Developing a Nonstationary Computational Framework With Application to Modeling Dynamic Modulations in Neural Spiking Responses

Abstract

In addition to being quite powerful in encoding time-varying response modulations, this general framework also enables a readout of the neural code while dissociating the influence of other nonstimulus covariates. This framework will advance our ability to understand sensory processing in higher brain areas when modulated by several behavioral or cognitive variables.

Characterizing and dissociating multiple time-varying modulatory computations influencing neuronal activity

“…A summary of the models’ structures and key properties is presented in Fig 4. The N-model was described in a previous publication [48] and is presented here for the purpose of comparison. The N-, S-, and F-models are all variations on the well-known GLM structure, using different approaches to capture the nonstationarities existing in the perisaccadic responses.…”

“…To prove that the S- and F-models better predict the perisaccadic responses compared to alternative models, the quality of perisaccadic response prediction by the S- and F-models was compared with the N-model -which is the state-of-the-art model in the perisaccadic response modeling as detailed in [48]- in terms of the log-likelihood per spike. For each model, the log-likelihood of the perisaccadic spikes was scatter plotted vs. the log-likelihood of the fixation spikes for the population of 41 MT neurons (Fig 5A).…”

“…Although these methods have been successful in modeling dynamic neural data and especially for neural decoding applications, similar to adaptive filters, they require a large amount of data to work, which makes them insufficient for the resolution or precision required for modeling the perisaccadic responses. To address the need for a quantitative means to study nonstationary responses across a saccade, we recently developed an extension of the widely-used generalized linear models (GLMs) [42–47], termed the nonstationary generalized linear model (NSGLM, referred to as the N-model in this article) to describe response dynamics in visual neurons across a saccade [48]. The multiplicative spatiotemporal gain kernels introduced in the N-model recovered the rapid eye displacement signal and the resulting nonstationarity in responses solely based on the statistical relationship between the stimulus and response across a saccade.…”

A Sensory Memory to Preserve Visual Representations Across Eye Movements

“…The sigmoidal nonlinearity in the S-model’s CIF (Eq. 5) makes the LL function not convex, meaning it may not give a unique optimal solution (more details in (Akbarian et al, 2017; Niknam et al, 2019)). Also, considering the number of data points (spiking events) relative to the number of model parameters to be estimated, this optimization may be subject to the overfitting problem.…”

“…Figure S4E shows the model’s performance in predicting the neural response in the perisaccadic period (from 0 to 150 ms after the saccade onset) versus that measured during fixation (−300 to −150 ms relative to saccade onset) by comparing the normalized log-likelihood of the model prediction in these time periods. The normalized LL, calculated as the LL of the spike trains using the predicted firing rate under the model minus that under a null model and normalized by spike counts, as reported in (Akbarian et al, 2017; Niknam et al, 2019), indicates the amount of information being conveyed by individual spikes and evaluates how closely the model describes the timing of recorded spikes. To calculate the normalized LL, the null model is assumed to be a model where the instantaneous firing rate of the neuron is set to its average firing rate.…”