To capture this, we also learn a pair of thresholds τ 0 and τ 1 (by grid search on the training set) such that Learning the Labeling Model with σ Once we have the σ function applied to all aligned training data, we mark in the output sequences in the training data the spurious insertions that should not be in the input sequence with a special symbol D (for deletion).
the learning algorithm is now also required to learn where to delete these extra insertions that σ elicits.