Probabilistic Neural Transfer Function Estimation with Bayesian System Identification

Neural population responses in sensory systems are driven by external physical stimuli. This stimulus-response relationship is typically characterized by receptive fields, which have been estimated by neural system identification approaches. Such models usually requires a large amount of training data, yet, the recording time for animal experiments is limited, giving rise to epistemic uncertainty for the learned neural transfer functions. While deep neural network models have demonstrated excellent power on neural prediction, they usually do not provide the uncertainty of the resulting neural representations and derived statistics, such as the stimuli driving neurons optimally, from in silico experiments. Here, we present a Bayesian system identification approach to predict neural responses to visual stimuli, and explore whether explicitly modeling network weight variability can be beneficial for identifying neural response properties. To this end, we use variational inference to estimate the posterior distribution of each model weight given the training data. Tests with different neural datasets demonstrate that this method can achieve higher or comparable performance on neural prediction, with a much higher data efficiency compared to Monte Carlo dropout methods and traditional models using point estimates of the model parameters. Furthermore, our approach enables to identify response properties with credible intervals and perform statistical test for the learned neural features, which avoid the idiosyncrasy of a single model. Finally, in silico experiments show that our model generates stimuli driving neuronal activity significantly better than traditional models, particularly in the limited-data regime.