AdaptiveLASSO.m is a Matlab package able to distinguish meaningful level shifts from typical signal fluctuations which, in a fiber monitoring context, is associated with the problem of identifying small losses within a noisy optical time-domain reflectometer (OTDR) profile. This is the original supplemental material for the paper "Adaptive Filter for Automatic Identification of Mulitple Fiber Faults in a Noisy OTDR Profile".