Bandwidth Estimator

A simple package that implements the maximum-likelihood leave-one-out cross-validated bandwidth parameter estimation algorithm from Prerau & Eden 2011.

How do I install this?

Clone the repository or download and extract the zip.

It has explicit dependencies on mtools.

getSpikeTrain and getSpikeTimes requires CMBHOME, since they get the spike times from a Session object.

This package has been written to function as a protocol in the RatCatcher data pipeline.

What does this do?

Firing rate is a convenient mathematical construct useful in analyzing spike trains. It's believed that firing rate (measured in number of spikes per unit time) plays an important role in neural coding. Since actual spike-timing is somewhat stochastic, determining the firing rate is often non-trivial. A 2011 paper describes a method by which Bayesian likelihood analysis and leave-one-out cross-validation can be used to determine an optimal bandwidth parameter for use in turning point-process spike-train data into smoothed firing rate vs. time curves.

Setting up a BandwidthEstimator object requires a fully-fleshed out Session object from CMBHOME.

best = BandwidthEstimator(root)

• timestamps holds the vector of time-stamps for the bins of the spike train. This property is copied from root.ts.
• spikeTimes holds the spike times from the root object.
• spikeTrain contains the result of BandwidthEstimator.getSpikeTrain, using the spike times and time stamps. The spike train is a binned vector containing the number of spikes in each diff(best.timestamps)-sized bin.
• Fs contains the sample rate of the video recording.
• range contains the bandwidth parameters over which tests should be performed. These values should be odd integers only. The default is 3:2:(60 * Fs).
• kernel holds a function handle to the kernel smoothing function used by the rest of this package. It can be set by pointing directly to a function handle (e.g. best.kernel = @fcn), or by a character vector describing a static method of BandwidthEstimator (e.g. best.kernel = 'hanning'). Currently, only the hanning and alpha kernels are defined in this way.
• verbosity determines how much info text to print to the console.

The core functionality of this package is in the cvKernel and kconv functions, written by Michael Prerau (c) 2011. These functions have been heavily modified from their original forms to be methods of the BandwidthEstimator class.

Performing the Maximum Likelihood Estimate with Cross-Validation

cvKernel computes the maximum likelihood estimate, the bandwidth parameter associated with the MLE, the log likelihoods for the range of tested bandwidths, and the tested bandwidths themselves. It takes a spike train, the time step, and the bandwidth range to be tested, in time-steps. It defaults to 3:2:N where N is 3/2 the length of the spike train. Generally, this is much too long, and it is advisable to put limits on the range of tested bandwidths.

For example, to test bandwidths up to 60 seconds:

best.range = 3:2:(60 * best.Fs);
[estimate, kmax, loglikelihoods, bandwidths, CI] = best.cvKernel();

Performing a Single Convolution

kconv performs the kernel convolution. It is called within cvKernel. Outside of the algorithm, kconv functions, essentially, as a wrapper for MATLAB's conv function that post-processes the signal to remove edge effects. It can be called as a method of the BandwidthEstimator object with either a scalar or vector argument. If the argument is an odd scalar integer, the convolution will use a kernel constructed using the function handle stored in the kernel field of the object. If the argument is a vector, the kernel field is ignored and the vector is treated as the kernel vector for the convolution. In either case, it relies on the fields of the object for the signal, time step, etc.

For example, to test a bandwidth of 60 seconds:

estimate = best.kconv(60*best.Fs);
estimate = best.kconv(hanning(60*best.Fs));

Note that it is generally best practice for the argument to be in units of timesteps (and thus a positive, odd, integral, scalar), since there is little guarantee that 60*best.Fs will return an odd integer.

The test script will test the algorithm for you. It uses data from the Hasselmo Lab at Boston University. Naturally, you will need to change the paths if you want to use it directly, but it should serve as an adequate scaffolding for using this algorithm yourself.

The batchFunction is used for generating batch scripts with RatCatcher.