[Paper Review] A model of sensory neural responses in the presence of unknown modulatory inputs

Neil C. Rabinowitz, Robbe L. T. Goris+2 more|arXiv (Cornell University)|Jul 6, 2015

Neural dynamics and brain function15 references3 citations

TL;DR

This paper proposes a modulated Poisson Generalized Linear Model (MoP-GLM) that accounts for unknown, slowly varying modulatory inputs in sensory neural responses by modeling them as a smooth, latent multiplicative gain signal. By integrating out this latent modulator during inference, the model improves receptive field estimation and predictive performance on both simulated and real ferret auditory neural data, reducing bias and enhancing robustness to non-stationarities.

ABSTRACT

Neural responses are highly variable, and some portion of this variability arises from fluctuations in modulatory factors that alter their gain, such as adaptation, attention, arousal, expected or actual reward, emotion, and local metabolic resource availability. Regardless of their origin, fluctuations in these signals can confound or bias the inferences that one derives from spiking responses. Recent work demonstrates that for sensory neurons, these effects can be captured by a modulated Poisson model, whose rate is the product of a stimulus-driven response function and an unknown modulatory signal. Here, we extend this model, by incorporating explicit modulatory elements that are known (specifically, spike-history dependence, as in previous models), and by constraining the remaining latent modulatory signals to be smooth in time. We develop inference procedures for fitting the entire model, including hyperparameters, via evidence optimization, and apply these to simulated data, and to responses of ferret auditory midbrain and cortical neurons to complex sounds. We show that integrating out the latent modulators yields better (or more readily-interpretable) receptive field estimates than a standard Poisson model. Conversely, integrating out the stimulus dependence yields estimates of the slowly-varying latent modulators.

Motivation & Objective

• To address the challenge of neural response variability caused by unmeasured, fluctuating modulatory factors such as attention, arousal, or anesthesia.
• To develop a statistical model that explicitly accounts for these unknown modulatory influences in sensory neural data.
• To improve the accuracy of stimulus-response relationship estimation by integrating out latent modulators rather than averaging across trials.
• To enable joint inference of both stimulus-driven receptive fields and slowly varying modulatory dynamics from spike train data.

Proposed method

• The model uses a modulated Poisson process where the firing rate is the product of a stimulus-driven component and a latent, smooth modulatory signal.
• The latent modulator is modeled as a Gaussian process with a squared exponential covariance function to enforce temporal smoothness.
• The model combines a GLM framework with evidence optimization to infer both the spike-history kernel and hyperparameters of the modulator.
• Inference is performed via variational approximation to marginalize over the latent modulator, avoiding bias from unmodeled non-stationarities.
• The method is applied to simulated data and real extracellular recordings from ferret auditory midbrain and cortex neurons.
• Model comparison uses held-out test data likelihoods to assess predictive performance, with cross-validation to validate hyperparameter selection.

Experimental results

Research questions

• RQ1 Can a latent, smooth modulatory signal account for non-stationarities in neural spiking responses that are not captured by standard Poisson GLMs?
• RQ2 Does integrating out the latent modulator lead to more accurate and less biased estimates of stimulus-driven receptive fields compared to standard GLM fitting?
• RQ3 How does the inclusion of a latent modulator improve predictive performance on held-out neural data?
• RQ4 To what extent do learned modulator time constants reflect the true timescales of physiological non-stationarities?

Key findings

• On simulated data, the MoP-GLM successfully recovered the true spike-history kernel and latent modulator, while the standard P-GLM produced significantly biased estimates.
• The MoP-GLM outperformed the P-GLM in predictive likelihood on 339 real ferret auditory neuron recordings, with improvement correlating with estimated non-stationarity (r = 0.6).
• When the modulator time constants were set to values higher or lower than the learned optimum, predictive performance degraded, confirming the model’s sensitivity to correct hyperparameter estimation.
• The model estimated modulator hyperparameters that were optimal for prediction, as shown by local sensitivity analysis on held-out data.
• The latent modulator estimates revealed slow, non-stationary fluctuations consistent with known physiological influences such as changing anesthesia depth.
• The method enables joint inference of both stimulus-response parameters and contextual modulatory dynamics without requiring direct measurement of modulatory states.