# Kernel methods on spike train space for neuroscience: a tutorial

arXiv: https://arxiv.org/abs/1302.5964 · HTML: https://mlsanity.com/paper/1302.5964/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2013.

## Built on by (most cited first, 4 of 4)

- [Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networks](https://mlsanity.com/paper/2305.16044/) (2023)
- [Temporal Conditioning Spiking Latent Variable Models of the Neural Response to Natural Visual Scenes](https://mlsanity.com/paper/2306.12045/) (2023)
- [Event-Driven Implementation of a Physical Reservoir Computing Framework for superficial EMG-based Gesture Recognition](https://mlsanity.com/paper/2503.13492/) (2025)
- [On the Information Processing of One-Dimensional Wasserstein Distances with Finite Samples](https://mlsanity.com/paper/2511.12881/) (2025)

## Abstract (arXiv)

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.