Measuring Fisher Information Accurately in Correlated Neural Populations

Neural responses are known to be variable. In order to understand how this neural variability constrains behavioral performance, we need to be able to measure the reliability with which a sensory stimulus is encoded in a given population. However, such measures are challenging for two reasons: First, they must take into account noise correlations which can have a large influence on reliability. Second, they need to be as efficient as possible, since the number of trials available in a set of neural recording is usually limited by experimental constraints. Traditionally, cross-validated decoding has been used as a reliability measure, but it only provides a lower bound on reliability and underestimates reliability substantially in small datasets. We show that, if the number of trials per condition is larger than the number of neurons, there is an alternative, direct estimate of reliability which consistently leads to smaller errors and is much faster to compute. The superior performance of the direct estimator is evident both for simulated data and for neuronal population recordings from macaque primary visual cortex. Furthermore we propose generalizations of the direct estimator which measure changes in stimulus encoding across conditions and the impact of correlations on encoding and decoding, typically denoted by Ishuffle and Idiag respectively.Author Summary: A central problem in systems neuroscience is to understand how the activity of neural populations is mapped onto behavior. Neural responses in sensory areas vary substantially upon repeated presentations of the same stimulus, and this limits the reliability with which two similar stimuli can be discriminated by any read-out of neural activity. Fisher information provides a quantitative measure of the reliability of the sensory representation, and it has been used extensively to analyze neural data. Traditional methods for quantifying Fisher information rely on decoding neural activity; however, optimizing a decoder requires larger amounts of data than available in typical experiments, and as a result decoding-based estimators systematically underestimate information. Here we introduce a novel estimator that can accurately determine information with far less data, and that runs orders of magnitude faster. The estimator is based on analytical calculation, and corrects the bias that arises when estimating information directly from limited data. The analytical guarantee of an unbiased estimator and its computational simplicity will allow experimentalists to compare coding reliability across behavioral conditions and monitor it over time.