an hdp model for inducing combinatory categorial grammars
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An HDP Model for Inducing Combinatory Categorial Grammars Yonatan Bisk & Julia Hockenmaier University of Illinois at Urbana-Champaign TACL Vol 1(2013):75 88 1 Thursday, June 13, 13 PRP VBD ADJ NN She ate crunchy granola 2

  1. Parameters for X i → X j X k X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 ... ? ? ? ? ? ? ? ? ? ? X 1 ? ? ? ? ? ? ? ? ? ? X 2 ? ? ? ? ? ? ? ? ? ? X 3 ? ? ? ? ? ? ? ? ? ? X 4 ? ? ? ? ? ? ? ? ? ? X 5 ? ? ? ? ? ? ? ? ? ? X 6 ? ? ? ? ? ? ? ? ? ? X 7 ? ? ? ? ? ? ? ? ? ? X 8 ? ? ? ? ? ? ? ? ? ? X 9 ... ? ? ? ? ? ? ? ? ? ? 23 Thursday, June 13, 13

  2. Parameters for X i → X j X k Problem for nonparametric PCFG models: X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 ... ? ? ? ? ? ? ? ? ? ? X 1 ? ? ? ? ? ? ? ? ? ? X 2 Each LHS nonterminal X i ? ? ? ? ? ? ? ? ? ? X 3 is allowed a ? ? ? ? ? ? ? ? ? ? X 4 ? ? ? ? ? ? ? ? ? ? X 5 doubly infinite ? ? ? ? ? ? ? ? ? ? X 6 cross-product ? ? ? ? ? ? ? ? ? ? X 7 ? ? ? ? ? ? ? ? ? ? X 8 of RHS children X j , X k ? ? ? ? ? ? ? ? ? ? X 9 ... ? ? ? ? ? ? ? ? ? ? 23 Thursday, June 13, 13

  3. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? ? ? ? ? ? ? ? ? ? S ? ? ? ? ? ? ? ? ? ? N ? ? ? ? ? ? ? ? ? ? S/S ? ? ? ? ? ? ? ? ? ? S\S ? ? ? ? ? ? ? ? ? ? S/N ? ? ? ? ? ? ? ? ? ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  4. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? ? ? ? ? ? ? ? ? ? N ? ? ? ? ? ? ? ? ? ? S/S ? ? ? ? ? ? ? ? ? ? S\S ? ? ? ? ? ? ? ? ? ? S/N ? ? ? ? ? ? ? ? ? ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  5. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? ? ? ? ? ? ? ? ? ? S/S ? ? ? ? ? ? ? ? ? ? S\S ? ? ? ? ? ? ? ? ? ? S/N ? ? ? ? ? ? ? ? ? ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  6. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? S/S ? ? ? ? ? ? ? ? ? ? S\S ? ? ? ? ? ? ? ? ? ? S/N ? ? ? ? ? ? ? ? ? ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  7. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? S/S S\S ? ? ? ? ? ? ? ? ? ? S/N ? ? ? ? ? ? ? ? ? ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  8. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? S/S S\S S/N ? ? ? ? ? ? ? ? ? ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  9. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? S/S S\S S/N ? S\N ? ? ? ? ? ? ? ? ? ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  10. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? S/S S\S S/N ? S\N ? (S\N)/N ? ? ? ? ? ? ? ? ? ? (S\N)\S ? ? ? ? ? ? ? ? ? ? (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  11. Parameters for S\N → ... ... S N S/S S\S S/N S\N (S\N)/N (S\N)\S (S\N)\N ... ? S ? N ? S/S S\S S/N ? S\N ? (S\N)/N (S\N)\S (S\N)\N ... ? ? ? ? ? ? ? ? ? ? 24 Thursday, June 13, 13

  12. CCG rules 25 Thursday, June 13, 13

  13. CCG rules Parent Combinator Left Right (S\N)/N N >B ((S\N)/N)/Y Y (S\N)/N /N (S\N)/N \N)/N (S\N)/N ((S\N)/N)\Y (S\N)/N (S\N)\Y (S\N)/N S\Y 25 Thursday, June 13, 13

  14. CCG rules Parent Combinator Left Right (S\N)/N N >B 0 ((S\N)/N)/Y Y (S\N)/N >B (S\N)/Y Y/N (S\N)/N \N)/N (S\N)/N ((S\N)/N)\Y (S\N)/N (S\N)\Y (S\N)/N S\Y 25 Thursday, June 13, 13

  15. CCG rules Parent Combinator Left Right (S\N)/N N >B 0 ((S\N)/N)/Y Y (S\N)/N >B 1 (S\N)/Y Y/N (S\N)/N >B S\Y (Y\N)/N (S\N)/N ((S\N)/N)\Y (S\N)/N (S\N)\Y (S\N)/N S\Y 25 Thursday, June 13, 13

  16. CCG rules Parent Combinator Left Right (S\N)/N N >B 0 ((S\N)/N)/Y Y (S\N)/N >B 1 (S\N)/Y Y/N (S\N)/N >B 2 S\Y (Y\N)/N (S\N)/N <B Y ((S\N)/N)\Y (S\N)/N (S\N)\Y (S\N)/N S\Y 25 Thursday, June 13, 13

  17. CCG rules Parent Combinator Left Right (S\N)/N N >B 0 ((S\N)/N)/Y Y (S\N)/N >B 1 (S\N)/Y Y/N (S\N)/N >B 2 S\Y (Y\N)/N (S\N)/N <B 0 Y ((S\N)/N)\Y (S\N)/N <B Y/N (S\N)\Y (S\N)/N S\Y 25 Thursday, June 13, 13

  18. CCG rules Parent Combinator Left Right (S\N)/N N >B 0 ((S\N)/N)/Y Y (S\N)/N >B 1 (S\N)/Y Y/N (S\N)/N >B 2 S\Y (Y\N)/N (S\N)/N <B 0 Y ((S\N)/N)\Y (S\N)/N <B 1 Y/N (S\N)\Y (S\N)/N <B (Y\N)/N S\Y 25 Thursday, June 13, 13

  19. CCG rules Parent Combinator Left Right (S\N)/N N >B 0 ((S\N)/N)/Y Y (S\N)/N >B 1 (S\N)/Y Y/N (S\N)/N >B 2 S\Y (Y\N)/N (S\N)/N <B 0 Y ((S\N)/N)\Y (S\N)/N <B 1 Y/N (S\N)\Y (S\N)/N <B 2 (Y\N)/N S\Y 25 Thursday, June 13, 13

  20. CCG rules 26 Thursday, June 13, 13

  21. CCG rules Parent Y (S\N)/N S (S\N)/N S (S\N)/N S (S\N)/N S (S\N)/N S (S\N)/N S 26 Thursday, June 13, 13

  22. CCG rules Parent Y Combinator (S\N)/N S (S\N)/N S (S\N)/N S (S\N)/N S (S\N)/N S (S\N)/N S 26 Thursday, June 13, 13

  23. CCG rules Parent Y Combinator Left (S\N)/N S >B 0 ((S\N)/N)/ (S\N)/N S >B 1 (S\N)/ (S\N)/N S >B 2 S\ (S\N)/N S <B 0 S (S\N)/N S <B 1 S/N (S\N)/N S <B 2 (S\N)/N 26 Thursday, June 13, 13

  24. CCG rules Parent Y Combinator Left Right (S\N)/N S >B 0 ((S\N)/N)/S S (S\N)/N S >B 1 (S\N)/S S/N (S\N)/N S >B 2 S\S (S\N)/N (S\N)/N S <B 0 S ((S\N)/N)\S (S\N)/N S <B 1 S/N (S\N)\S (S\N)/N S <B 2 (S\N)/N S\S 26 Thursday, June 13, 13

  25. CCG rules Parent Y Combinator Left Right (S\N)/N S >B 0 ((S\N)/N)/S S CCG rules are (S\N)/N S >B 1 (S\N)/S S/N heavily constrained: (S\N)/N S >B 2 S\S (S\N)/N (S\N)/N S <B 0 S ((S\N)/N)\S For a given parent category, (S\N)/N S <B 1 S/N (S\N)\S (S\N)/N S <B 2 (S\N)/N S\S the Y category and combinator determine both children 26 Thursday, June 13, 13

  26. HDPs for CCGs 27 Thursday, June 13, 13

  27. HDPs for CCGs S 27 Thursday, June 13, 13

  28. HDPs for CCGs Y = N S Combinator = <B 0 27 Thursday, June 13, 13

  29. HDPs for CCGs Y = N S Combinator = <B 0 S\N N 27 Thursday, June 13, 13

  30. HDPs for CCGs S S\N N 27 Thursday, June 13, 13

  31. HDPs for CCGs Y = N S Combinator = >B 0 S\N S\N N N (S\N)/N 27 Thursday, June 13, 13

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