In the Gaussian process code [1] of Carl Edward Rasmussen, you find two approxi-
mation methods, namely Laplace's Approximation (approxLA.m) and Expectation 
Propagation (approxEP.m). Examples and documentation is provided there.

In the paper, Approximations for binary Gaussian process classification, we 
compare and analyze several other non-sparse methods:
- Direct Kullback-Leibler divergence minimization (approxKL.m)
- Individual variational site bounding (approxVB.m)
- Factorial Variational approximation (approxFV.m)
- Label Regression (approxLR.m)
The ADATAP approach (approxTAP.m) yields the same solution as EP but at higher
computational cost; the implementation is numerically not favorable and only 
included for reasons of completeness. A simpler variant (approxTAPnaive.m) is 
also provided.
Recently, we became aware of a fast single loop algorithm (approxEC.m) finding
the same solution as EP but faster.

Three sparse/online methods are included. This code is not discussed in the 
paper but yields similar performance. It is primarily included to show that the
interface of the GPML code treats sparse methods as well. The code is tested
but far less reliable than the working horses (approxLA.m, approxEP.m).
- Informative Vector Machine (approxIVM.m)
- Sparse Online Gaussian Processes (approxSO.m)
- Online-EP (approxOLEP,m)

Hannes Nickisch, February 2, 2009

[1] http://www.gaussianprocess.org/gpml/code/matlab/doc/classification.html
[2] http://jmlr.csail.mit.edu/papers/volume9/nickisch08a/nickisch08a.pdf
