 All learning methods referred to so far have been supervised learning methods—a corpus of correctly labeled texts was assumed to be available for inferring model parameters. But methods have been developed for unsupervised (or semi-supervised) learning as well. An important unsupervised method of discovering HMM models for sequence labeling is the forward-backward (or Baum-Welch) algorithm. A simple version of this algorithm in the case of POS tagging relies on a lexicon containing the possible tags for each word (which are easily obtained from a standard lexicon). Some initial, more or less arbitrarily chosen values of the HMM transition and emission probabilities are then iteratively refined based on a training corpus. A caricature of the iterative process would be this: We use the current guesses of the HMM parameters to tag the training corpus; then we re-estimate those parameters just as if the corpus were hand-tagged. We repeat these two steps till convergence. The actual method used is more subtle in the way it uses the current HMM parameters. (It is a special case of EM—Expectation Maximization.) Rather than re-estimating the parameters based on occurrence frequencies in the current “best” tag sequence, it uses the expected number of occurrences of particular pairs of successive states (labels), dividing this by the expected number of occurrences of the first member of the pair. These expected values are determined by the conditional probability distribution over tag sequences, given the training corpus and the current HMM parameters, and can be obtained using the forward and backward probabilities as described above (and thus, conditioned on the entire corpus). Revised emission probabilities for any X → w can be computed as the sum of probabilities of X-labels at all positions where word w occurs in the corpus, divided by the sum of probabilities of X-labels at all positions, again using (products of) forward and backward probabilities.