated ten times and overfitting was penalized. Forward variable selection was conducted to find the range of variables that best predicts the single-neuron's firing rate using cross-validation log-likelihood.