Kernel methods on spike train space for neuroscience: a tutorial

TL;DR

This tutorial explores how kernel methods can revolutionize spike train analysis in neuroscience by providing mathematical insights, practical examples, and discussing current challenges and future directions.

Contribution

It offers a comprehensive overview of positive definite kernels for spike trains, illustrating their potential and encouraging further research in the field.

Findings

Kernel methods enable new ways to analyze spike trains.

Practical examples demonstrate the effectiveness of kernel approaches.

Discussion of future challenges guides ongoing research.

Abstract

Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space. However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and signal processing experts. This tutorial illustrates why kernel methods can, and have already started to, change the way spike trains are analyzed and processed. The presentation incorporates simple mathematical analogies and convincing practical examples in an attempt to show the yet unexplored potential of positive definite functions to quantify point processes. It also provides a detailed overview of the current state of the art and future challenges with the hope of engaging the readers in active participation.