Depth-Based Statistical Inferences in the Spike Train Space

Abstract: Metric-based summary statistics such as mean and covariance have been introduced in neural spike train space. They can properly describe template and variability in spike train data, but are often sensitive to outliers and expensive to compute. Recent studies also examine outlier detection and classification methods on point processes. These tools provide reasonable and efficient result, whereas the accuracy remains at a low level in certain cases. In this study, we propose to adopt a well-established notion of statistical depth to the spike train space. This framework can naturally define the median in a set of spike trains, which provides a robust description of the 'center' or 'template' of the observations. It also provides a principled method to identify 'outliers' in the data and classify data from different categories. We systematically compare the median with the state-of-the-art 'mean spike trains' in terms of robustness and efficiency. The performance of our novel outlier detection and classification tools will be compared with previous methods. The result shows the median has superior description for 'template' than the mean. Moreover, the proposed outlier detection and classification perform more accurately than previous methods. The advantages and superiority are well illustrated with simulations and real data.