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Probabilistic and Lexicalized Parsing. Probabilistic CFGs. The probabilistic model Assigning probabilities to parse trees Disambiguate, LM for ASR, faster parsing Getting the probabilities for the model Parsing with probabilities Slight modification to dynamic programming approach
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Probabilistic and Lexicalized Parsing COMS 4705 Fall 2004
Probabilistic CFGs • The probabilistic model • Assigning probabilities to parse trees • Disambiguate, LM for ASR, faster parsing • Getting the probabilities for the model • Parsing with probabilities • Slight modification to dynamic programming approach • Task: find max probability tree for an input string COMS 4705 – Fall 2004
Probability Model • Attach probabilities to grammar rules • Expansions for a given non-terminal sum to 1 VP -> V .55 VP -> V NP .40 VP -> V NP NP .05 • Read this as P(Specific rule | LHS) • “What’s the probability that VP will expand to V, given that we have a VP?” COMS 4705 – Fall 2004
Probability of a Derivation • A derivation (tree) consists of the set of grammar rules that are in the parse tree • The probability of a tree is just the product of the probabilities of the rules in the derivation • Note the independence assumption – why don’t we use conditional probabilities? COMS 4705 – Fall 2004
Probability of a Sentence • Probability of a word sequence (sentence) is probability of its tree in unambiguous case • Sum of probabilities of possible trees in ambiguous case COMS 4705 – Fall 2004
Getting the Probabilities • From an annotated database • E.g. the Penn Treebank • To get the probability for a particular VP rule just count all the times the rule is used and divide by the number of VPs overall • What if you have no treebank (e.g. for a ‘new’ language)? COMS 4705 – Fall 2004
Assumptions • We have a grammar to parse with • We have a large robust dictionary with parts of speech • We have a parser • Given all that… we can parse probabilistically COMS 4705 – Fall 2004
Typical Approach • Bottom-up (CYK) dynamic programming approach • Assign probabilities to constituents as they are completed and placed in the table • Use the max probability for each constituent going up the tree COMS 4705 – Fall 2004
How do we fill in the DP table? • Say we’re talking about a final part of a parse– finding an S, e.g., of the rule • S->0NPiVPj The probability of S is… P(S->NP VP)*P(NP)*P(VP) The acqua part is already known, since we’re doing bottom-up parsing. We don’t need to recalculate the probabilities of constituents lower in the tree. COMS 4705 – Fall 2004
Using the Maxima • P(NP) is known • But what if there are multiple NPs for the span of text in question (0 to i)? • Take the max (Why?) • Does not mean that other kinds of constituents for the same span are ignored (i.e. they might be in the solution) COMS 4705 – Fall 2004
S -> NP VP VP -> V NP NP -> NP PP VP -> VP PP PP -> P NP NP -> John, Mary, Denver V -> called P -> from CYK Parsing: John called Mary from Denver COMS 4705 – Fall 2004
Example S NP VP PP VP V NP NP P John called Mary from Denver COMS 4705 – Fall 2004
Example S NP VP NP NP PP V John called Mary from Denver COMS 4705 – Fall 2004
Example COMS 4705 – Fall 2004
Base Case: Aw COMS 4705 – Fall 2004
Recursive Cases: ABC COMS 4705 – Fall 2004
Problems with PCFGs • The probability model we’re using is just based on the rules in the derivation… • Doesn’t use the words in any real way – e.g. PP attachment often depends on the verb, its object, and the preposition (I ate pickles with a fork. I ate pickles with relish.) • Doesn’t take into account where in the derivation a rule is used – e.g. pronouns more often subjects than objects (She hates Mary. Mary hates her.) COMS 4705 – Fall 2004
Solution • Add lexical dependencies to the scheme… • Add the predilections of particular words into the probabilities in the derivation • I.e. Condition the rule probabilities on the actual words COMS 4705 – Fall 2004
Heads • Make use of notion of the headof a phrase, e.g. • The head of an NP is its noun • The head of a VP is its verb • The head of a PP is its preposition • Phrasal heads • Can ‘take the place of’ whole phrases, in some sense • Define most important characteristics of the phrase • Phrases are generally identified by their heads COMS 4705 – Fall 2004
Example (correct parse) Attribute grammar COMS 4705 – Fall 2004
Example (wrong) COMS 4705 – Fall 2004
How? • We started with rule probabilities • VP -> V NP PP P(rule|VP) • E.g., count of this rule divided by the number of VPs in a treebank • Now we want lexicalized probabilities • VP(dumped)-> V(dumped) NP(sacks)PP(in) • P(r|VP ^ dumped is the verb ^ sacks is the head of the NP ^ in is the head of the PP) • Not likely to have significant counts in any treebank COMS 4705 – Fall 2004
Declare Independence • So, exploit independence assumption and collect the statistics you can… • Focus on capturing two things • Verb subcategorization • Particular verbs have affinities for particular VPs • Objects have affinities for their predicates (mostly their mothers and grandmothers) • Some objects fit better with some predicates than others COMS 4705 – Fall 2004
Verb Subcategorization • Condition particular VP rules on their head… so r: VP -> V NP PP P(r|VP) Becomes P(r | VP ^ dumped) What’s the count? How many times was this rule used with dump, divided by the number of VPs that dump appears in total COMS 4705 – Fall 2004
Preferences • Subcat captures the affinity between VP heads (verbs) and the VP rules they go with. • What about the affinity between VP heads and the heads of the other daughters of the VP? COMS 4705 – Fall 2004
Example (correct parse) COMS 4705 – Fall 2004
Example (wrong) COMS 4705 – Fall 2004
Preferences • The issue here is the attachment of the PP • So the affinities we care about are the ones between dumped and into vs. sacks and into. • Count the times dumped is the head of a constituent that has a PP daughter with into as its head and normalize (alternatively, P(into|PP,dumped is mother’s head)) • Vs. the situation where sacks is a constituent with into as the head of a PP daughter (or, P(into|PP,sacks is mother’s head)) COMS 4705 – Fall 2004
Another Example • Consider the VPs • Ate spaghetti with gusto • Ate spaghetti with marinara • The affinity of gusto for eat is much larger than its affinity for spaghetti • On the other hand, the affinity of marinara for spaghetti ismuch higher than its affinity for ate COMS 4705 – Fall 2004
But not a Head Probability Relationship • Note the relationship here is more distant and doesn’t involve a headword since gusto and marinara aren’t the heads of the PPs (Hindle & Rooth ’91) Vp (ate) Vp(ate) Np(spag) Vp(ate) Pp(with) np Pp(with) v np v Ate spaghetti with marinara Ate spaghetti with gusto COMS 4705 – Fall 2004
Next Time • Midterm • Covers everything assigned and all lectures up through today • Short answers (2-3 sentences), exercises, longer answers (1 para) • Closed book, calculators allowed but no laptops COMS 4705 – Fall 2004