Dynamic Alignment Models for Neural Coding
Figure 5
The MPH applied to white noise stimuli and switched responses.
(A) A white noise stimulus (top), the randomly switched states of a switching LNP model (middle, black curve), and the observed spike train (middle, black rasters) and firing rate (bottom, gray line). The MPH-predicted firing rate (bottom, black line) to a test stimulus is closer to the observed firing rate than is the STA prediction (blue line) or the STC prediction (dotted green line). (B) The MPH RF estimates (MPH, 2nd column) capture well the underlying true RFs (True RFs, 1st column) for all relative angles, unlike the STA RF estimates (STA, 3rd column) or the STC RF estimates (STC, 4th column). (C) We evaluated the models by computing CCs between predicted and observed firing rates on a validation set and for different pairs of LNP filters that were generated by rotating one of the RFs. The cascaded MPH (black line) performs slightly better than the non-cascaded MPH (gray line). Both MPHs perform better than STC (green line) and STA (blue line). (D) Quality of RF reconstruction, shown is the cosine angle between true and model RFs (compare main text). The MPH reconstructed the true RFs more faithfully (black line) than did STA (blue line) and STC (green line). The occasional drops in MPH performance (larger error bars) are due to local optima that can be circumvented by starting the MPH-parameter optimization from different initial conditions (the orange line is from the best model – in terms of likelihood on the training set – out of 3 initial conditions). Both, panels (C) and (D) show average results from 10 simulations (with standard errors indicated).