Dynamic Alignment Models for Neural Coding

doi:10.1371/journal.pcbi.1003508

Dynamic Alignment Models for Neural Coding

Figure 4

The MPH applied to natural stimuli and jittered spike responses.

(A) An example log-spectrogram of zebra finch song (top, high sound amplitudes in red and low amplitudes in blue), spiking responses generated by an LNP-type model (middle, LNP output), their jittered versions (below), and the corresponding jittered firing rate (bottom, gray line). The MPH-predicted response (MPH, full line) of the jittered firing rate is more accurate than the reverse correlation prediction (RC, dashed line). (B) Applied spike jitter is i.i.d. among spikes and log-normally distributed with zero mean. Two different jitter distributions are shown, they differ in terms of variance and symmetric/asymmetric shape (gray curves left, and right). The MPH-estimated jitter kernels are shown in black. The MPH misses some jittered spikes (right), as revealed by the excessive peak at zero time lag. Results for the jitter kernel with variance are shown in panels A, C, and D. (C) RFs estimated through reverse correlation for unjittered data (true RF), jittered data (RC) as well as the MPH receptive field estimate (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), as well the MPH reconstruction (right, obtained via dynamic alignment using the generalized Viterbi algorithm). (E) Correlation coefficients (CCs) between predicted and true firing rates on the validation set for different jitter variances. Also shown is an upper bound for the CC computed by sampling and cross-correlating jittered responses. For small overall jitter, performances of reverse correlation and MPH are comparable. As the overall jitter magnitude increases, reverse correlation performance drops much more severely than does MPH performance. (F) RC performance drops even stronger when assessed in terms of similarity between the estimated and the true RFs.

doi: https://doi.org/10.1371/journal.pcbi.1003508.g004