Methods for word graphs.

The evaluation experiments were performed using just the semantic DOP-model as it was described above.

For every word graph the most probable intersection derivation was determined. The leaf-nodes of this derivation constitute the best path through the word graph. The probability of a derivation is calculated on the basis of both the probabilities of the subtrees extracted from the OVIS tree-bank, and the acoustic likelihoods of the words in the word graph.

We created several instances of the semantic DOP-parser, with differing constraints on the form of possible subtrees. Four parameters can be distinguished, whose values determine the constraints on subtrees. Below the parameters are given, with the letters we commonly use to refer to each parameter.

d The maximal depth of subtrees.

l The maximal number of lexical items in a subtree.

L The maximal number of consecutive lexical items in a subtree.

n The maximal number of substitution sites in a subtree.

Obviously, the number of possible combinations is huge. We chose to use the parameter settings for which previous experiments yielded the best results.

The results presented in this document are all obtained using the following settings: l=9, L=3, n=2. For the maximum depth we used d=2 and d=4. No constraints were applied to subtrees of depth 1.

If a word graph contains more than 350 transitions, the maximum depth of subtrees is automatically limited to two, to avoid excessive memory requirements. About 3% of word graphs in the testing material do contain more than 350 transitions.