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Introduction Our Model Experiments Ambiguity Conclusion Appendix Learning to Recognize Discontiguous Entities Aldrian Obaja Muis and Wei Lu Singapore University of Technology and Design aldrian muis@sutd.edu.sg luwei@sutd.edu.sg

  1. Introduction Our Model Experiments Ambiguity Conclusion Appendix Discontiguous Entity Recognition Definition A task to recognize entities in text, where they can be discontiguous (and possibly overlapping with each other) Examples from SemEval 2014 Task 7: Analysis of Clinical Text: EGD showed hiatal hernia and vertical laceration in distal esophagus with blood in stomach and overlying lac. hiatal hernia 1 laceration . . . esophagus 2 blood in stomach 3 stomach . . . lac 4 Infarctions either water shed or embolic Infarctions 1 Infarctions . . . water shed 2 Infarctions . . . embolic 3 4 / 37

  2. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: line1 line2 line1 line2 line1 line2 5 / 37

  3. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 line1 line2 line1 line2 5 / 37

  4. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 Standard NER using BIO tagset pipelined with SVM to combine the spans 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 line1 line2 line1 line2 5 / 37

  5. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 Standard NER using BIO tagset pipelined with SVM to combine the spans 2 Zhang et al. (2014) 6 (best team) 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 6 Yaoyun Zhang et al. (2014). “UTH CCB: A report for SemEval 2014 – Task 7 Analysis of Clinical Text”. In: SemEval 2014 line1 line2 5 / 37

  6. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 Standard NER using BIO tagset pipelined with SVM to combine the spans 2 Zhang et al. (2014) 6 (best team) Use extended BIO tagset coupled with heuristics 7 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 6 Yaoyun Zhang et al. (2014). “UTH CCB: A report for SemEval 2014 – Task 7 Analysis of Clinical Text”. In: SemEval 2014 7 Buzhou Tang et al. (2013). “Recognizing and Encoding Discorder Concepts in Clinical Text using Machine Learning and Vector Space”. In: ShARe/CLEF Eval. Lab 5 / 37

  7. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 Standard NER using BIO tagset pipelined with SVM to combine the spans 2 Zhang et al. (2014) 6 (best team) Use extended BIO tagset coupled with heuristics 7 B , I for contiguous tokens 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 6 Yaoyun Zhang et al. (2014). “UTH CCB: A report for SemEval 2014 – Task 7 Analysis of Clinical Text”. In: SemEval 2014 7 Buzhou Tang et al. (2013). “Recognizing and Encoding Discorder Concepts in Clinical Text using Machine Learning and Vector Space”. In: ShARe/CLEF Eval. Lab 5 / 37

  8. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 Standard NER using BIO tagset pipelined with SVM to combine the spans 2 Zhang et al. (2014) 6 (best team) Use extended BIO tagset coupled with heuristics 7 B , I for contiguous tokens BD , ID for discontiguous tokens 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 6 Yaoyun Zhang et al. (2014). “UTH CCB: A report for SemEval 2014 – Task 7 Analysis of Clinical Text”. In: SemEval 2014 7 Buzhou Tang et al. (2013). “Recognizing and Encoding Discorder Concepts in Clinical Text using Machine Learning and Vector Space”. In: ShARe/CLEF Eval. Lab 5 / 37

  9. Introduction Our Model Experiments Ambiguity Conclusion Appendix Previous Approaches In SemEval 2014 Task 7, there were only two teams that could handle discontiguous and overlapping entities: 1 Pathak et al. (2014) 5 Standard NER using BIO tagset pipelined with SVM to combine the spans 2 Zhang et al. (2014) 6 (best team) Use extended BIO tagset coupled with heuristics 7 B , I for contiguous tokens BD , ID for discontiguous tokens BH , IH for overlapping tokens 5 Parth Pathak et al. (2014). “ezDI: A Hybrid CRF and SVM based Model for Detecting and Encoding Disorder Mentions in Clinical Notes”. In: SemEval 2014 6 Yaoyun Zhang et al. (2014). “UTH CCB: A report for SemEval 2014 – Task 7 Analysis of Clinical Text”. In: SemEval 2014 7 Buzhou Tang et al. (2013). “Recognizing and Encoding Discorder Concepts in Clinical Text using Machine Learning and Vector Space”. In: ShARe/CLEF Eval. Lab 5 / 37

  10. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. Infarctions either water shed or embolic Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  11. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [Infarctions] 1 either [water shed] 1 or embolic 1 Infarctions ... water shed Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  12. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[Infarctions] 1 ] 2 either [water shed] 1 or [embolic] 2 1 Infarctions ... water shed 2 Infarctions ... embolic Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  13. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[[Infarctions] 1 ] 2 ] 3 either [water shed] 1 or [embolic] 2 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  14. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[[Infarctions] 1 ] 2 ] 3 either [water shed] 1 or [embolic] 2 O O 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  15. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[[Infarctions] 1 ] 2 ] 3 either [water shed] 1 or [embolic] 2 BH O O 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  16. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[[Infarctions] 1 ] 2 ] 3 either [water shed] 1 or [embolic] 2 BH O BD ID O 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  17. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[[Infarctions] 1 ] 2 ] 3 either [water shed] 1 or [embolic] 2 BH O BD ID O BD 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  18. Introduction Our Model Experiments Ambiguity Conclusion Appendix Encoding in Model of Zhang et al. [[[Infarctions] 1 ] 2 ] 3 either [water shed] 1 or [embolic] 2 BH O BD ID O BD 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions This is the canonical encoding of this particular set of entities Example taken from the full sentence: “ ... protocol to evaluate for any infarctions, either water shed or embolic, ... ” 6 / 37

  19. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. Infarctions either water shed or embolic BH O BD ID O BD 7 / 37

  20. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. Infarctions either [water shed] 1 or [embolic] 1 BH O BD ID O BD 7 / 37

  21. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. Infarctions either water shed or embolic BH O BD ID O BD 7 / 37

  22. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. [Infarctions] 1 either [water shed] 1 or embolic BH O BD ID O BD 1 Infarctions ... water shed 7 / 37

  23. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. [[Infarctions] 1 ] 2 either [water shed] 1 or [embolic] 2 BH O BD ID O BD 1 Infarctions ... water shed 2 Infarctions ... embolic 7 / 37

  24. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. [[Infarctions] 1 ] 2 either [water shed] 1 or [embolic] 2 BH O BD ID O BD 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions (?) 7 / 37

  25. Introduction Our Model Experiments Ambiguity Conclusion Appendix Decoding in Model of Zhang et al. [[Infarctions] 1 ] 2 either [water shed] 1 or [embolic] 2 BH O BD ID O BD 1 Infarctions ... water shed 2 Infarctions ... embolic 3 Infarctions (?) Ambiguous! 7 / 37

  26. Introduction Our Model Experiments Ambiguity Conclusion Appendix Number of Entity Combinations In a sentence with n words, there are: 1 2 n − 1 possible discontiguous entities 8 / 37

  27. Introduction Our Model Experiments Ambiguity Conclusion Appendix Number of Entity Combinations In a sentence with n words, there are: 1 2 n − 1 possible discontiguous entities 2 2 2 n − 1 possible combinations of discontiguous entities * 8 / 37

  28. Introduction Our Model Experiments Ambiguity Conclusion Appendix Discontiguous Entities Recognition 1 How to efficiently model these discontiguous (and possibly overlapping) entities? 9 / 37

  29. Introduction Our Model Experiments Ambiguity Conclusion Appendix Discontiguous Entities Recognition 1 How to efficiently model these discontiguous (and possibly overlapping) entities? 2 How to compare the ambiguity between models for discontiguous entities? 9 / 37

  30. Introduction Our Model Experiments Ambiguity Conclusion Appendix Contributions In this paper, we contributed: 1 A new hypergraph-based model to handle discontiguous entities better 10 / 37

  31. Introduction Our Model Experiments Ambiguity Conclusion Appendix Contributions In this paper, we contributed: 1 A new hypergraph-based model to handle discontiguous entities better 2 A simple theoretical framework to compare ambiguity between models 10 / 37

  32. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model water or Infarctions either shed embolic A A A A A A E E E E E E T T T T T T X X X X X X B 0 B 0 B 0 B 0 B 0 B 0 X X X X X X O 1 O 1 O 1 O 1 O 1 O 1 B 1 B 1 B 1 B 1 B 1 B 1 X X X X X X 11 / 37

  33. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model water water or Infarctions Infarctions either shed shed embolic embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 O 1 O 1 Infarctions B 1 B 1 B 1 Infarctions . . . water shed X Infarctions . . . embolic X 12 / 37

  34. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model Key ideas: 1 Build a hypergraph that can encode any entity combination 13 / 37

  35. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model Key ideas: 1 Build a hypergraph that can encode any entity combination 2 For any sentence annotated with entities, there would be a unique subgraph that represents it (canonical encoding) 13 / 37

  36. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model Key ideas: 1 Build a hypergraph that can encode any entity combination 2 For any sentence annotated with entities, there would be a unique subgraph that represents it (canonical encoding) 3 Each entity is represented as a path in the entity-encoded hypergraph, where the B -nodes indicate which tokens are part of the entity 13 / 37

  37. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 O 1 O 1 Infarctions B 1 B 1 B 1 Infarctions . . . water shed X Infarctions . . . embolic X 14 / 37

  38. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X 14 / 37

  39. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 14 / 37

  40. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X Infarctions 14 / 37

  41. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 Infarctions 14 / 37

  42. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 Infarctions B 1 14 / 37

  43. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 Infarctions B 1 B 1 14 / 37

  44. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions Infarctions either water water shed shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 Infarctions B 1 B 1 Infarctions . . . water shed X 14 / 37

  45. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 Infarctions B 1 B 1 Infarctions . . . water shed X 14 / 37

  46. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 O 1 Infarctions B 1 B 1 Infarctions . . . water shed X 14 / 37

  47. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 O 1 O 1 Infarctions B 1 B 1 Infarctions . . . water shed X 14 / 37

  48. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions either water shed embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 O 1 O 1 Infarctions B 1 B 1 B 1 Infarctions . . . water shed X 14 / 37

  49. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model or Infarctions Infarctions either water shed embolic embolic A A A A A A E E E E E E T T T T T T X X X X X B 0 X O 1 O 1 O 1 O 1 Infarctions B 1 B 1 B 1 Infarctions . . . water shed X Infarctions . . . embolic X 14 / 37

  50. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model Training and predicting: 1 Training: Maximize conditional log-likelihood of training data 15 / 37

  51. Introduction Our Model Experiments Ambiguity Conclusion Appendix Our Hypergraph-based Model Training and predicting: 1 Training: Maximize conditional log-likelihood of training data 2 Predicting: Use Viterbi to find the highest-scoring subgraph 15 / 37

  52. Introduction Our Model Experiments Ambiguity Conclusion Appendix Experiments 16 / 37

  53. Introduction Our Model Experiments Ambiguity Conclusion Appendix Experimental Setup Dataset taken from SemEval 2014 Task 7, taking sentences containing discontiguous entities 17 / 37

  54. Introduction Our Model Experiments Ambiguity Conclusion Appendix Experimental Setup Dataset taken from SemEval 2014 Task 7, taking sentences containing discontiguous entities Two setups for training set: “Discontiguous” (smaller) and “Original” (larger) 17 / 37

  55. Introduction Our Model Experiments Ambiguity Conclusion Appendix Experimental Setup Dataset taken from SemEval 2014 Task 7, taking sentences containing discontiguous entities Two setups for training set: “Discontiguous” (smaller) and “Original” (larger) Models optimized for F1-score in dev set by varying λ 17 / 37

  56. Introduction Our Model Experiments Ambiguity Conclusion Appendix Experimental Setup Dataset taken from SemEval 2014 Task 7, taking sentences containing discontiguous entities Two setups for training set: “Discontiguous” (smaller) and “Original” (larger) Models optimized for F1-score in dev set by varying λ Features followed Tang et al. (2013): words, POS, Brown cluster, semantic category, . . . 17 / 37

  57. Introduction Our Model Experiments Ambiguity Conclusion Appendix Results Using Smaller Training Set Li-Enh Li-All Sh-Enh Sh-All 100 80 76 . 90 76 . 00 Score (%) 60 54 . 70 52 . 70 52 . 80 47 . 00 44 . 90 41 . 20 40 . 10 40 . 50 40 22 . 70 20 15 . 20 0 Precision Recall F1-score 18 / 37

  58. Introduction Our Model Experiments Ambiguity Conclusion Appendix Results Using Larger Training Set Li-Enh Li-All Sh-Enh Sh-All 100 80 73 . 90 73 . 40 64 . 10 59 . 00 59 . 10 Score (%) 60 53 . 90 52 . 80 51 . 10 49 . 40 49 . 10 49 . 50 46 . 50 40 20 0 Precision Recall F1-score 19 / 37

  59. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity 20 / 37

  60. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity One encoding can have multiple interpretations (set of entities) apparent [atrial [pacemaker] 2 artifact] 1 without [capture] 2 A A A A A A 1 atrial pacemaker artifact 2 E E E E E E pacemaker . . . capture T T T T T T X X X X B 0 B 0 B 0 1 pacemaker artifact atrial pacemaker artifact 2 atrial pacemaker . . . capture X pacemaker artifact O 1 O 1 B 1 pacemaker . . . capture X atrial pacemaker . . . capture 1 infarctions . . . water shed 2 infarctions . . . embolic Infarctions either water shed or embolic BH O BD ID O BD 1 infarctions 2 infarctions . . . water shed 3 infarctions . . . embolic 21 / 37

  61. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity The models need further processing after prediction to generate one set of entities 22 / 37

  62. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity The models need further processing after prediction to generate one set of entities We compare two heuristics: 22 / 37

  63. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity The models need further processing after prediction to generate one set of entities We compare two heuristics: All : Return the union of all possible interpretations 1 22 / 37

  64. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity The models need further processing after prediction to generate one set of entities We compare two heuristics: All : Return the union of all possible interpretations 1 Enough : Return one possible interpretation 2 22 / 37

  65. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity 23 / 37

  66. Introduction Our Model Experiments Ambiguity Conclusion Appendix Ambiguity Definition Ambiguity level A ( M ) of model M is the average number of interpretations of each canonical encoding in the model 23 / 37

  67. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? 24 / 37

  68. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: 24 / 37

  69. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) 24 / 37

  70. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n 24 / 37

  71. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n 24 / 37

  72. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n For our hypergraph-based model: 24 / 37

  73. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n For our hypergraph-based model: Number of canonical encoding = number of subgraphs 24 / 37

  74. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline model: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n For our hypergraph-based model: Number of canonical encoding = number of subgraphs Q : How to calculate the number of subgraphs? 24 / 37

  75. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings A : Use dynamic programming on combination of nodes 25 / 37

  76. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings A : Use dynamic programming on combination of nodes Fig. 1: Simplified graph to illustrate subgraph counting 25 / 37

  77. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings A : Use dynamic programming on combination of nodes Fig. 1: Simplified graph to illustrate Fig. 2: State transitions subgraph counting 25 / 37

  78. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings A : Use dynamic programming on combination of nodes Fig. 1: Simplified graph to illustrate Fig. 2: State transitions subgraph counting f 11 ( n ) = 2 ∗ f 11 ( n − 1) + f 01 ( n − 1) (1) 25 / 37

  79. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n For our hypergraph-based model: Number of canonical encoding = number of subgraphs 26 / 37

  80. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n For our hypergraph-based model: Number of canonical encoding = number of subgraphs After more calculations: M Sh ( n ) > C · 2 10 n 26 / 37

  81. Introduction Our Model Experiments Ambiguity Conclusion Appendix Counting Number of Encodings How many canonical encodings do the models have? For the baseline: There are 7 possible tags per word (B, I, BD, ID, BH, IH, O) The model can output any combination of those: 7 n Not all are canonical, so: M Li ( n ) < 7 n < 2 3 n For our hypergraph-based model: Number of canonical encoding = number of subgraphs After more calculations: M Sh ( n ) > C · 2 10 n So our model is less ambiguous compared to the baseline model 26 / 37

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