Outline. Parsing. Approximations Some tricks Learning agenda-based parsers

Transcription

1 Outline Parsing CKY Approximations Some tricks Learning agenda-based parsers 0

2 Parsing We need to compute compute argmax d D(x) p θ (d x) Inference: Find best tree given model 1

3 Parsing We need to compute compute argmax d D(x) p θ (d x) Inference: Find best tree given model E qθ (d x)[φ(x, d)] E pθ (d x)[φ(x, d)] Learning: Computing gradient O(θ) = E qθ (d x)[φ(x, d)] E pθ (d x)[φ(x, d)] 1

4 Outline Parsing CKY Approximations Some tricks Learning agenda-based parsers 2

5 Finding best tree Can we use CKY? Only if f(x, y) = r d g(x, r) θ r = (A, B, C, i, j, k) is a rule production Why not? is g sufficient? 3

6 Finding best tree Maybe we can only have type features? Root :WonElection(Type(Country)) Root :WonAward(Type(Country)) Binary :WonElection Set :Type(Country) Binary :WonAward Set :Type(Country) won country won country Type features: binary-unary type match 4

7 Finding best tree Maybe we can only have type features? Root :WonElection(Type(Country)) Root :WonAward(Type(Country)) Binary :WonElection Set :Type(Country) Binary :WonAward Set :Type(Country) won country won country Type features: binary-unary type match We can get exact decoding if augment state: Binary-Person-Country, Binary-Person-Award, Set-Country, Set-Award Explosion in grammar size! If number of types is T, then N grows by at least T 2 4

8 Finding best tree In practice many features depend on the logical form itself Bridging features If we could hold the logical form as part of the state we could use dynamic programming, but usually that is not possible 5

9 E qθ (d x)[φ(x, d)] = d D(x) Logical form features exp(φ(x,d) θ) R(d) φ(x, d) d exp(φ(x,d ) θ) R(d ) R(d) depends on entire logical form - too large! 6

10 E qθ (d x)[φ(x, d)] = d D(x) Logical form features exp(φ(x,d) θ) R(d) φ(x, d) d exp(φ(x,d ) θ) R(d ) R(d) depends on entire logical form - too large! Do approximate inference! 6

11 Outline Parsing CKY Approximations Some tricks Learning agenda-based parsers 7

12 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways abraham lincoln born in 8

13 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways 20 abraham lincoln born in 8

14 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K abraham lincoln born in 8

15 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K 20 abraham lincoln born in 8

16 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K abraham lincoln born in 8

17 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K 391 abraham lincoln born in 8

18 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K abraham lincoln born in 8

19 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K 508 abraham lincoln born in 8

20 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K abraham lincoln born in 8

21 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K 2 K K abraham lincoln K born K in 8

22 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K abraham lincoln K born K in 8

23 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K 2 K K K K abraham lincoln born in 8

24 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K abraham lincoln born in 8

25 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K 2 K K K K abraham lincoln born in 8

26 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K K abraham lincoln born in 8

27 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K 2 K K K K K K K abraham lincoln born in 8

28 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K K K abraham lincoln born in 8

29 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K 2 K K K K K K K abraham lincoln born in 8

30 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K K K K abraham lincoln born in 8

31 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K 2 K K K K K K K K K abraham lincoln born in 8

32 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K K K K K abraham lincoln born in 8

33 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K K K K K abraham lincoln born in Building a chart cell is now O(K 2 + L) and not O(1) 8

34 Beam parsing Keep top-k derivations in every chart cell Combine chart cells in all possible ways K K K K K K K K K K abraham lincoln born in Building a chart cell is now O(K 2 + L) and not O(1) Assume root beam ˆD(x) D(x) E pθ [φ(x, d)] = d ˆD(x) p θ(d)φ(x, d) E qθ [φ(x, d)] = d ˆD(x) q θ(d)φ(x, d) 8

35 Beam Parsing variants Keep top-k for every span (i, j) and category A Keep top-k for every span (i, j) 9

36 Beam Parsing variants Keep top-k for every span (i, j) and category A Keep top-k for every span (i, j) Prune cell with probability ratio 9

37 Beam Parsing variants Keep top-k for every span (i, j) and category A Keep top-k for every span (i, j) Prune cell with probability ratio for α = 10: [0.6, 0.2, 0.1, 0.05, 0.03, 0.02] 9

38 Beam Parsing variants Keep top-k for every span (i, j) and category A Keep top-k for every span (i, j) Prune cell with probability ratio for α = 10: [0.6, 0.2, 0.1] 9

39 Beam Parsing variants Keep top-k for every span (i, j) and category A Keep top-k for every span (i, j) Prune cell with probability ratio for α = 10: [0.6, 0.2, 0.1] Learn a classifier that predict K for every chart cell, [Bodenstab et al., 2011] 9

40 Outline Parsing CKY Approximations Some tricks Learning agenda-based parsers 10

41 Coarse pruning Most of parsing time is in building logical forms and extracting features Extracting lexical items Executing logical forms Suggesting binary predicates for bridging Do 2-pass parsing. First only recognizing chart cells (without feature extraction), and then again pruning unnecessary chrat cells 11

42 Coarse pruning 1. Build derivations without logical forms and features (one derivation per rule application) - fast! 12

43 Coarse pruning 1. Build derivations without logical forms and features (one derivation per rule application) - fast! 2. Record cell reachability for every rule application: (A, i, j) (B, i, k), (C, k, j) 12

44 Coarse pruning 1. Build derivations without logical forms and features (one derivation per rule application) - fast! 2. Record cell reachability for every rule application: (A, i, j) (B, i, k), (C, k, j) 3. Collect all chart cells that are reachable from (S, 1, n) 12

45 Coarse pruning 1. Build derivations without logical forms and features (one derivation per rule application) - fast! 2. Record cell reachability for every rule application: (A, i, j) (B, i, k), (C, k, j) 3. Collect all chart cells that are reachable from (S, 1, n) 4. Parse again ignoring unreachable states 12

46 Coarse pruning 1. Build derivations without logical forms and features (one derivation per rule application) - fast! 2. Record cell reachability for every rule application: (A, i, j) (B, i, k), (C, k, j) 3. Collect all chart cells that are reachable from (S, 1, n) 4. Parse again ignoring unreachable states We know unreachable states do not contribute to root derivations over sentence 12

47 Coarse parsing Root Root Root Binary 0.9 Set 0.7 won Binary 0.1 Set 0.3 Mod 1.0 Conj 1.0 country 13

48 Coarse parsing Root Root Root Binary 0.9 Set 0.7 won Binary 0.1 Set 0.3 Mod 1.0 Conj 1.0 country π(0, 2, Root) (π(0, 1, Binary), π(1, 2, Set)) (π(0, 1, Set), π(1, 2, Binary)) (π(0, 1, Set), π(1, 2, Mod)) π(0, 1, Binary) π(0, 1, Set) π(1, 2, Binary) π(1, 2, Set) π(1, 2, Mod) π(1, 2, Conj) 13

49 Unary rules in CKY Unary rules are convenient when desinging grammars Set Entity Set Unary 14

50 Unary rules in CKY Unary rules are convenient when desinging grammars Set Entity Set Unary Assume: rules A B and B C A derivation d C i:j Computing π(i, j, A) before π(i, j, B) Why this fails? 14

51 Unary rules Solution: Construct an acyclic (!) directed graph G = (V, E): V = N E are unary rules B A D C 15

52 Unary rules Solution: Construct an acyclic (!) directed graph G = (V, E): V = N E are unary rules A B D Sort topolocially edges and apply rules from end to start after binary rules Guaranteed to apply B C before A B C 15

53 Unary rules Solution: Construct an acyclic (!) directed graph G = (V, E): V = N E are unary rules A B D Sort topolocially edges and apply rules from end to start after binary rules Guaranteed to apply B C before A B Need to verify grammar has no unary cycles 15 C

54 Outline Parsing CKY Approximations Some tricks Learning agenda-based parsers 16

55 [Daume et al., 2009; Ross et al., 2011; Jiang et al., 2012, Goldberg & Nivre, 2013] Learning to search We have a globaly-normalized model, but our search procedure is inexact and slow Perhaps we can make it faster with transition-style methods? Let s try to change the learning problem so that we explicitly learn to search 17

56 Fixed-order beam parsing abraham lincoln born in 18

57 Fixed-order beam parsing 20 abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... 18

58 Fixed-order beam parsing K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... 18

59 Fixed-order beam parsing K 20 abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... 18

60 Fixed-order beam parsing K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... 18

61 Fixed-order beam parsing K K 391 abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... 18

62 Fixed-order beam parsing K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... 18

63 Fixed-order beam parsing K K K 508 abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... 18

64 Fixed-order beam parsing K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... 18

65 Fixed-order beam parsing K 2 K K abraham lincoln K born K in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... 18

66 Fixed-order beam parsing K K K abraham lincoln K born K in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... 18

67 Fixed-order beam parsing K K 2 K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

68 Fixed-order beam parsing K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

69 Fixed-order beam parsing K K K 2 K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

70 Fixed-order beam parsing K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

71 Fixed-order beam parsing K 2 K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

72 Fixed-order beam parsing K K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

73 Fixed-order beam parsing K K 2 K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

74 Fixed-order beam parsing K K K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

75 Fixed-order beam parsing K 2 K K K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

76 Fixed-order beam parsing K K K K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... 18

77 Fixed-order beam parsing K K K K K K K K K K abraham lincoln born in (lexicon) Set Phrase Abraham, AbeLincoln, AbrahamFilm,... (lexicon) Set Phrase AbeLincoln, LincolTown, LincolnFilm,... (lexicon) Binary Phrase BirthPlaceOf, BirthDateOf, ReleaseDateOf,... (lexicon) Set Phrase BornBelgium, BornThisWay, BornAlbum,... (inters) Set Set Set AbeLincoln AbeLincoln,... (join) Set Set Binary BirthPlaceOf.AbeLincoln, ReleaseDateOf.LincolnFilm,... Many improbable derivations generated 18

78 Goal: control parsing order abraham lincoln born in 19

79 Goal: control parsing order 1 abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln 19

80 Goal: control parsing order 2 abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument 19

81 Goal: control parsing order 2 1 abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln 19

82 Goal: control parsing order 2 1 abraham lincoln 1 born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf 19

83 Goal: control parsing order 2 1 abraham lincoln 2 born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf 19

84 Goal: control parsing order 2 1 abraham lincoln 3 born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded 19

85 Goal: control parsing order abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded (skip) Binary Binary Token born in BirthPlaceOf 19

86 Goal: control parsing order abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded (skip) Binary Binary Token born in BirthPlaceOf (skip) Binary Binary Token born in BirthDate 19

87 Goal: control parsing order abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded (skip) Binary Binary Token born in BirthPlaceOf (skip) Binary Binary Token born in BirthDate (skip) Binary Binary Token born in OrganizationFounded 19

88 Goal: control parsing order abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded (skip) Binary Binary Token born in BirthPlaceOf (skip) Binary Binary Token born in BirthDate (skip) Binary Binary Token born in OrganizationFounded (join) Set Set Binary BirthPlaceOf.AbeLincoln 19

89 Goal: control parsing order abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded (skip) Binary Binary Token born in BirthPlaceOf (skip) Binary Binary Token born in BirthDate (skip) Binary Binary Token born in OrganizationFounded (join) Set Set Binary BirthPlaceOf.AbeLincoln (join) Set Set Binary BirthDateOf.AbeLincoln 19

90 Goal: control parsing order K abraham lincoln born in (lexicon) Set Phrase abraham lincoln AbeLincoln (lexicon) Set Phrase abraham lincon LincolnMonument (lexicon) Set Phrase lincon AbeLincoln (lexicon) Binary Phrase born BirthPlaceOf (lexicon) Binary Phrase born BirthDateOf (lexicon) Binary Phrase born OrganizationFounded (skip) Binary Binary Token born in BirthPlaceOf (skip) Binary Binary Token born in BirthDate (skip) Binary Binary Token born in OrganizationFounded (join) Set Set Binary BirthPlaceOf.AbeLincoln (join) Set Set Binary BirthDateOf.AbeLincoln 19

91 20

92 Agenda-based parsing Control order of derivation generation! [Kay, 1986; Klein and Manning, 2003; Pauls and Klein, 2009] agenda + chart 21

93 Agenda-based parsing Control order of derivation generation! [Kay, 1986; Klein and Manning, 2003; Pauls and Klein, 2009] Parsing action agenda + chart Choose derivation (based on p θ (d x)) 21

94 Agenda-based parsing [Kay, 1986; Klein and Manning, 2003; Pauls and Klein, 2009] Control order of derivation generation! agenda + chart Parsing action Choose derivation (based on p θ (d x)) Execute action: Add derivation to chart 21

95 Agenda-based parsing [Kay, 1986; Klein and Manning, 2003; Pauls and Klein, 2009] Control order of derivation generation! Parsing action agenda + chart Choose derivation (based on p θ (d x)) Execute action: Add derivation to chart Combine and add to agenda 21

96 Agenda-based parsing [Kay, 1986; Klein and Manning, 2003; Pauls and Klein, 2009] Control order of derivation generation! Parsing action agenda + chart Choose derivation (based on p θ (d x)) Execute action: Add derivation to chart Combine and add to agenda Stop when K root derivations, rerank, and return best 21

97 Learning a scoring function Scoring function: A distribution over full derivations p θ (d x): Type.City PlaceOfBirth.AbeLincoln intersect Type.Loc ContainedBy.LincolnTown intersect Type.City PlaceOfBirth.AbeLincoln intersect Type.Loc ContainedBy.LincolnTown intersect Type.City PlaceOfBirth.AbeLincoln intersect what Type.City lexicon was PlaceOfBirth.AbeLincoln join what Type.Loc lexicon was ContainedBy.LincolnTown join what Type.City lexicon was PlaceOfBirth.AbeLincoln join what Type.Loc lexicon was ContainedBy.LincolnTown join what Type.City lexicon was PlaceOfBirth.AbeLincoln join city AbeLincoln PlaceOfBirth city LincolnTown ContainedBy city AbeLincoln PlaceOfBirth city LincolnTown ContainedBy city AbeLincoln PlaceOfBirth lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon abraham lincoln born in abraham lincoln born in abraham lincoln born in abraham lincoln born in abraham lincoln born in 22

98 Learning a scoring function Scoring function: A distribution over full derivations p θ (d x): Type.City PlaceOfBirth.AbeLincoln intersect Type.Loc ContainedBy.LincolnTown intersect Type.City PlaceOfBirth.AbeLincoln intersect Type.Loc ContainedBy.LincolnTown intersect Type.City PlaceOfBirth.AbeLincoln intersect what Type.City lexicon was PlaceOfBirth.AbeLincoln join what Type.Loc lexicon was ContainedBy.LincolnTown join what Type.City lexicon was PlaceOfBirth.AbeLincoln join what Type.Loc lexicon was ContainedBy.LincolnTown join what Type.City lexicon was PlaceOfBirth.AbeLincoln join city AbeLincoln PlaceOfBirth city LincolnTown ContainedBy city AbeLincoln PlaceOfBirth city LincolnTown ContainedBy city AbeLincoln PlaceOfBirth lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon abraham lincoln born in abraham lincoln born in abraham lincoln born in abraham lincoln born in abraham lincoln born in But search over partial derivations: LincolnTown USSLincoln BirthplaceOf.Lincoln lincoln lincoln AbeLincoln BirthplaceOf lincoln born in 22

99 Learning a scoring function Scoring function: A distribution over full derivations p θ (d x): Type.City PlaceOfBirth.AbeLincoln intersect Type.Loc ContainedBy.LincolnTown intersect Type.City PlaceOfBirth.AbeLincoln intersect Type.Loc ContainedBy.LincolnTown intersect Type.City PlaceOfBirth.AbeLincoln intersect what Type.City lexicon was PlaceOfBirth.AbeLincoln join what Type.Loc lexicon was ContainedBy.LincolnTown join what Type.City lexicon was PlaceOfBirth.AbeLincoln join what Type.Loc lexicon was ContainedBy.LincolnTown join what Type.City lexicon was PlaceOfBirth.AbeLincoln join city AbeLincoln PlaceOfBirth city LincolnTown ContainedBy city AbeLincoln PlaceOfBirth city LincolnTown ContainedBy city AbeLincoln PlaceOfBirth lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon lexicon abraham lincoln born in abraham lincoln born in abraham lincoln born in abraham lincoln born in abraham lincoln born in But search over partial derivations: LincolnTown USSLincoln BirthplaceOf.Lincoln lincoln lincoln AbeLincoln BirthplaceOf lincoln born in Idea: learn explcitly to make good search choices 22

100 Markov Decision Process [Sutton et al., 1999] s 1 state s derivations on chart and agenda 23

101 Markov Decision Process [Sutton et al., 1999] s 1 s 2 a 1 state s derivations on chart and agenda action a choosing an agenda derivation p θ (a s) 23

102 Markov Decision Process [Sutton et al., 1999] s 1 s 2 s 3 s T +1 a 1 a 2 a 3 a T... state s derivations on chart and agenda action a choosing an agenda derivation p θ (a s) History h = (s 1, a 1,..., a T, s T +1 ) p θ (h) = T t=1 p(a t s t ) 23

103 Markov Decision Process [Sutton et al., 1999] s 1 s 2 s 3 s T +1 a 1 a 2 a 3 a T... state s derivations on chart and agenda action a choosing an agenda derivation p θ (a s) History h = (s 1, a 1,..., a T, s T +1 ) p θ (h) = T t=1 p(a t s t ) Objective: O(θ) = E pθ [Acc(h)] = h p θ(h)acc(h) Explicitly model all parsing actions in all states. 23

104 Learning is hard! s t 1 s t s t+1 a t 1 a t O(θ) = E pθ (h) [ Acc(h) ] T t=1 log p θ(a t s t ) 24

105 Learning is hard! s t 1 s t s t+1 a t 1 a t O(θ) = E pθ (h) Challenge: [ Acc(h) ] T t=1 log p θ(a t s t ) Sampling from p θ leads to slow learning. 24

106 Learning is hard! s t 1 s t s t+1 a t 1 a t O(θ) = E pθ (h) Challenge: [ Acc(h) ] T t=1 log p θ(a t s t ) Sampling from p θ leads to slow learning. Imitation Learning: follow a proposal distribution. 24

107 Proposal distribution - local reweighting Assume a oracle d : e β e β d q θ (a s) p θ (a s) exp[β I[a in d ]] 25

108 Proposal distribution - local reweighting Assume a oracle d : e β e β d q θ (a s) p θ (a s) exp[β I[a in d ]] Prefer sampling from oracle sub-derivations 25

109 Proposal distribution - compression a 4 = d a 1 a 3 h : a 1 a 2 a 3 a 4 s 1 s 2 s 3 s 4 s 5 compressed history c(h) = (s 1, a 1, s 3, a 3, s 4, a 4 ) 26

110 Proposal distribution - compression a 4 = d a 1 a 3 h : a 1 a 2 a 3 a 4 s 1 s 2 s 3 s 4 s 5 compressed history c(h) = (s 1, a 1, s 3, a 3, s 4, a 4 ) q θ (h) = h :c(h )=h p θ(h) 26

111 Proposal distribution - compression a 4 = d a 1 a 3 h : a 1 a 2 a 3 a 4 s 1 s 2 s 3 s 4 s 5 compressed history c(h) = (s 1, a 1, s 3, a 3, s 4, a 4 ) q θ (h) = h :c(h )=h p θ(h) Ignore non-oracle actions 26

112 Proposal distribution city lincoln born Hodgenville, KY 27

113 Proposal distribution city lincoln born Hodgenville, KY H H KY 27

114 Proposal distribution city lincoln born Hodgenville, KY H H KY d Type.CityTown BirthPlaceOf.ABeLincoln Type.CityTown BirthPlaceOf.ABeLincoln city ABeLincoln BirthPlaceOf lincoln born 27

115 Proposal distribution city lincoln born Hodgenville, KY H H KY d Type.CityTown BirthPlaceOf.ABeLincoln Type.CityTown BirthPlaceOf.ABeLincoln Prefer sampling subtrees of d city ABeLincoln BirthPlaceOf lincoln born 27

116 Learning Input: {x i, y i } n i=1 Output: θ 28

117 Learning Input: {x i, y i } n i=1 Output: θ θ 0 28

118 Learning Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i h 0 parse x i sampling from model distribution 28

119 Learning Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i h 0 parse x i sampling from model distribution d choose oracle from h 0 28

120 Learning Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i h 0 parse x i sampling from model distribution d choose oracle from h 0 h parse x i sampling from proposal distribution 28

121 Learning Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i h 0 parse x i sampling from model distribution d choose oracle from h 0 h parse x i sampling from proposal distribution Update θ using proposed history h 28

122 Learning Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i h 0 parse x i sampling from model distribution d choose oracle from h 0 h parse x i sampling from proposal distribution Update θ using proposed history h Test time: standard agenda-based parsing 28

123 Summary Agenda-based parsing Learning to search Oracle (imitation learning) guides learning 29

124 Evaluation: WebQuestions dataset [Berant et al. 2013] What character did Natalie Portman play in Star Wars? Padmé Amidala What kind of money to take to Bahamas? Bahamian dollar What currency do you use in Costa Rica? Costa Rican colón What did Obama study in school? political science What do Michelle Obama do for a living? writer, lawyer What killed Sammy Davis Jr? throat cancer 30

125 Comparison with beam parsing (test) Test Train actions Time (ms) +learn +parse AgendaIL , learn -parse FixedOrder ,127 1,782 Comparable accuarcy 13 times fewer actions 6 times faster 31

126 Learning analysis (dev) Dev actions Time (ms) +learn +parse AgendaIL , learn -parse FixedOrder ,259 1,972 -learn +parse Agenda , AgendaIL is faster and better 32

127 Beam size analysis (dev) 33

128 WebQuestions SOTA [Yao, 2015] [Yih et al., 2015] [BH, 2015] [this work] [Reddy et al., 2016] [Yih et al., 2015] 34