Receptive Field Inference with Localized Priors

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets. Author Summary: A central problem in systems neuroscience is to understand how sensory neurons convert environmental stimuli into spike trains. The receptive field (RF) provides a simple model for the first stage in this encoding process: it is a linear filter that describes how the neuron integrates the stimulus over time and space. A neuron's RF can be estimated using responses to white noise or naturalistic stimuli, but traditional estimators such as the spike-triggered average tend to be noisy and require large amounts of data to converge. Here, we introduce a novel estimator that can accurately determine RFs with far less data. The key insight is that RFs tend to be localized in spacetime and spatiotemporal frequency. We introduce a family of prior distributions that flexibly incorporate these tendencies, using an approach known as empirical Bayes. These methods will allow experimentalists to characterize RFs more accurately and more rapidly, freeing more time for other experiments. We argue that locality, which is a structured form of sparsity, may play an important role in a wide variety of biological inference problems.