Outline. Learning. Overview Details

Transcription

1 Outline Learning Overview Details 0

2 Outline Learning Overview Details 1

3 Supervision in syntactic parsing Input: S NP VP NP NP V VP ESSLLI 2016 the known summer school is V PP located in Bolzano Output: S They play football NP They V VP NP play football 2

4 [Zelle & Mooney, 1996; Zettlemoyer & Collins, 2005; Clarke et al. 2010; Liang et al., 2011] Supervision in semantic parsing Input: Heavy supervision How tall is Lebron James? HeightOf.LebronJames What is Steph Curry s daughter called? ChildrenOf.StephCurry Gender.Female Youngest player of the Cavaliers arg min(playerof.cavaliers, BirthDateOf)... Light supervision How tall is Lebron James? 203cm What is Steph Curry s daughter called? Riley Curry Youngest player of the Cavaliers Kyrie Irving... 3

5 [Zelle & Mooney, 1996; Zettlemoyer & Collins, 2005; Clarke et al. 2010; Liang et al., 2011] Supervision in semantic parsing Input: Heavy supervision How tall is Lebron James? HeightOf.LebronJames What is Steph Curry s daughter called? ChildrenOf.StephCurry Gender.Female Youngest player of the Cavaliers arg min(playerof.cavaliers, BirthDateOf)... Light supervision How tall is Lebron James? 203cm What is Steph Curry s daughter called? Riley Curry Youngest player of the Cavaliers Kyrie Irving... Output: WeightOf.ClayThompson Clay Thompson s weight ClayThompson s Weight Weight.ClayThompson 205 lbs Clay Thompson weight 3

6 Learning in a nutshell utterance 0. Define model for derivations 4

7 Learning in a nutshell utterance Parsing. 0. Define model for derivations 1. Generate candidate derivations (later) 4

8 Learning in a nutshell utterance Parsing.. Label 0. Define model for derivations 1. Generate candidate derivations (later) 2. Label as correct and incorrect 4

9 Learning in a nutshell utterance Parsing.. Label Update model 0. Define model for derivations 1. Generate candidate derivations (later) 2. Label as correct and incorrect 3. Update model to favor correct trees 4

10 Training intuition Where did Mozart tupress? Vienna 5

11 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna 5

12 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna 5

13 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna 5

14 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna Where did Hogarth tupress? 5

15 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna Where did Hogarth tupress? PlaceOfBirth.WilliamHogarth PlaceOfDeath.WilliamHogarth PlaceOfMarriage.WilliamHogarth London 5

16 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna Where did Hogarth tupress? PlaceOfBirth.WilliamHogarth London PlaceOfDeath.WilliamHogarth London PlaceOfMarriage.WilliamHogarth Paddington London 5

17 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna Where did Hogarth tupress? PlaceOfBirth.WilliamHogarth London PlaceOfDeath.WilliamHogarth London PlaceOfMarriage.WilliamHogarth Paddington London 5

18 Training intuition Where did Mozart tupress? PlaceOfBirth.WolfgangMozart PlaceOfDeath.WolfgangMozart PlaceOfMarriage.WolfgangMozart Vienna Salzburg Vienna Vienna Where did Hogarth tupress? PlaceOfBirth.WilliamHogarth London PlaceOfDeath.WilliamHogarth London PlaceOfMarriage.WilliamHogarth Paddington London 5

19 Outline Learning Overview Details 6

20 Constructing derivations Type.Person PlaceLived.Chicago intersect Type.Person lexicon who PlaceLived.Chicago join people PlaceLived lived in lexicon Chicago Chicago lexicon 7

21 Many possible derivations! x = people who have lived in Chicago? set of candidate derivations D(x) Type.Person PlaceLived.Chicago intersect Type.Org PresentIn.ChicagoMusical intersect Type.Person lexicon who PlaceLived.Chicago join Type.Org lexicon who PresentIn.ChicagoMusical join people PlaceLived Chicago people PresentIn ChicagoMusical lexicon lexicon lexicon lexicon lived in Chicago lived in Chicago 8

22 Type.Person PlaceLived.Chicago intersect x: utterance d: derivation Type.Person people lexicon who PlaceLived.Chicago join PlaceLived Chicago lived in lexicon Chicago lexicon Feature vector and parameters in R F : φ(x, d) θ learned apply join apply intersect apply lexicon lived maps to PlacesLived lived maps to PlaceOfBirth born maps to PlaceOfBirth

23 Type.Person PlaceLived.Chicago intersect x: utterance d: derivation Type.Person people lexicon who PlaceLived.Chicago join PlaceLived Chicago lived in lexicon Chicago lexicon Feature vector and parameters in R F : φ(x, d) θ learned apply join apply intersect apply lexicon lived maps to PlacesLived lived maps to PlaceOfBirth born maps to PlaceOfBirth Score θ (x, d) = φ(x, d) θ =

24 Deep learning alert! The feature vector φ(x, d) is constructed by hand 10

25 Deep learning alert! The feature vector φ(x, d) is constructed by hand Constructing good features is hard 10

26 Deep learning alert! The feature vector φ(x, d) is constructed by hand Constructing good features is hard Algorithms are likely to do it better 10

27 Deep learning alert! The feature vector φ(x, d) is constructed by hand Constructing good features is hard Algorithms are likely to do it better Perhaps we can train φ(x, d) φ(x, d) = F ψ (x, d), where ψ are the parameters 10

28 Candidate derivations: D(x) Log-linear model Model: distribution over derivations d given utterance x p θ (d x) = exp(score θ (x,d)) d D(x) exp(score θ(x,d )) 11

29 Candidate derivations: D(x) Log-linear model Model: distribution over derivations d given utterance x p θ (d x) = exp(score θ (x,d)) d D(x) exp(score θ(x,d )) score θ (x, d) [1, 2, 3, 4] p θ (d x) [ e e+e 2 +e 3 +e 4, e 2 e+e 2 +e 3 +e 4, e 3 e+e 2 +e 3 +e 4, e 4 e+e 2 +e 3 +e 4 ] 11

30 Candidate derivations: D(x) Log-linear model Model: distribution over derivations d given utterance x p θ (d x) = exp(score θ (x,d)) d D(x) exp(score θ(x,d )) score θ (x, d) [1, 2, 3, 4] p θ (d x) [ e e+e 2 +e 3 +e 4, e 2 e+e 2 +e 3 +e 4, e 3 e+e 2 +e 3 +e 4, e 4 e+e 2 +e 3 +e 4 ] Parsing: find the top-k derivation trees D θ (x) 11

31 Features Dense features: intersection=0.67 ent-popularity:high denoation-size:1 12

32 Features Dense features: intersection=0.67 ent-popularity:high denoation-size:1 Sparse features: bridge-binary:study born:placeofbirth city:type.location 12

33 Features Dense features: intersection=0.67 ent-popularity:high denoation-size:1 Sparse features: bridge-binary:study born:placeofbirth city:type.location Syntactic features: ent-pos:nnp NNP join-pos:v NN skip-pos:in 12

34 Features Dense features: intersection=0.67 ent-popularity:high denoation-size:1 Sparse features: bridge-binary:study born:placeofbirth city:type.location Syntactic features: ent-pos:nnp NNP join-pos:v NN skip-pos:in Grammar features: Binary->Verb 12

35 Learning θ: marginal maximum-likelihood Training data: What s Bulgaria s capital? Sofia What movies has Tom Cruise been in? TopGun,VanillaSky, What s Bulgaria s capital? CapitalOf.Bulgaria What movies has Tom Cruise been in? Type.Movie HasPlayed.TomCruise... 13

36 Learning θ: marginal maximum-likelihood Training data: What s Bulgaria s capital? Sofia What movies has Tom Cruise been in? TopGun,VanillaSky, What s Bulgaria s capital? CapitalOf.Bulgaria What movies has Tom Cruise been in? Type.Movie HasPlayed.TomCruise... arg max θ n i=1 log p θ(y (i) x (i) ) = arg max θ n i=1 log d (i) p θ (d (i) x (i) )R(d (i) ) 13

37 Learning θ: marginal maximum-likelihood Training data: What s Bulgaria s capital? Sofia What movies has Tom Cruise been in? TopGun,VanillaSky, What s Bulgaria s capital? CapitalOf.Bulgaria What movies has Tom Cruise been in? Type.Movie HasPlayed.TomCruise... arg max θ n i=1 log p θ(y (i) x (i) ) = arg max θ n i=1 log d (i) p θ (d (i) x (i) )R(d (i) ) R(d) = { 1 d.z = z (i) 0 o/w R(d) = { 1 [d.z] K = y (i) 0 o/w R(d) = F 1 ([d.z] K, y (i) ) 13

38 Optimization: stochastic gradient descent For every example: O(θ) = log d p θ(d x)r(d) O(θ) = E qθ (d x)[φ(x, d)] E pθ (d x)[φ(x, d)] p θ (d x) exp(φ(x, d) θ) q θ (d x) exp(φ(x, d) θ) R(d) 14

39 Optimization: stochastic gradient descent For every example: O(θ) = log d p θ(d x)r(d) O(θ) = E qθ (d x)[φ(x, d)] E pθ (d x)[φ(x, d)] p θ (d x) exp(φ(x, d) θ) q θ (d x) exp(φ(x, d) θ) R(d) p θ (D(x)) = [0.2, 0.1, 0.1, 0.6] R(D(x)) = [1, 0, 0, 1] 14

40 Optimization: stochastic gradient descent For every example: O(θ) = log d p θ(d x)r(d) O(θ) = E qθ (d x)[φ(x, d)] E pθ (d x)[φ(x, d)] p θ (d x) exp(φ(x, d) θ) p θ (D(x)) = [0.2, 0.1, 0.1, 0.6] R(D(x)) = [1, 0, 0, 1] q θ (D(x)) = [0.25, 0, 0, 0.75] q θ = p θ p θ R q θ (d x) exp(φ(x, d) θ) R(d) 14

41 Optimization: stochastic gradient descent For every example: O(θ) = log d p θ(d x)r(d) O(θ) = E qθ (d x)[φ(x, d)] E pθ (d x)[φ(x, d)] p θ (d x) exp(φ(x, d) θ) p θ (D(x)) = [0.2, 0.1, 0.1, 0.6] R(D(x)) = [1, 0, 0, 1] q θ (D(x)) = [0.25, 0, 0, 0.75] q θ = p θ p θ R Gradient: q θ (d x) exp(φ(x, d) θ) R(d) 0.05 φ(x, d 1 ) 0.1 φ(x, d 2 ) 0.1 φ(x, d 3 ) φ(x, d 4 ) 14

42 Training Input: {x i, y i } n i=1 Output: θ 15

43 Training Input: {x i, y i } n i=1 Output: θ θ 0 15

44 Training Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i D(x i ) arg max K (p θ (d x i )) 15

45 Training Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i D(x i ) arg max K (p θ (d x i )) θ θ + η τ,i (E qθ (d x i )[φ(x i, d)] E pθ (d x i )[φ(x i, d)]) 15

46 Training Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i D(x i ) arg max K (p θ (d x i )) θ θ + η τ,i (E qθ (d x i )[φ(x i, d)] E pθ (d x i )[φ(x i, d)]) η τ,i : learning rate Regularization often added (L2, L1,...) 15

47 Training (structured perceptron) Input: {x i, y i } n i=1 Output: θ 16

48 Training (structured perceptron) Input: {x i, y i } n i=1 Output: θ θ 0 16

49 Training (structured perceptron) Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i ˆd arg max(p θ (d x i )) d arg max(q θ (d x i )) 16

50 Training (structured perceptron) Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i ˆd arg max(p θ (d x i )) d arg max(q θ (d x i )) if [d ] K [ ˆd] K θ θ + φ(x i, d ) φ(x i, ˆd)) 16

51 Training (structured perceptron) Input: {x i, y i } n i=1 Output: θ θ 0 for iteration τ and example i ˆd arg max(p θ (d x i )) d arg max(q θ (d x i )) if [d ] K [ ˆd] K θ θ + φ(x i, d ) φ(x i, ˆd)) Regularization often added with weight averaging 16

52 Training Other simple variants exist: E.g., cost-sensitive max-margin training That is, find pairs of good and bad derivations that look different but have similar scores and update on those 17