# What is the difference between spike-triggered averaging and reverse correlation?

I'm interested in the difference between spike-triggered averaging and reverse correlation.

In some papers (i.e., Schwartz, Odelia, et al) I see the term 'Spike Triggered Averaging'. In others, (ie Ringach et al 2004) I see the term 'Reverse Correlation'. According to wikipedia, they are the same:

Spike-triggered averaging is also commonly referred to as “reverse correlation″ or “white-noise analysis”

I was wondering though: Is there a subtle difference between spike-triggered averaging and reverse correlation?

### References

• Schwartz, Odelia, et al (2006). "Spike-triggered neural characterization." Journal of Vision 6.4
• Ringach, Dario, and Robert Shapley. "Reverse correlation in neurophysiology." Cognitive Science 28.2 (2004): 147-166

## 2 Answers

There's the naïve version of spike triggered averaging, and the sophisticated version. Both of them are consistent estimators for a linear-nonlinear system under certain conditions (Paninski, 2003). If your stimulus is $x_i$ and your spike count in a small bin is $y_i$, naïve version is $$\mathrm{STA} = \frac{1}{N} \sum_i x_i y_i$$ The sophisticated version is equivalent to linear regression where a (pseudo-)inverse of the stimulus covariance is premultiplied to the naïve version. The naïve version converges slower in general.

In short, both of them are trying to estimate the same thing and will converge to the same thing, and sometimes called the same thing. However, it could refer to different things too, so read the methods section of papers before figuring out which one is which.

• Paninski, L. (2003). Convergence properties of three spike-triggered analysis techniques. Network: Computation in Neural Systems, 14, 437–464.
• Dayan, P. and Abbott, L. F. (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Massachusetts Institute of Technology Press. http://amzn.to/1nGUdII

Spike trigger is a specific type or you could say a sub-set of reverse correlations, covariance and probabilities. Other various examples include differential reverse correlation, Poisson spike trains, nonlinear reverse correlation and motion reverse correlation.