Perform stability selection using the MATLAB function lassoglm. The function stabilityPaths estimates the probability of a variable to be chosen in a sparse model by repeatedly subsampling the data, calculating the reguralisation path for each subsample, and counting how frequently the variable was chosen at each point in the path.

The resulting stability paths can be used to select or rank variables based on, for example, the maximum selection probability they achieved.

For more on the method, see Meinshausen & Bühlmann, 2010, and Shah & Samworth, 2013.

Meinshausen, Nicolai, and Peter Bühlmann. "Stability selection." Journal of the Royal Statistical Society Series B: Statistical Methodology 72.4 (2010): 417-473.

Shah, Rajen D., and Richard J. Samworth. "Variable selection with error control: another look at stability selection." Journal of the Royal Statistical Society Series B: Statistical Methodology 75.1 (2013): 55-80.

a = [1:-0.1:0.1 zeros(1,40)];
Y = randn(100,1);
X = normrnd(Y*a,0.2);
Y = Y>0;
[selProb maxProb numSel Lambda] = stabilityPaths(X,Y);
plotStabilityPaths(selProb,1:10);