Embedding optimization reveals long-lasting history dependence in neural spiking activity
AbstractInformation processing can leave distinct footprints on the statistical history dependence in single neuron spiking. Statistical history dependence can be quantified using information theory, but its estimation from experimental recordings is only possible for a reduced representation of past spiking, a so called past embedding. Here, we present a novel embedding-optimization approach that optimizes temporal binning of past spiking to capture most history dependence, while a reliable estimation is ensured by regularization. The approach does not only quantify non-linear and higher-order dependencies, but also provides an estimate of the temporal depth that history dependence reaches into the past. We benchmarked the approach on simulated spike recordings of a leaky integrate-and-fire neuron with long lasting spike-frequency-adaptation, where it accurately estimated history dependence over hundreds of milliseconds. In a diversity of extra-cellular spike recordings, including highly parallel recordings using a Neuropixel probe, we found some neurons with surprisingly strong history dependence, which could last up to seconds. Both aspects, the magnitude and the temporal depth of history dependence, showed interesting differences between recorded systems, which points at systematic differences in information processing between these systems. We provide practical guidelines in this paper and a toolbox for Python3 at https://github.com/Priesemann-Group/hdestimator for readers interested in applying the method to their data.Author summaryEven with exciting advances in recording techniques of neural spiking activity, experiments only provide a comparably short glimpse into the activity of only a tiny subset of all neurons. How can we learn from these experiments about the organization of information processing in the brain? To that end, we exploit that different properties of information processing leave distinct footprints on the firing statistics of individual spiking neurons. In our work, we focus on a particular statistical footprint: How much does a single neuron’s spiking depend on its own preceding activity, which we call history dependence. By quantifying history dependence in neural spike recordings, one can, in turn, infer some of the properties of information processing. Because recording lengths are limited in practice, a direct estimation of history dependence from experiments is challenging. The embedding optimization approach that we present in this paper aims at extracting a maximum of history dependence within the limits set by a reliable estimation. The approach is highly adaptive and thereby enables a meaningful comparison of history dependence between neurons with vastly different spiking statistics, which we exemplify on a diversity of spike recordings. In conjunction with recent, highly parallel spike recording techniques, the approach could yield valuable insights on how hierarchical processing is organized in the brain.