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Dynamic Alignment Models for Neural Coding

Figure 3

The MXR-MPH applied to white noise stimuli and spike-time-jitter.

(A) A white noise stimulus (top) with spiking responses (black bars) generated by an LNP-type model neuron (LNP output, the LNP RF size is indicated by the black rectangle). The jittered versions (jittered) of the LNP spike trains with corresponding firing rate (thick gray line) are shown below. The MPH estimate of firing rate (black full line) is more accurate than the STA estimate (dashed line). (B) Applied spike jitter is i.i.d. among spikes and log-normally distributed with zero mean (3 different jitter distributions are shown; they differ in terms of variance and symmetric/asymmetric shape). Results for the jitter kernel with variance are shown in panels A, C and D. (C) RFs estimated through STA on unjittered spikes (true RF), STA on jittered spikes (STA), and MPH on jittered spikes (MPH). The STA RF is blurred whereas the MPH RF closely resembles the true RF. Dotted black lines indicate the midpoints of the RFs. (D) Projections of all stimuli (gray lines) and the spike triggered stimulus ensembles (black lines) onto the underlying (true) RF for the unjittered spikes (left), the jittered spikes (middle), and the MPH reconstruction (right, obtained via dynamic alignment using the generalized Viterbi algorithm). (E) Response prediction. To evaluate the models we computed correlation coefficients (CCs) between predicted and actual firing rates on the validation set and for different jitter variances. For small spike jitter, performances of STA and MPH are comparable. As the jitter magnitude increases, STA performance drops much more severely than does MPH performance. Also shown is an upper bound for the CC computed by sampling and cross-correlating jittered responses. (F) MPH robustness to jitter is demonstrated also when assessed as similarity between the estimated RF and the true RF (similarity computed as normalized scalar product, i.e. cosine of angle between RFs). (G) We assessed the influence of different non-linearities (labeled A–E, ordered by steepness) on prediction quality for both the MPH as well as the cascaded MPH (cMPH). (H) Shallow non-linearities decrease the upper bound of prediction quality (black line) as well as the MPH (red lines) and STA (green line) performance for the unjittered (left) and the jittered case (right). The cascaded MPH (red line) shows slight improvements over the non-cascaded one (dotted red line).

doi: https://doi.org/10.1371/journal.pcbi.1003508.g003