A Kernel-Based Calculation of Information on a Metric Space

Estimating Mutual Information for Spike Trains: A Bird Song Example

Zebra finches are a model animal used in the study of audition. They are adept at recognizing zebra finch songs, and the neural pathway involved in song recognition is well studied. Here, this example is used to illustrate the estimation of mutual information between stimuli and responses using a Kozachenko-Leonenko estimator. The challenge in calculating mutual information for spike trains is that there are no obvious coordinates for the data. The Kozachenko-Leonenko estimator does not require coordinates; it relies only on the distance between data points. In the case of bird songs, estimating the mutual information demonstrates that the information content of spiking does not diminish as the song progresses.

Calculating the Mutual Information between Two Spike Trains

It is difficult to estimate the mutual information between spike trains because established methods require more data than are usually available. Kozachenko-Leonenko estimators promise to solve this problem but include a smoothing parameter that must be set. We propose here that the smoothing parameter can be selected by maximizing the estimated unbiased mutual information. This is tested on fictive data and shown to work very well.

Calculating mutual information for spike trains and other data with distances but no coordinates

Many important data types, such as the spike trains recorded from neurons in typical electrophysiological experiments, have a natural notion of distance or similarity between data points, even though there is no obvious coordinate system. Here, a simple Kozachenko-Leonenko estimator is derived for calculating the mutual information between datasets of this type.