Paper:
A Multigraph-based Model for Overlapping Entity Recognition
In this paper, we propose a new model that is capable of recognizing overlapping entities based on multigraphs, as opposed to simple graphs commonly used in graphical models for structured prediction. Through extensive experiments on standard datasets containing overlapping and non-overlapping entities, we demonstrate that our model outperforms previous models. We also present some analysis on the differences between our model and the previous models and discuss the possible implications of the differences. To the best of our knowledge, this is the first structured prediction model utilizing multigraphs to predict overlapping structures.
1 Introduction
Named entity recognition (NER), or in general the task of recognizing entities in a text, has been a research topic for many years (McCallum and Li, 2003; Nadeau and Sekine, 2007; Ratinov and Roth, 2009). However, as previously noted by Finkel and Manning (2009), many previous works ignored overlapping entities, although they are quite common. For example, the location entity China appears within the organization entity Bank of China. In practice, overlapping entities have been found in many existing datasets, including ACE (Doddington et al., 2004), GENIA (Kim et al., 2003), and in a clinical text dataset (Suominen et al., 2013). Figure 1 illustrates some examples of overlapping entities adapted from existing datasets.
Solving this task is non-trivial, as the typical way of modeling entity recognition as a sequence prediction problem (e.g., using linear-chain CRF
which utilizes simple graphs) has difficulties handling overlapping entities (Alex et al., 2007). Finkel and Manning (2009) proposed to use a treebased constituency parsing model to handle nested entities with a time complexity that is cubic in n for its inference procedure with n being the number of words in the sentence. This complexity was later improved by Lu and Roth (2015) with a hypergraph-based model, which shows a time complexity that is linear in n.
In this work, as opposed to using simple graphs or hypergraphs, we introduce a novel multigraphbased model to tackle the problem of overlapping entity extraction. We show it is possible to assign explicit semantics to different edges connecting the same pair of nodes when representing structures, leading to the novel multigraph representations that can be used to represent overlapping structures. We present the training and inference procedures over such a novel representation. To the best of our knowledge, this is the first structured prediction model utilizing multigraphs to predict overlapping structures.
In this paper we make the following major contributions: • We propose a novel multigraph-based model
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for predicting overlapping entities. • Empirically, we show that our model is able
to achieve higher F1-scores compared to previous models in multiple datasets. • Theoretically, we show that unlike a previ-
ous state-of-the-art model that we compare against, our model does not present the spurious structures issue in its inference procedure and is therefore nondeficient. On the other hand, it still maintains the same inference time complexity as the previous model.
We also believe our proposed multigraph-based structured prediction framework can be used to solve other problems involving overlapping structures, and we hope this work can inspire further research along such a direction. We will make our system and code available for research purposes.
2 Related Work
Named entity recognition (NER) has been a research focus for quite some time. It is normally regarded as chunking task similar to base NP chunking (Kudo and Matsumoto, 2001; Shen and Sarkar, 2005), and hence the entities are usually represented in a similar way, using BILOU (Beginning of an entity, In the middle of an entity, Last token of an entity, Outside of any entity, Unit-length entity) or the simpler BIO annotation scheme (Ratinov and Roth, 2009). Some previous works have focused on getting the best representation of the chunks (Sang and Veenstra, 1999; Loper, 2007) and Ratinov and Roth (2009) showed that between BIO and BILOU scheme, the latter is the better approach for recognizing non-overlapping entities. As a chunking task, it is commonly modeled using sequence labeling models, such as the linear-chain CRF (Lafferty et al., 2001), which has time complexityO(nT 2) with n being the number of words in the sentence and T the number of entity types.
On the task of recognizing entities that may overlap with one another, one of the earliest works that attempted to regard this task as a structured prediction task was McDonald et al. (2005). They represented entities as top-k predictions with positive score from a structured multilabel classification model. This model resembles structured SVM (Tsochantaridis et al., 2005) in terms of the objective function used. Since they set k = n, their model has a time complexity of O(n3T ).
Alex et al. (2007) proposed a cascading approach using multiple sequence labeling models,
each handling a subset of all the possible entity types, where the models which come later in the pipeline have access to the predictions of the models earlier in the pipeline. For each entity type, they used a standard linear-chain CRF model to predict entities, resulting in the time complexity of roughly O(nT ) depending on how the pipeline is designed. However, they noted that “it involves extensive amounts of experimentation to determine the best model combination”, due to the many possible ways to arrange the order of the pipeline. Their model only handles overlapping entities of different types.
Finkel and Manning (2009) later proposed a constituency parser to handle nested entities by converting each sentence as a tree, and each entity is represented as one of the subtrees. Their model has the standard time complexity for a binary parser: O(n3 |G|), where |G| is the size of the grammar that is proportional to T in the best case, and T 3 in the worst case. They showed that their model is able to outperform a semi-CRF baseline. By design, their model cannot handle crossing entities (overlapping entities which are not nested).
More recently, Lu and Roth (2015) proposed a hypergraph-based model called mention hypergraphs that is able to handle overlapping entities, yet it retains the linear time complexity O(nT ). The model was shown to achieve competitive results compared to previous models on standard datasets. As we will be making extensive comparisons against this pervious state-of-the-art model, we will briefly discuss this approach in the next section.
3 Mention Hypergraph
In the mention hypergraph model of Lu and Roth (2015), nodes and directed hyperedges1 are used together to encode entities and their combinations. The following 5 types of states are used at the position k of a sentence: • Ak denotes all entities starting at k or later • Ek denotes all entities starting at k • Tkt denotes all entities of type t starting at k • Ikt denotes all entities of type t covering k • X denotes the end of an entity (the leaf node) Different hyperedges connecting these nodes are used to represent how the semantics of a node is composed from those of its child nodes.
1For brevity, in this paper we may also use edge to refer to hyperedge in some discussions.
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T
O O O O
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the human TCF-1 proteinX [ -[ ]- ]
X
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CS EC
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T T T T
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X X X X
the [human [TCF-1]2 protein]1
Figure 2: (Top) Our multigraph model representing overlapping entities, with the entity separators shown in red. (Bottom) The corresponding mention hypergraph (A- and E-nodes not shown).
Specifically, each Ak is connected to Ak+1 and Ek through the hyperedge Ak → (Ak+1,Ek), denoting the fact that the set of entities that start at k or later is the union of the set of entities that start at k+1 or later and the set of entities that start at k. Each Ek is connected to Tk1,T k 2, . . . ,T k T through a hyperedge, denoting the fact that the entities that start at k must be one of the T types. Each Tkt is connected to Ikt through an edge (denoting there is an entity of type t that starts at the k-th token) and to X through another edge (denoting there are no entities of type t that start at the k-th token). Each Ikt is connected to I k+1 t (denoting there is an entity continuing to the next token), to X (denoting there is an entity ending here), or to both (with a single hyperedge, denoting the two cases above occur at the same time, a case of overlapping entities).
In this mention hypergraph, each possible entity is represented as a path from a T-node to the X-node through a sequence of I-nodes (each denoting the words which are part of the entity), and the set of all entities present in a sentence forms a sub-hypergraph of the overall hypergraph.
The bottom part of Figure 2 shows how the mention hypergraph represents the two entities in the phrase “the human TCF-1 protein”, which are “TCF-1” and “human TCF-1 protein” 2.
4 Multigraph-based Model
We now describe our proposed multigraph-based model for recognizing overlapping entities. In our
2Note that the word “protein” does not form an entity, due to the missing edge between the corresponding T node and I node.
C CS EC ECS
model, we assign for each token two states for each entity type, representing whether the token is part of an entity of a certain type. Formally, we define the following three types of nodes for each token: • Tt denotes the set of entities of type t • Ikt denotes that the k-th token is part of an
entity of type t • Okt denotes that the k-th token is not part of
any entities of type t To represent the distinct roles a token can take, we consider the incoming edge and outgoing edge of that state. Unlike previous approaches, we assign explicit semantics to the edges in our multigraph-based model, which we call entity separators. We consider the 8 possible types of entity separators based on the combination of the following three cases: 1. An entity is starting at the next token (S) 2. An entity is ending at the current token (E) 3. An entity is continuing to the next token (C)
For each token, the possible combinations of cases are as follows: ECS, EC, CS, C, ES, E, S, and X, where Xmeans none of the three cases applies. For example, the separator EC means there is one entity ending at the current token and another entity (overlapping) continuing to the next token. See Figure 3 for an illustration of these separators.
Next we define the edges between the states according to the 8 possible entity separators between adjacent tokens. Each entity separator is mapped to an edge connecting one state in the current position to another state in the next position depending on whether the separator defines current and next words as part of an entity, so in total we have 8 edges between two positions in the model. Some entity separators may connect the same two states, for example, the ES and C separator both connect Ikt to I k+1 t since in both cases the current token and the next token are part of an entity. In those cases, we simply define multiple edges between the pair of states, hence the multigraph aspect of
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R
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E ES C CS EC ECS
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Figure 4: Example multigraph used in our model.
our model. The first I- and O-nodes in the sentence are connected to the T-node of the corresponding entity type, and the last I- and O-nodes are connected to the unique leaf node X. Finally, a designated root node R is added and is connected to all T-nodes by a single hyperedge to complete the multigraph structure. Figure 4 shows an example of our multigraph model considering 2 entity types and 4 input tokens. Note that the edges in our multigraph representations are directed, with nodes on the left serving as parents to the nodes on the right. Such directed edges will be helpful when performing inference, to be discussed in the next section.
The top part of Figure 2 shows how we can model the two entities “human TCF-1 protein” and “TCF-1” in the phrase “the human TCF-1 protein”. Note how each edge maps to a distinct entity separator visualized in the text. Note how the roles of T-I edge and I-I edge in mention hypergraph are combined in our model using the single edge connecting the two I nodes for the token “human” and “TCF-1” to represent the entity separator CS.
4.1 Training, Inference and Decoding
We follow the log-linear approach to define our model, using the following regularized loglikelihood in training dataD as our objective function:
LD(w)= ∑
(x,y)∈D [ ∑ e∈y w · f(e)− logZw(x) ] −λ||w||2
(1)
where (x,y) is a training instance consisting of the sentence x and the correct output y, w is the weight vector, f(e) is the feature vector defined over the edge e, Zw(x) is the normalization term, and λ is the l2-regularization parameter. The objective function is then optimized until convergence using L-BFGS (Liu and Nocedal, 1989).
We note the mention hypergraph model also defines the objective in a similar manner. For both models, the inference is done based on a generalized inside-outside algorithm. Both models involve directed structures, on top of which the inference algorithm first calculates the inside score for each node from the leaf node to root, and then the outside score from the root to the leaf node, in very much the same way as how inference is done in a classic graphical model. Specifically, for our multigraph-based model, the inside scores are calculated using a bottom-up (right-to-left) dynamic programming procedure, where we calculate the inside score at each node by summing up the scores associated with each path connecting the current node to one of its child nodes. Each such path score is in turn defined as the product of the inside score stored in that child node and the score defined over the edge connecting them. The computation of the outside scores can be done in an analogous manner from left to right. It can be verified that the time complexity of such an inference procedure for our model is O(nT ), which is the same as the mention hypergraph model.
During decoding, we perform MPE inference using a max-product procedure that is analogous to how the Viterbi decoding algorithm is used in conventional tree-structured graphical models to find out from the overall multigraph the highestscoring subgraph, from which we extract entities3
5 Model Analysis
In this section we make two analytical comparisons between our model and the previous models.
5.1 State-based vs Edge-based Paradigm
Based on how previous works model the role of each token in defining the predicted entity spans, we can classify the previous works into two paradigms, namely state-based paradigm and edge-based paradigm, which we detail below.
State-based Paradigm In conventional graph-based models for structured prediction such as linear-chain conditional random fields (Lafferty et al., 2001) and tree-based models (Finkel and Manning, 2009), typically nodes
3We note that both models involve interpretation of the output structures when recovering the entities. We implemented the same interpretation process as that was done in the mention hypergraph model, and we resolved ambiguous structures by considering them as nested entities instead of crossing entities.
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B B B B
I I I I
O O O O
R X
the [human TCF-1 protein]1
Figure 5: A linear-chain CRF model representing an entity in BIO scheme.
and edges are used together to encode structured output information. A linear-chain CRF model is shown in Figure 5 to model the protein entity “human TCF-1 protein” using the BIO scheme. In general, given an input sentence, a possible output can be represented using a linear-chain structure that involves states (nodes) and their connections (edges). One could observe that, in this case, given the state at each position in the structure, we already have enough information to interpret the output, without relying on the edge information. Similarly, this is also true for tree-based models. This leads to the following definition of what we call the state-based paradigm – the approach where the set of states alone can be used to interpret the predicted entities.
We observe that the majority of previous works fall into this paradigm (McDonald et al., 2005; Alex et al., 2007; Finkel and Manning, 2009; Tang et al., 2013).
Edge-based Paradigm Modeling the roles each token can take as states is, however, not the only possible paradigm. In the mention hypergraph model by Lu and Roth (2015), they used only a small number of possible states for each token. Their approach does not model the roles that each token can take directly using the states only. In fact, in addition to states, they used edges (or hyperedges, and their combinations) to capture the complex combination of roles each token can take. This leads to an alternative paradigm called edge-based paradigm: the approach where the set of states together with the edges are used to define the predicted entities.
To see the importance of edges in the edgebased paradigm, we show a simple illustrative example based on the hypergraph model of Lu and Roth (2015) with two words in Figure 6. The left graph and the right graph have exactly the same states. However, due to different edges (or hyperedges), these two graphs correspond to different entity combinations. Specifically, the left graph captures the set of non-overlapping entities {w1,
w2}, whereas the right graph captures the the following three entities: {w1, w2, w1 w2} with the third entity being overlapping with the first two.
It is easy to see that our multigraph-based model falls into this paradigm. Since there are multiple edges between the same pair of states, the combination of states alone do not define the roles of the tokens, and semantics are clearly assigned to the edges.
One might notice that there exists some equivalence between the two paradigms. For example, in our multigraph-based model, we can represent each edge (separator) as a separate state (such as a state named ES or CS) and assign such states to the gaps between two adjacent words using a linear-chain sequence labeling model, arriving at a “state-based” model. While this is feasible, we note that such an approach, however, will typically result in modeling unnecessary dependencies between the adjacent “states” (such as the dependencies between ES and CS, under the simple firstorder assumption), leading to additional model complexity and computation overhead. Alternative approaches such as using nodes to replace the edges such as ES in our representation between adjacent I nodes are also possible. However, such approaches essentially exploit ad-hoc representations derived from the multigraph representation, making the model significantly less intuitive and less concise.
Since the edge-based paradigm is relatively unexplored compared to the state-based paradigm, we hope that this discussion can ignite further research in this direction.
5.2 Spurious Structures
In previous section we see that our model falls into the same edge-based paradigm as the mention hypergraph model. One might notice that our model is similar to the mention hypergraph model, in the sense that the edges in our model represent combinations of multiple edges in the mention hypergraph model. Since the objective function is de-
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ACE2004 ACE2005 GENIA Train (%) Dev (%) Test (%) Train (%) Dev (%) Test (%) Train (%) Dev (%) Test (%)
# sentence 6,799 829 879 7,336 958 1,047 14,836 1,855 1,855 w/ o.l. 2,685 (39) 293 (35) 373 (42) 2,686 (37) 341 (36) 330 (32) 3,199 (22) 366 (20) 448 (24) # entities 22,207 2,511 3,031 24,687 3,217 3,027 46,473 5,014 5,600 o.l. 10,170 (46) 1,091 (43) 1,418 (47) 9,937 (40) 1,192 (37) 1,184 (39) 8,337 (18) 915 (18) 1,217 (22)
Table 1: Statistics of the datasets used in this experiments. w/ o.l.: sentences containing overlapping entities; o.l.: overlapping/nested entities.
fined using features over the edges, this raises the question: are the two models actually optimizing the same objective function?
To answer this question, let us look into the normalization term Zw(x) calculated by each model using the inside-outside algorithm. Let β(m) denote the inside score of the node m. Recall that in the inside-outside algorithm, the inside score of a node m represents the sum of the scores of all paths from m to the leaf node. Since in mention hypergraph a path from a T-node to the leaf node represents an entity, β(Tkt ) represents the scores of all entities starting at position k of type t. Similarly, β(Ek) represents the scores of all entities starting at position k of any type. Now, since β(Ak) is calculated as the product between β(Ak+1) and β(Ek), it represents the score of all combinations of entities starting at k or later. Therefore, the normalization term Zw(x) = β(A0) represents the score of all combinations of entities in the sentence.
Consider a sentence with three words w0, w1, w2. The normalization term includes the scores of both these distinct entity combinations: 1. Entities w0w1 and w1w2 (crossing entities) 2. Entities w0w1w2 and w1 (nested entities)
However, as also noted by Lu and Roth (2015)4, these two combinations share the same subgraph in the model.5 On the other hand, in the mention hypergraph model, only one of the many combinations would be considered in the first term of the objective of equation 1 – ∑ e∈y w · f(e), whose score can be calculated efficiently using the inside algorithm. The other structures that share the same subgraph will become what we call spurious structures – the structures that would never be predicted by the model. Also note that the score of each of these distinct interpretation of the same sub-hypergraph might differ from each other. Refer to the supplementary material for more details. We call a model with normalization term Zw(x)
4See Figure 3 in Section 3.2 in their paper. 5In fact, there are 7 distinct entity combinations which
have the same subgraph.
that contains spurious structures a deficient model. In contrast, we can observe that, unlike the mention hypergraph model, our model is nondeficient – the normalization term Zw(x) calculated by our multigraph-based model does not contain spurious structures. This can be verified by the fact that the inside score of each node in our multigraph is calculated as the sum of the scores associated with each path following that node.
6 Experiments
6.1 Datasets
To assess our model’s capability in recognizing overlapping entities and make comparisons with previous models, we looked at datasets where overlapping entities are explicitly annotated. Specifically, we looked at the following standard datasets which were used in several previous works (Finkel and Manning, 2009; Lu and Roth, 2015): ACE2004, ACE2005, and GENIA. For ACE datasets, we used the same splits as used by Lu and Roth (2015) published in their website6. For GENIA, we used GENIAcorpus3.02p7 that comes with POS tags for each word (Tateisi and Tsujii, 2004). Following previous works (Finkel and Manning, 2009; Lu and Roth, 2015), we first split the last 10% of the data as the test set. Next we used the first 80% and the subsequent 10% for training and development, respectively. We made the same modifications as described by Finkel and Manning (2009) by collapsing all DNA, RNA, and protein subtypes into DNA, RNA, and protein, keeping cell line and cell type, and removing other entity types, resulting in 5 entity types. The statistics of each dataset is shown in Table 1. We can see overlapping entities are common in such datasets.
6.2 Features
For both models (mention hypergraph and our model) that fall under the edge-based paradigm, we define features over the edges in the models.
6http://statnlp.org/research/ie#mention-hypergraph 7http://geniaproject.org/genia-corpus/pos-annotation
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ACE2004 ACE2005 P R F1 P R F1
Lin-CRF 70.3 42.0 52.6 67.0 45.6 54.3 MH 80.7 46.1 58.7 77.6 47.3 58.8 MH (*) 71.0 55.4 62.2 67.0 57.3 61.7 Ours 76.3 52.0 61.9 73.5 51.6 60.6 Ours (*) 71.6 58.3 64.3 67.5 59.1 63.0
Table 2: Results on ACE2004 and ACE2005.
Features are defined as string concatenations of input features – information defined over the inputs (such as current word and POS tags of surrounding words) and output features – structured information defined over the output structure. In our model, when an edge represents a combination of roles, a feature is defined for each output feature. This allows us to use to make use of the identical set of features for both our multigraph model and the baseline mention hypergraph model, in order to make a proper comparison. We also followed Lu and Roth (2015) to add the additional mention penalty feature defined over the edges that represents the start of an entity to tune F1-scores on the development set.
When defining the input features for both our model and the mention hypergraph model, we tried to follow as close as possible to the features used by previous works in each dataset: we followed Lu and Roth (2015) for the features used in ACE datasets, and Finkel and Manning (2009) for features used in GENIA dataset. In general, they include surrounding words, surrounding POS tags, bag-of-words, Brown clusters (for GENIA only), and orthographic features. See the supplementary material for more details on the features.
6.3 Experimental Setup
We trained each model in the training set, then tuned the l2-regularization parameter based on the development set from the values in {0.0, 0.001, 0.01, 0.1, 1.0}. For GENIA experiments, we also tuned the number of Brown clusters from the values in {100, 1000}. Following (Lu and Roth, 2015), we also used each development set to tune the mention penalty to optimize the F1-score and report the scores on the corresponding test sets separately. Similar to Finkel and Manning (2009), as another baseline model we also trained a standard linear-chain CRF using BILOU scheme. Although this model does not support overlapping entities, it gives us a baseline to see the extent to which our model’s ability to recognize overlapping entities can help the overall performance.
7 Results and Discussion
Table 2 and 3 show the results on the ACE and GENIA datasets, respectively. Following previous works (Finkel and Manning, 2009; Lu and Roth, 2015), we report standard precision (P ), recall (R) and F1 percentage scores. For the ACE datasets, we make comparisons with the linear-chain CRF baseline (Lin-CRF), which does not support overlapping entities, as well as our implementation of the mention hypergraph baseline (MH). For the GENIA experiments, besides our implementation of the mention hypergraph baseline, we also make comparisons with the results of the two systems reported in (Finkel and Manning, 2009) – a model based on semi-Markov CRF (Semi-CRF) that cannot handle overlapping entities and their proposed constituency tree based model (F&M (’09)) that can support overlapping entities. The (*) marks the results after optimizing the F1-score in development set. Best results are highlighted in bold.
From such empirical results we can see that our proposed multigraph-based model yields significantly better results than the mention hypergraph model, with the highest improvement in F1 of 2.1 points observed in ACE2004. In GENIA dataset, our implementation of mention hypergraph matches the performance of the constituency parser-based model of Finkel and Manning (2009), while our multigraph-based model outperforms both by about 0.4 point. As expected, the linear-chain CRF baseline yields relatively lower results compared to the other models, since it cannot predict overlapping entities. However, such results give us some idea on how much performance increase we can gain by properly recognizing overlapping entities.
As these datasets consist of both overlapping and non-overlapping entities, to further understand the effectiveness of each model in recognizing overlapping entities (and non-overlapping entities), we performed some additional experiments. Specifically, we split the test data into two portions, one that consists of only sentences that
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% MH (*) Ours (*) P R F1 P R F1
ACE2004 w/ o.l. 42 72.8 51.0 60.0 71.3 56.2 62.8 w/o o.l. 58 73.1 62.8 67.5 72.5 64.2 68.1 ACE2005 w/ o.l. 32 68.6 52.8 59.7 68.5 55.7 61.4 w/o o.l. 68 64.8 64.8 64.8 66.0 64.7 65.4 GENIA w/ o.l. 24 77.1 60.3 67.7 75.6 60.7 67.3 w/o o.l. 76 73.9 70.1 71.9 74.1 71.6 72.9
Table 4: Scores on different types of sentences.
contain at least one entity that overlaps with another (w/ o.l.), and the other consisting of sentences that do not contain any overlapping entity (w/o o.l.). The results are shown in Table 4.
We can see that in ACE datasets, our model achieves higher F1-score compared to the mention hypergraph for both portions, but it achieves slightly lower results in GENIA dataset for the portion that contains overlapping entities. Noticing that GENIA dataset has relatively lower percentage of overlapping entities compared to ACE, we believe that this low recall is due to insufficient amount of training data on overlapping entities for this dataset, which affected the models’ confidence in predicting overlapping entities. When given sufficient training data on overlapping entities, which is the case for ACE, our model is able to better recognize overlapping entities.
Such results also lead to the interesting empirical finding that our model appears to be able to do well on the task of recognizing non-overlapping entities. As a further investigation, we performed yet one additional set of experiments, on the standard CONLL2003 dataset, which consists of only entities that do not overlap with one another.
The results are shown in Table 5. Again we see that our multigraph model outperforms all baseline models, including the Illinois NER system where external resources are not used (Ratinov and Roth, 2009), and a linear-chain CRF model, although the linear-chain CRF baseline models some interactions between distinct entity types and our model does not. Such results also suggest that modeling the interactions between distinct entity types may not be crucial for achieving a good performance in entity recognition. By examining the outputs, we found that although the training set is not annotated with overlapping entities, our model (and mention hypergraph model) will be able to predict overlapping entities when it is confident, leading to improved performance.
When comparing the basic version of our model (without optimizing F1) against that of the men-
0 100 200 300 400 500 600 700 800 900 1,000 0
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# iterations
O b j.
V al u e
Mention Hypergraph
Multigraph (This work)
Figure 7: Objective vs. training iterations.
tion hypergraph model, we note that our model consistently yields a higher recall. We speculate this is due to the fact that as a nondeficient model that resolves the issue of spurious structures we discussed in Section 5.2, our model is more confident in making its predictions.
We also empirically analyzed the training speed and convergence properties of the two models. Empirically, as illustrated in Figure 7 which shows how the objective improves when the training progresses on ACE2004, we found our multigraphbased model requires significantly less iterations to converge than mention hypergraph, though each training iteration requires 12% more time.
8 Conclusion and Future Work
We presented a novel multigraph-based model for entity recognition from text where entities may overlap with one another. We showed that empirically our model is able to yield better recognition results compared to previous models. We also performed theoretical analysis on the model and showed that our model resolves the spurious structures issue associated with a previous stateof-the-art model, while still maintaining the same inference time complexity.
Future work includes further investigations on how to apply the proposed multigraph-based formalism to other structured prediction problems involving complex structures, as well as finding applications of the proposed model in other related NLP tasks that involve the prediction of overlapping structures, such as equation parsing (Roy et al., 2016).
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A Details on Spurious Structures
About mention hypergraph, we remarked that the normalization term includes spurious structures. This section shows in more details how this is the case using some examples.
Consider the simplified mention hypergraph as shown in Figure 8 (left) consisting of three words and where the possible edges have been restricted to what are shown in the figure. Namely, there are only three possible subgraphs here, one for each of the three (hyper-)edges coming out from the node I1 associated with the word “Apache”. 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 8 (left). Further assume that features are only defined on these labeled edges.
Now we consider the normalization term Zw(x) = β(A0) calculated by inside-outside algorithm on this graph. The inside score β(I1) is the sum of the scores of the three possible entity combinations that include the word “Apache” as the first token in the entities, namely: {Apache} (using the edge I1 → (X)), {Apache helicopter} (using the edge I1 → (I2)), and {Apache helicopter, Apache} (using the hyperedge I1 → (I2,X)). Let us call this set of three entities as S1. The inside scores of I0, A1, the T-nodes, the E-nodes will be the same as this as there are no features along the unique edges between these
nodes and the node I1. Note that the inside score I(T0) represents the set of entities S2 which is the same as S1 except that each entity also includes the word “an” as the first word.
Now, the normalization term A0 includes the 9 possible entity combinations which are the results of taking all possible combinations between S1 and S2. The list of paths used to represent each of these combinations is as follows (only part of the paths is shown, the rest is implied as there is only one way to connect to the root node A0): 1. A-C-F and B-C-F (Apache helicopter, an
Apache helicopter) 2. A-C-F and B-E-F (Apache helicopter, an
Apache helicopter, an Apache) 3. A-C-F and B-D (Apache helicopter, an
Apache) 4. A-E-F and B-C-F (Apache helicopter,
Apache, an Apache helicopter) 5. A-E-F and B-E-F (Apache helicopter,
Apache, an Apache helicopter, an Apache) 6. A-E-F and B-D (Apache helicopter, Apache,
an Apache) 7. A-D and B-C-F (Apache, an Apache heli-
copter) 8. A-D and B-E-F (Apache, an Apache heli-
copter, an Apache) 9. A-D and B-D (Apache, an Apache)
Note that except the first one (the X-node associated with I1 is missing) and the last one (I2 and the last X-node are missing), the other 7 entity combinations are actually represented using the same subgraph consisting of the edges {A, B, E, F}, which is what is calculated in the fifth item (A-E-F and B-E-F). The other combinations represent entity combinations which, while valid, are not represented in the model as such, and so never appear as numerator in the likelihood. This is because whenever that entity combination appears, the model will represent it using the subgraph shown in Figure 8 (right).
B Features
For ACE datasets we used these features: 1. Words and POS tags (with window of 3
words to the left and right of current word) 2. Words and POS tags n-gram (up to length 4
containing current word) 3. Bag-of-word (with window of 5 words to the
left and to the right of current word) 4. Orthographic (following Lu and Roth (2015))
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A0 A1
E0 E1
T0 T1
I0 I1 I2
X X
an Apache helicopter
A
D F
B C
E
A0 A1
E0 E1
T0 T1
I0 I1 I2
X X
an Apache helicopter
A
F
B
E
Figure 8: (left) A simplified example of a mention hypergraph with restricted edges. (right) The subgraph associated with 7 out of 9 possible entity combinations.
5. Parent node type For GENIA we used these features: 1. Words and POS tags (with window of 2 words to the left and right of current word) 2. Words and POS tags n-gram (up to length 4 containing current word) 3. Bag-of-word (with window of 5 words to the left and right of current word) 4. Brown clusters with window of 1 word to the left and right of current word (using 100 or 1000 clusters built from training data only) 5. Word shape (Finkel and Manning (2009)) 6. Prefixes and suffixes of current word (up to
length 6) 7. Edge type
For CoNLL 2003 we used these features: 1. Words and POS tags (with window of 2
words to the left and right of current word) 2. Words and POS tags n-gram (up to length 4
containing current word) 3. Bag-of-word (with window of 5 words to the
left and right of current word) 4. Word shape (with window of 2 words to the
left and right of current word) 5. Prefixes and suffixes of current word (up to
length 5) 6. Orthographic (following Lu and Roth (2015)) 7. Edge type
C Hyperparameter
Table 6 lists the best l2-regularization coefficient λ for each dataset and model. For GENIA, the
ACE2004 ACE2005 GENIA CoNLL MH 0.001 0.0 1.0 0.01 MH (*) 0.001 0.1 1.0 0.001 Ours 0.001 0.001 1.0 0.001 Ours (*) 0.1 0.1 1.0 0.001
optimal Brown cluster size was found to be 1000, except for ‘Ours (*)’, where the best cluster size is 100.
D GENIA Preprocessing
For GENIA, we used GENIAcorpus3.02p that comes with POS tags for each word (Tateisi and Tsujii, 2004). Similar to the problem faced by Finkel and Manning (2009) on JNLPBA dataset, we also find tokenization issues in this corpus. As described by Tateisi and Tsujii (2004), when a hyphenated word such as IL-2-induced is partially annotated as an entity (in this case IL-2), the POS annotation corpus splits it into two tokens, which when done in test set will leak some information about the presence of entity. Unlike Finkel and Manning (2009) which tried to match the tokenization during testing, we simply further split all tokens at some punctuations (those matching the regular expression [-/,.+]), while keeping the information that they all originally come from the same word. This has the advantage of simplifying the tokenization procedure, although it makes the task slightly more difficult due to the higher number of tokens.
Also, to handle the discontiguous entities present in GENIA dataset (mainly due to coordinated entities involving ellipsis), following the approach used by the JNLPBA shared task organizer (Kim et al., 2004), we consider a group of coordinated entities as one structure. For example, in “. . . the [T- and B-lymphocytes] count in . . . ”, the entities “T-lymphocytes” and “Blymphocytes” are annotated as one structure “Tand B-lymphocytes”.

Review:
The paper suggests an approach based on multigraphs (several edges may link two nodes) for detecting potentially overlapping entities.  Strengths: The problem itself could be rather interesting especially for crossing entities to decide which one might actually be mentioned in some text. The technique seems to work although the empirically results do not show some  dramatic  effect. I like that some words are spent on efficiency compared to a previous system. The paper in general is well-written but also needs some further polishing in some details (see minor remarks below).  Weaknesses: The problem itself is not really well motivated. Why is it important to detect China as an entity within the entity Bank of China, to stay with the example in the introduction? I do see a point for crossing entities but what is the use case for nested entities? This could be much more motivated to make the reader interested. As for the approach itself, some important details are missing in my opinion: What is the decision criterion to include an edge or not? In lines 229--233 several different options for the I^k_t nodes are mentioned but it is never clarified which edges should be present!  As for the empirical evaluation, the achieved results are better than some previous approaches but not really by a large margin. I would not really call the slight improvements as  outperformed  as is done in the paper. What is the effect size? Does it really matter to some user that there is some improvement of two percentage points in F_1? What is the actual effect one can observe? How many  important  entities are discovered, that have not been discovered by previous methods? Furthermore, what performance would some simplistic dictionary-based method achieve that could also be used to find overlapping things? And in a similar direction: what would some commercial system like Google's NLP cloud that should also be able to detect and link entities would have achieved on the datasets. Just to put the results also into contrast of existing  commercial  systems.  As for the result discussion, I would have liked to see some more emphasis on actual crossing entities. How is the performance there? This in my opinion is the more interesting subset of overlapping entities than the nested ones. How many more crossing entities are detected than were possible before? Which ones were missed and maybe why? Is the performance improvement due to better nested detection only or also detecting crossing entities? Some general error discussion comparing errors made by the suggested system and previous ones would also strengthen that part.  General Discussion: I like the problems related to named entity recognition and see a point for recognizing crossing entities. However, why is one interested in nested entities? The paper at hand does not really motivate the scenario and also sheds no light on that point in the evaluation. Discussing errors and maybe advantages with some example cases and an emphasis on the results on crossing entities compared to other approaches would possibly have convinced me more. So, I am only lukewarm about the paper with maybe a slight tendency to rejection. It just seems yet another try without really emphasizing the in my opinion important question of crossing entities.  Minor remarks:  - first mention of multigraph: some readers may benefit if the notion of a multigraph would get a short description  - previously noted by ... many previous: sounds a little odd  - Solving this task: which one?  - e.g.: why in italics?  - time linear in n: when n is sentence length, does it really matter whether it is linear or cubic?  - spurious structures: in the introduction it is not clear, what is meant  - regarded as _a_ chunk  - NP chunking: noun phrase chunking?  - Since they set: who?  - pervious to previous  - of Lu and Roth~(2015)  - the following five types: in sentences with no large numbers, spell out the small ones, please  - types of states: what is a state in a (hyper-)graph? later state seems to be used analogous to node?!  - I would place commas after the enumeration items at the end of page 2 and a period after the last one  - what are child nodes in a hypergraph?  - in Figure 2 it was not obvious at first glance why this is a hypergraph. colors are not visible in b w printing. why are some nodes edges in gray. it is also not obvious how the highlighted edges were selected and why the others are in gray ...  - why should both entities be detected in the example of Figure 2? what is the difference to  just  knowing the long one?  - denoting ...: sometimes in brackets, sometimes not ... why?  - please place footnotes not directly in front of a punctuation mark but afterwards  - footnote 2: due to the missing edge: how determined that this one should be missing?  - on whether the separator defines ...: how determined?  - in _the_ mention hypergraph  - last paragraph before 4.1: to represent the entity separator CS: how is the CS-edge chosen algorithmically here?  - comma after Equation 1?  - to find out: sounds a little odd here  - we extract entities_._  footnote  - we make two: sounds odd; we conduct or something like that?  - nested vs. crossing remark in footnote 3: why is this good? why not favor crossing? examples to clarify?  - the combination of states alone do_es_ not?  - the simple first order assumption: that is what?  - In _the_ previous section  - we see that our model: demonstrated? have shown?  - used in this experiments: these  - each of these distinct interpretation_s_  - published _on_ their website  - The statistics of each dataset _are_ shown  - allows us to use to make use: omit  to use   - tried to follow as close ... : tried to use the features suggested in previous works as close as possible?  - Following (Lu and Roth, 2015): please do not use references as nouns: Following Lu and Roth (2015)  - using _the_ BILOU scheme  - highlighted in bold: what about the effect size?  - significantly better: in what sense? effect size?  - In GENIA dataset: On the GENIA dataset  - outperforms by about 0.4 point_s_: I would not call that  outperform   - that _the_ GENIA dataset  - this low recall: which one?  - due to _an_ insufficient  - Table 5: all F_1 scores seems rather similar to me ... again,  outperform  seems a bit of a stretch here ...  - is more confident: why does this increase recall?  - converge _than_ the mention hypergraph  - References: some paper titles are lowercased, others not, why?