Comparing gradient boosted trees (XGB) with classical methods.

<p><b>A</b> Using the angle as the input feature (red), the Machine Learning algorithm is trained to minimize the error in predicting the firing rate of one HD neuron over time (yellow, spiking activity below) during the training phase. For each angular position in the test set, the algorithm predicts a firing rate (blue curve). The score of the algorithm measures how close the prediction is to the real value. <b>B</b> Using an 8-fold cross-validation, XGB was compared to model-based tuning curves (MB) with 60 bins, a linear regression model and a linear regression model with preprocessing of the features i.e the first six harmonics of the angular direction of the head were used instead of the raw angle. Recordings from ADn and PoSub were used to benchmark each model. <b>C</b> To find the optimal number of trees and the optimal depth of XGB, a grid-search was performed for each neuron using the Bayesian Information Criterion (BIC). <b>D</b> Distribution of the set of optimal parameters for all neurons. Overall, a maximum number of 100 trees with a depth of 5 was used to learn and predict spiking activity as in <b>A</b>.