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600.465 - Intro to NLP - J. Eisner1 Probabilistic CKY.

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1 600.465 - Intro to NLP - J. Eisner1 Probabilistic CKY

2 600.465 - Intro to NLP - J. Eisner2 Our bane: Ambiguity  John saw Mary  Typhoid Mary  Phillips screwdriver Mary note how rare rules interact  I see a bird  is this 4 nouns – parsed like “city park scavenger bird”? rare parts of speech, plus systematic ambiguity in noun sequences  Time flies like an arrow  Fruit flies like a banana  Time reactions like this one  Time reactions like a chemist  or is it just an NP?

3 600.465 - Intro to NLP - J. Eisner3 Our bane: Ambiguity  John saw Mary  Typhoid Mary  Phillips screwdriver Mary note how rare rules interact  I see a bird  is this 4 nouns – parsed like “city park scavenger bird”? rare parts of speech, plus systematic ambiguity in noun sequences  Time | flies like an arrow NP VP  Fruit flies | like a banana NP VP  Time | reactions like this one V[stem] NP  Time reactions | like a chemist S PP  or is it just an NP?

4 600.465 - Intro to NLP - J. Eisner4 How to solve this combinatorial explosion of ambiguity? 1.First try parsing without any weird rules, throwing them in only if needed. 2.Better: every rule has a weight. A tree’s weight is total weight of all its rules. Pick the overall lightest parse of sentence. 3.Can we pick the weights automatically? We’ll get to this later …

5 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 1 NP4 VP4 2 P2V5P2V5 3 Det1 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

6 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 1 NP4 VP4 2 P2V5P2V5 3 Det1 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

7 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 1 NP4 VP4 2 P2V5P2V5 3 Det1 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

8 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 1 NP4 VP4 2 P2V5P2V5 3 Det1 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

9 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 3 Det1 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

10 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 3 Det1 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

11 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

12 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

13 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 PP12 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

14 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

15 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

16 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 NP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

17 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 NP18 S21 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

18 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

19 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

20 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

21 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

22 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

23 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

24 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

25 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

26 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

27 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP

28 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP S Follow backpointers …

29 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP S NP VP

30 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP S NP VP PP

31 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP S NP VP PP PNP

32 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP S NP VP PP PNP DetN

33 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Which entries do we need?

34 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Which entries do we need?

35 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Not worth keeping …

36 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP … since it just breeds worse options

37 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Keep only best-in-class! inferior stock

38 time 1 flies 2 like 3 an 4 arrow 5 NP3 Vst3 NP10 S8 NP24 S22 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Keep only best-in-class! (and backpointers so you can recover parse)

39 600.465 - Intro to NLP - J. Eisner39 Probabilistic Trees  Instead of lightest weight tree, take highest probability tree  Given any tree, your assignment 1 generator would have some probability of producing it!  Just like using n-grams to choose among strings …  What is the probability of this tree? S NP time VP flies PP P like NP Det an N arrow

40 600.465 - Intro to NLP - J. Eisner40 Probabilistic Trees  Instead of lightest weight tree, take highest probability tree  Given any tree, your assignment 1 generator would have some probability of producing it!  Just like using n-grams to choose among strings …  What is the probability of this tree?  You rolled a lot of independent dice … S NP time VP flies PP P like NP Det an N arrow p( | S )

41 600.465 - Intro to NLP - J. Eisner41 Chain rule: One word at a time p(time flies like an arrow) =p(time) * p(flies | time) * p(like | time flies) * p(an | time flies like) * p(arrow | time flies like an)

42 600.465 - Intro to NLP - J. Eisner42 Chain rule + backoff (to get trigram model) p(time flies like an arrow) =p(time) * p(flies | time) * p(like | time flies) * p(an | time flies like) * p(arrow | time flies like an)

43 600.465 - Intro to NLP - J. Eisner43 Chain rule – written differently p(time flies like an arrow) =p(time) * p(time flies | time) * p(time flies like | time flies) * p(time flies like an | time flies like) * p(time flies like an arrow | time flies like an ) Proof: p(x,y | x) = p(x | x) * p(y | x, x) = 1 * p(y | x)

44 600.465 - Intro to NLP - J. Eisner44 Chain rule + backoff p(time flies like an arrow) =p(time) * p(time flies | time) * p(time flies like | time flies) * p(time flies like an | time flies like) * p(time flies like an arrow | time flies like an ) Proof: p(x,y | x) = p(x | x) * p(y | x, x) = 1 * p(y | x)

45 600.465 - Intro to NLP - J. Eisner45 Chain rule: One node at a time S NP time VP flies PP P like NP Det an N arrow p( | S ) = p( S NP VP | S ) * p( S NP time VP | S NP VP ) * p( S NP time VP PP | S NP time VP ) * p( S NP time VP flies PP | S NP time VP ) * … VP PP

46 600.465 - Intro to NLP - J. Eisner46 Chain rule + backoff S NP time VP flies PP P like NP Det an N arrow p( | S ) = p( S NP VP | S ) * p( S NP time VP | S NP VP ) * p( S NP time VP PP | S NP time VP ) * p( S NP time VP flies PP | S NP time VP ) * … VP PP model you used in homework 1! (called “PCFG”)

47 600.465 - Intro to NLP - J. Eisner47 Simplified notation S NP time VP flies PP P like NP Det an N arrow p( | S ) = p( S  NP VP | S ) * p( NP  flies | NP ) * p( VP  VP NP | VP ) * p( VP  flies | VP ) * … model you used in homework 1! (called “PCFG”)

48 48 Already have a CKY alg for weights … S NP time VP flies PP P like NP Det an N arrow w( | S ) = w( S  NP VP ) + w( NP  flies | NP ) + w( VP  VP NP ) + w( VP  flies ) + … Just let w( X  Y Z ) = -log p( X  Y Z | X ) Then lightest tree has highest prob

49 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP multiply to get 2 -22 2 -8 2 -12 2 -2

50 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP multiply to get 2 -22 2 -8 2 -12 2 -2 2 -13 Need only best-in-class to get best parse

51 600.465 - Intro to NLP - J. Eisner51 Why probabilities not weights?  We just saw probabilities are really just a special case of weights …  … but we can estimate them from training data by counting and smoothing! Yay!  Warning: What kind of training corpus do we need?

52 600.465 - Intro to NLP - J. Eisner52 A slightly different task  Been asking: What is probability of generating a given tree with your homework 1 generator?  To pick tree with highest prob: useful in parsing.  But could also ask: What is probability of generating a given string with the generator? (i.e., with the –t option turned off)  To pick string with highest prob: useful in speech recognition, as substitute for an n-gram model.  (“Put the file in the folder” vs. “Put the file and the folder”)  To get prob of generating string, must add up probabilities of all trees for the string …

53 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S8 S13 NP24 S22 S27 NP24 S27 S22 S27 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Could just add up the parse probabilities 2 -22 2 -27 2 -22 2 -27 oops, back to finding exponentially many parses

54 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S S 2 -13 NP24 S22 S27 NP24 S27 S 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP 2 -12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 -2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Any more efficient way? 2 -8 2 -22 2 -27

55 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S NP24 S22 S27 NP24 S27 S 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP 2 -12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 -2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Add as we go … (the “inside algorithm”) 2 -8 +2 -13 2 -22 +2 -27

56 time 1 flies 2 like 3 an 4 arrow 5 0 NP3 Vst3 NP10 S NP S 1 NP4 VP4 NP18 S21 VP18 2 P2V5P2V5 PP 2 -12 VP16 3 Det1NP10 4 N8N8 1 S  NP VP 6 S  Vst NP 2 -2 S  S PP 1 VP  V NP 2 VP  VP PP 1 NP  Det N 2 NP  NP PP 3 NP  NP NP 0 PP  P NP Add as we go … (the “inside algorithm”) 2 -8 +2 -13 +2 -22 +2 -27 2 -22 +2 -27 2 -22 +2 -27

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GRAMMARS David Kauchak CS159 – Fall 2014 some slides adapted from Ray Mooney.

GRAMMARS David Kauchak CS159 – Fall 2014 some slides adapted from Ray Mooney.
SI485i : NLP Set 8 PCFGs and the CKY Algorithm. PCFGs We saw how CFGs can model English (sort of) Probabilistic CFGs put weights on the production rules.

SI485i : NLP Set 8 PCFGs and the CKY Algorithm. PCFGs We saw how CFGs can model English (sort of) Probabilistic CFGs put weights on the production rules.
PROBABILITY David Kauchak CS159 – Spring 2011. Admin  Posted some links in Monday’s lecture for regular expressions  Logging in remotely  ssh to vpn.cs.pomona.edu.

PROBABILITY David Kauchak CS159 – Spring Admin  Posted some links in Monday’s lecture for regular expressions  Logging in remotely  ssh to vpn.cs.pomona.edu.

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