CS626-449: Speech, NLP and the Web/Topics in AI p

CS626-449: Speech, NLP and the Web/Topics in AI p

Pushpak Bhattacharyya

CSE Dept., IIT Bombay

Lecture-17: PCFG; Arguments and Adjuncts

Compare

• P(w_1,m) = P(w₁) * _i=1π^i=m P(w_i/w_{1, n-i} ) Æ Statistics

(S h)

(Speech)

• P(w_1,m) = ∑_{t Ԗ} all parses P(t) Æ Statistics + Linguistics

• w_1,m = yield(s) Æ linguistics

Probability of a parse tree (cont.)

S_1,l

NP_1,2 VP_3,l

N_2,2 V_3,3 PP_4,l

P NP

w DT₁

w P ( t|s ) = P (t | S_1,l )

= P ( NP_1,2, DT_1,1 , w_1,

N ^w2 ^P4,4 NP_5,l

w₄

w₁ w₃

w₅ w_l

N_2,2, w_2,

VP_3,l, V_3,3 , w_3,

PP_{4 l}, P_{4 4} , w₄ NP_{5 l}, w_{5 l}

|

PP_4,l, P_4,4 , w_4, NP_5,l, w_5…l

|

= P ( NP_1,2 , VP_3,l | S_1,l) * P ( DT_1,1 , N_2,2 | NP_1,2) * D(w₁ | DT_1,1) * P (w₂ | N_2,2) * P (V_{3 3} PP_{4 l} | VP_{3 l}) * P(w₃ | V_{3 3}) * P( P_{4 4} NP _l | PP_{4 l} ) * P(w₄|P_{4 4}) * P

P (V_3,3, PP_4,l | VP_3,l) P(w₃ | V_3,3) P( P_4,4, NP_5,l | PP_4,l ) P(w₄|P_4,4) P (w_5…l | NP_5,l)

(Using Chain Rule, Context Freeness and Ancestor Freeness )

Example PCFG Rules &

Probabilities Probabilities

• S → NP VP 1.0

• NP → DT NN 0.5

• DT → the 1.0

• NN → gunman 0.5

• NP → NNS 0.3

• NP → NP PP 0.2

• NN → building 0.5

• VBD → sprayed 1.0

• PP → P NP 1.0

• VP → VP PP 0.6

• NNS → bullets 1.0

• VP → VBD NP 0.4

Example Parse t

• The gunman sprayed the building with bullets.

S_1.0

NP_0.5 VP_0.6

P (t₁)

= 1.0 * 0.5 * 1.0 * 0.5 * 0.6 * 0.4 * 1.0 * 0.5 * 1.0 * 0.5 * 1.0

0.5 0.6

DT_1.0 NN_0.5 PP_1.0

* 1.0 * 0.3 * 1.0

= 0.00225 VP_0.4

VBD_1.0 NP_0.5 P_1.0 NP_0.3 The gunman

DT_1.0 NN_0.5with NNS_1.0

building the

sprayed

bullets building

the

Another Parse t

S

• The gunman sprayed the building with bullets.

S_1.0

NP_0.5 VP_0.4

P (t₂)

= 1.0 * 0.5 * 1.0 * 0.5 * 0.4 * 1.0 * 0.2 * 0.5 * 1.0 * 0.5 * 1.0 DT_1.0 NN_0.5VBD_1.0 NP_0.2

* 1.0 * 0.3 * 1.0

= 0.0015

NP_0.5 PP_1.0 The gunman sprayed

DT_1.0 NN_0.5 P_1.0 NP_0.3

ith NNS b ilding

the NNS_1.0

bullets building with

the

Complements and Adjuncts Complements and Adjuncts

or

A t d Adj t

Arguments and Adjuncts

Rules in bar notation: Noun

• NPÆ (D) N’

• N’Æ (AP) N’

• N’Æ N’ (PP)

• N’Æ N (PP)

Rules in bar notation: Verb

• VPÆ V’

• V’Æ V’ (PP)

• V’Æ V (NP)

Rules in bar notation: Adjective

• APÆ A’

• A’Æ (AP) A’

• A’Æ A (PP)

Rules in bar notation: Preposition

• PPÆ P’

• P’Æ P’ (PP)

• P’Æ P (NP)

Introducing the “X factor”

• Let X stand for any category N, V, A, P

• Let XP stand for NP, VP, AP and PP

• Let X’ stand for N’, V’, A’ and P’

XP to X’

• Collect the first level rules

– NPÆ (D) N’

– VPÆ V’

APÆ A’

– APÆ A’

– PPÆ P’

• And produce

• And produce

– XPÆ (YP) X’

X’ to X’

• Collect the 2^nd level rules

– N’Æ (AP) N’ or N’ (PP) – V’Æ V’ (PP)

A’Æ (AP) A’

– A’Æ (AP) A’

– P’Æ P’ (PP)

• And produce

• And produce

– X’Æ (ZP) X’ or X (ZP)

X’ to X

• Collect the 3^rd level rules

– N’Æ N (PP) – V’Æ V (NP) A’Æ A (PP) – A’Æ A (PP) – P’Æ P (NP)

• And produce

• And produce

– X’Æ X (WP)

Basic observations about X and X’

• X’Æ X (WP)

• X’Æ X’ (ZP)

• X is called Head

• Phrases must have Heads: Headedness property

• Category of XP and X must match: Endocentricity

Basic observations about X and X’

• X’Æ X (WP)

• X’Æ X’ (ZP)

• Sisters of X are complements

– Roughly correspond to objects

• Sisters of X’ are Adjuncts

– PPs and Adjectives are typical adjuncts

• We have adjunct rules and complement rules

Structural difference between complements and adjuncts complements and adjuncts

XP X’

X’

ZP

WP X

Adjunct

Complement X

Complements and Adjuncts in NPs

NP N’

N’

ZP

PP N

with red cover N

book

of poems

NP

N’

Any number of Adjuncts

N’

N’

ZP from Oxford Press

PP N

with red cover N

book

of poems