Supplementary Material for Labeling Gaps Between Words: Recognizing Overlapping Mentions with Mention Separators

This is the supplementary material for “Labeling Gaps Between Words: Recognizing Overlapping Mentions with Mention Separators” (Muis and Lu, 2017). This material explains in more depth the issue of spurious structures and also the experiments settings. 1 Details on Spurious Structures About mention hypergraph, we remarked in Section 3.1 that the normalization term calculated by the forward-backward algorithm includes spurious structures, which are structures that are not part of the true normalization term. This section shows in more details how this is the case using some examples. Consider the simplified mention hypergraph as shown in Figure 1 (top left) consisting of three words and where the possible edges have been restricted to what are shown in the figure. Also, let A, B, C, D, E, F respectively denote the edges T1 → (I1), I0 → (I1), I1 → (I2), I1 → (X), I1 → (I2,X), and I2 → (X) as shown in Figure 1 (left). Further assume that features are only defined on these labeled edges. Recall that in graphical models, any prediction by the model forms a (hyper-)path from the root node (here A0) to the leaf node (X), which means each node other than the leaf node has exactly one outgoing (hyper-)edge. Now, notice that there are only three possible paths here, one for each of the three (hyper-)edges coming out from the node I1 associated with the word “Apache”. See the top right, bottom left, and bottom right of Figure 1 for the visualization. Now recall that in mention hypergraph, each node is assigned a certain set of mention combinations which the node represents, as defined A0 A1