acl acl2010 acl2010-127 knowledge-graph by maker-knowledge-mining

127 acl-2010-Global Learning of Focused Entailment Graphs

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Author: Jonathan Berant ; Ido Dagan ; Jacob Goldberger

Abstract: We propose a global algorithm for learning entailment relations between predicates. We define a graph structure over predicates that represents entailment relations as directed edges, and use a global transitivity constraint on the graph to learn the optimal set of edges, by formulating the optimization problem as an Integer Linear Program. We motivate this graph with an application that provides a hierarchical summary for a set of propositions that focus on a target concept, and show that our global algorithm improves performance by more than 10% over baseline algorithms.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 i l dagan@ Abstract We propose a global algorithm for learning entailment relations between predicates. [sent-4, score-0.697]

2 We define a graph structure over predicates that represents entailment relations as directed edges, and use a global transitivity constraint on the graph to learn the optimal set of edges, by formulating the optimization problem as an Integer Linear Program. [sent-5, score-1.521]

3 We motivate this graph with an application that provides a hierarchical summary for a set of propositions that focus on a target concept, and show that our global algorithm improves performance by more than 10% over baseline algorithms. [sent-6, score-0.614]

4 ’ TE systems require extensive knowledge of entailment patterns, often captured as entailment rules: rules that specify a directional inference relation between two text fragments (when the rule is bidirectional this is known as paraphrasing). [sent-12, score-1.03]

5 An important type of entailment rule refers to propositional templates, i. [sent-13, score-0.709]

6 Because f wacotsu adn bde knowledge are mostly expressed by propositions, such entailment rules are central to the TE task. [sent-17, score-0.515]

7 i l on broad-scale acquisition of entailment rules for predicates, e. [sent-24, score-0.515]

8 Previous work has focused on learning each entailment rule in isolation. [sent-27, score-0.547]

9 A prominent example is that entailment is a transitive relation, and thus the rules ‘X → Y ’ and ‘Y → Z’ imply tahned ru thleu s‘X th → Zles’ . [sent-29, score-0.563]

10 First, we describe a structure termed an entailment graph that models entailment relations between propositional templates (Section 3). [sent-32, score-1.706]

11 Next, we show that we can present propositions according to an entailment hierarchy derived from the graph, and suggest a novel hierarchical presentation scheme for corpus propositions referring to a target concept. [sent-33, score-0.988]

12 As in this application each graph focuses on a single concept, we term those focused entailment graphs (Section 4). [sent-34, score-0.851]

13 In the core section of the paper, we present an algorithm that uses a global approach to learn the entailment relations of focused entailment graphs (Section 5). [sent-35, score-1.352]

14 We define a global function and look for the graph that maximizes that function under a transitivity constraint. [sent-36, score-0.556]

15 We show that this leads to an optimal solution with respect to the global function, and demonstrate that the algorithm outperforms methods that utilize only local information by more than 10%, as well as methods that employ a greedy optimization algorithm rather than an ILP solver (Section 6). [sent-38, score-0.402]

16 2 Background Entailment learning Two information types have primarily been utilized to learn entailment rules between predicates: lexicographic resources and distributional similarity resources. [sent-39, score-0.735]

17 WordNet (Fellbaum, 1998), by far the most widely used resource, specifies relations such as hyponymy, derivation, and entailment that can be used for semantic inference (Budanitsky and Hirst, 2006). [sent-43, score-0.55]

18 Global learning It is natural to describe entailment relations between predicates by a graph. [sent-54, score-0.621]

19 Nodes represent predicates, and edges represent entailment between nodes. [sent-55, score-0.691]

20 Nevertheless, using a graph for global learning of entailment between predicates has attracted little attention. [sent-56, score-0.936]

21 Recently, Szpektor and Dagan (2009) presented the resource Argument-mapped WordNet, providing entailment relations for predicates in WordNet. [sent-57, score-0.621]

22 Their resource was built on top of WordNet, and makes simple use of WordNet’s global graph structure: new rules are suggested by transitively chaining graph edges, and verified against corpus statistics. [sent-58, score-0.609]

23 Their algorithm incrementally adds hyponyms to an existing taxonomy (WordNet), using a greedy search algorithm that adds at each step the set of hyponyms that maximize the probability of the evidence while respecting the transitivity constraint. [sent-63, score-0.347]

24 In this paper we formulate the entailment graph learning problem as an Integer Linear Program, and find that this leads to an optimal solution with respect to the target function in our experiment. [sent-69, score-0.771]

25 3 Entailment Graph This section presents an entailment graph structure, which resembles the graph in (Szpektor and Dagan, 2009). [sent-70, score-0.977]

26 The nodes of an entailment graph are propositional templates. [sent-71, score-1.003]

27 A propositional template is a path in a dependency tree between two arguments of a common predicate1 (Lin and Pantel, 2001 ; Szpektor and Dagan, 2008). [sent-72, score-0.296]

28 An edge (u, v) represents the fact that template u entails template v. [sent-75, score-0.294]

29 For example, the template X is diagnosed with asthma entails the template X suffers from asthma, although one is not a hyponoym of the other. [sent-77, score-0.295]

30 An example of an entailment graph is given in Figure 1, left. [sent-78, score-0.746]

31 Since entailment is a transitive relation, an entailment graph is transitive, i. [sent-79, score-1.309]

32 Because graph nodes represent propositions, which generally have a clear truth value, we can nau- assume that transitivity is indeed maintained along paths of any length in an entailment graph, as entailment between each pair of nodes either occurs or doesn’t occur with very high probability. [sent-83, score-1.561]

33 For clarity, edges that can be inferred by transitivity are omitted. [sent-87, score-0.393]

34 Right: A hierarchical summary of propositions involving nausea as an argument, such as headache is related to nausea, acupuncture helps with nausea, and Lorazepam treats nausea. [sent-88, score-0.605]

35 that in our experimental setting the length of paths in the entailment graph is relatively small. [sent-89, score-0.746]

36 Moreover, if we merge every strong connectivity component to a single node, the graph becomes a Directed Acyclic Graph (DAG), and the graph nodes can be sorted and presented component2 hierarchically. [sent-91, score-0.569]

37 4 Motivating Application In this section we propose an application that provides a hierarchical view of propositions extracted from a corpus, based on an entailment graph. [sent-93, score-0.751]

38 Thus, when querying about nausea, one might find it is related to vomitting and chicken pox, but not that chicken pox is a cause of nausea, 2A strong connectivity component is a subset of nodes in the graph where there is a path from any node to any other node. [sent-104, score-0.434]

39 We propose using the entailment graph structure, which describes entailment relations between predicates, to naturally present propositions hierarchically. [sent-108, score-1.503]

40 That is, the entailment hierarchy can be used as an additional facet, which can improve navigation and provide a compact hierarchical summary of the propositions. [sent-109, score-0.574]

41 We can extract the set of propositions where nausea is an argument automatically from a corprus, and learn an entailment graph over propositional templates derived from the extracted propositions, as illustrated in Figure 1, left. [sent-112, score-1.664]

42 Then, we follow the steps in the process described in Section 3: merge synonymous nodes that are in the same strong connectivity component, and turn the resulting DAG into a predicate hierarchy, which we can then use to present the propositions (Figure 1, right). [sent-113, score-0.366]

43 Note that in all propositional templates one argument is the target concept (nausea), and the other is a variable whose corpus instantiations can be presented according to another hierarchy (e. [sent-114, score-0.526]

44 Moreover, new propositions are inferred from the graph by transitivity. [sent-117, score-0.481]

45 For example, from the proposition ‘relaxation reduces nausea ’ we can in1222 fer the proposition ‘relaxation helps with nausea ’. [sent-118, score-0.514]

46 1 Focused entailment graphs The application presented above generates entailment graphs of a specific form: (1) Propositional templates have exactly one argument instantiated by the same entity (e. [sent-120, score-1.401]

47 Generalizing this notion, we define a focused entailment graph to be an entailment graph where the number of nodes is relatively small (and consequently paths in the graph are short), and predicates have a single sense (so transitivity is maintained without sense specification). [sent-124, score-2.063]

48 Section 5 presents an algorithm that given the set of nodes of a focused entailment graph learns its edges, i. [sent-125, score-0.869]

49 For brevity, from now on the term entailment graph will stand for focused entailment graph. [sent-129, score-1.293]

50 5 Learning Entailment Graph Edges In this section we present an algorithm for learning the edges of an entailment graph given its set of nodes. [sent-130, score-0.95]

51 The first step is preprocessing: We use a large corpus and WordNet to train an entailment classifier that estimates the likelihood that one propositional template entails another. [sent-131, score-0.9]

52 1 Training an entailment classifier We describe a procedure for learning an entailment classifier, given a corpus and a lexicographic resource (WordNet). [sent-134, score-1.118]

53 First, we extract a large set of propositional templates from the corpus. [sent-135, score-0.377]

54 Next, we represent each pair of propositional templates with procedure used by Lin and Pantel (2001). [sent-136, score-0.377]

55 The arguments are replaced with variables, resulting in propositional as X←su −b −j −o − →bj templates such affect Y. [sent-138, score-0.377]

56 Distributional similarity representation We aim to train a classifier that for an input template pair (t1, t2) determines whether t1 entails t2. [sent-139, score-0.262]

57 Therefore, information about the direction of entailment is provided by the BInc measure. [sent-153, score-0.515]

58 Let T be the set of propositional templates extracted from the corpus. [sent-160, score-0.377]

59 2 Global learning of edges Once the entailment classifier is trained we learn the graph edges given its nodes. [sent-169, score-1.179]

60 This is equivalent to learning all entailment relations between all propositional template pairs for that graph. [sent-170, score-0.846]

61 To learn edges we consider global constraints, which allow only certain graph topologies. [sent-171, score-0.561]

62 Since we seek a global solution under transitivity and other constraints, linear programming is a natural choice, enabling the use of state of the art optimization packages. [sent-172, score-0.433]

63 We describe two formulations ofinteger linear programs that learn the edges: one maximizing a global score function, and another maximizing a global probability function. [sent-173, score-0.351]

64 Our goal is to learn the edges E over a set of nodes V . [sent-175, score-0.274]

65 Score-based target function We assume an entailment classifier estimating a positive score Suv if it believes Iuv = 1and a negative score otherwise (for example, an SVM classifier). [sent-182, score-0.561]

67 We assume an entailment classifier estimating the probability of an edge given its features: Puv = P(Iuv = 1|Fuv). [sent-186, score-0.608]

68 Second, we assume Pth(eF f|eGat)ure =s fQoru =thve pair (u, v) are generated by a dthiestfr eibaututiroens depending only on whether entailment holds for (u, v). [sent-191, score-0.515]

69 Now we look for the graph that maximizes log P(G|F) : Gˆ = argGmax(uX,v)∈ElogPuv+(u,Xv) ∈/Elog(1 − Puv) = argmGaxuX6=v[Iuv· logPuv + (1 − Iuv) · log(1 − Puv)] = argmGaxXu6=vlog1 −Pu Pvuv· Iuv (Pin the last transition we omit the constant Pu6=v log(1 −Puv)). [sent-197, score-0.263]

71 ’s in that both try to learn graph edges given a transitivity constraint. [sent-201, score-0.616]

72 ’s model attempts to determine the graph that maximizes the likelihood P(F|G) athned gnraotp hth teh posterior P(G|F). [sent-204, score-0.263]

73 We extracted all propositional templates from the corpus, where both argument instantiations are medical concepts, i. [sent-221, score-0.509]

74 To evaluate the performance of our algorithm, we constructed 23 gold standard entailment graphs. [sent-225, score-0.542]

75 gov/research/umls 1225 templates for which the target concept instantiated an argument at least K(= 3) times (average number of graph nodes=22. [sent-230, score-0.506]

76 Ten medical students constructed the gold standard of graph edges. [sent-233, score-0.321]

77 The entailment graph fragment in Figure 1is from the gold standard. [sent-243, score-0.773]

78 The graphs learned by our algorithm were evaluated by two measures, one evaluating the graph directly, and the other motivated by our application: (1) F1 of the learned edges compared to the gold standard edges (2) Our application provides a summary of propositions extracted from the corpus. [sent-244, score-0.918]

79 Thus, we compute F1 for the set of propositions inferred from the learned graph, compared to the set inferred based on the gold standard graph. [sent-246, score-0.32]

80 For example, given the proposition from the corpus ‘relaxation reduces nausea ’ and the edge ‘X reduce nausea → X help with nausea ’, we evaluate tdhuec ese nta { ‘sreeala →xat Xion h rlped wucitehs nausea ’, ‘reel eavxaalutiaotne helps tw {ith‘r nausea ’}. [sent-247, score-1.332]

81 For each measure we computed for each template t a list of templates most similar to t (or entailing t for directional measures). [sent-253, score-0.285]

82 For each distributional similarity measure (altogether 16 measures), we learned a graph by inserting any edge (u, v), when u is in the top K templates most similar to v. [sent-255, score-0.604]

83 The similarity lists were computed using: (1) Unary templates and the Lin function (2) Unary templates and the BInc function (3) Binary templates and the Lin function 8http://lpsolve. [sent-272, score-0.62]

84 Constructing graph nodes and learning its edges given an input concept took 2-3 seconds on a standard desktop. [sent-276, score-0.52]

85 The row Local-LP is achieved by omitting global transitivity constraints, making the algorithm completely local. [sent-282, score-0.321]

86 The global methods clearly outperform local methods: Tuned-LP outperforms significantly all local methods that require a development set both on the edges F1 measure (p<. [sent-290, score-0.409]

87 The untunedLP algorithm also significantly outperforms all local methods that do not require a development set on the edges F1 measure (p<. [sent-293, score-0.261]

88 Omitting the global transitivity constraints decreases performance, as shown by Local-LP. [sent-296, score-0.293]

89 To further establish the merits of global algorithms, we compare (Table 2) tuned-LP, the best global algorithm, with Local1∗, the best local algorithm. [sent-298, score-0.295]

90 This is because tunedLP refrains from adding edges that subsequently induce many undesirable edges through transitivity. [sent-301, score-0.352]

91 Figures 2 and 3 illustrate this by comparing tuned-LP and Local1∗ on a subgraph of the Headache concept, before adding missing edges to satisfy transitivity to Local1∗ . [sent-302, score-0.402]

92 This is the type of global consideration that is addressed in an ILP formulation, but is ignored in a local approach and often overlooked when employing a greedy algorithm. [sent-304, score-0.264]

93 Figure 2 also illustrates the utility of a local entailment graph for information presentation. [sent-305, score-0.803]

94 Presenting information according to this subgraph distinguishes between propositions dealing with headache treatments and 1227 propositions dealing with headache risk groups. [sent-306, score-0.69]

95 The results clearly demonstrate that a global approach improves performance on the entailment graph learning task, and the overall advantage of employing an ILP solver rather than a greedy al- gorithm. [sent-313, score-0.953]

96 7 Conclusion This paper presented a global optimization algorithm for learning entailment relations between predicates represented as propositional templates. [sent-314, score-1.019]

97 We modeled the problem as a graph learning problem, and searched for the best graph under a global transitivity constraint. [sent-315, score-0.755]

98 We used Integer Linear Programming to solve the optimization problem, which is theoretically sound, and demonstrated empirically that this method outperforms local algorithms as well as a greedy optimization algorithm on the graph learning task. [sent-316, score-0.518]

99 In future work, we would like to learn general entailment graphs over a large number of nodes. [sent-318, score-0.623]

100 Additionally, we will investigate novel features for the entailment classifier. [sent-320, score-0.515]

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