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(Some issues in) Text Ranking

(Some issues in) Text Ranking. Recall General Framework. Crawl Use XML structure Follow links to get new pages Retrieve relevant documents Today Rank PageRank, HITS Rank Aggregation. Relevant documents. Usually: relevant with respect to a keyword, set of keywords, logical expression..

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(Some issues in) Text Ranking

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  1. (Some issues in) Text Ranking

  2. Recall General Framework • Crawl • Use XML structure • Follow links to get new pages • Retrieve relevant documents • Today • Rank • PageRank, HITS • Rank Aggregation

  3. Relevant documents • Usually: relevant with respect to a keyword, set of keywords, logical expression.. • Closely related to ranking • “How” relevant is it can be considered another measure • Usually done as a separate step • Recall the Online vs. offline issue.. • But some techniques are reusable

  4. Defining Relevant Documents • Common strategy: treat text documents as “bag of words” (BOW) • Denote BOW(D) for a document D • Bag rather than set (i.e. multiplicity is kept) • Words are typically stemmed • Reduced to root form • Loses structure, but simplifies life • Simple definition: • A document D is relevant to a keyword W if W is in BOW(D)

  5. Cont. • Simple variant • The level of relevance of D to W is the multiplicity of W in BOW(D) • Problem: Bias towards long documents • So divide by the document length |BOW(D)| • This is called term frequency (TF)

  6. A different angle • Given a document D, what are the “most important” words in D? • Clearly high term frequency should be considered • Rank terms according to TF?

  7. Ranking according to TF A 2022 Is 1023 He 350 . . . Liverpool 25 Beatles 12

  8. IDF • Observation: if w is rare in the documents set, but appears many times in a document D, then w is “important” for D • IDF(w) = log(|Docs| / |Docs’|) • Docs is the set of all documents in the corpus, Docs’ is the subset of documents that contain w • TFIDF(D,W)=TF(W,D)*IDF(W) • “Correlation” of D and W

  9. Inverted Index • For every term we keep a list of all documents in which it appears • The list is sorted by TFIDF scores • Scores are also kept • Given a keyword it is then easy to give the top-k

  10. Ranking • Now assume that these documents are web pages • How do we return the most relevant? • How do we combine with other rankings? (e.g. PR?) • How do we answer boolean queries? • X1 AND (X2 OR X3)

  11. Rank Aggregation • To combine TFIDF, PageRank.. • To combine TFIDF with respect to different keywords

  12. Part-of-Speech Tagging • So far we have considered documents only as bags-of-words • Computationally efficient, easy to program, BUT • We lost the structure that may be very important: • E.g. perhaps we are interested (more) in documents for which W is often the sentence subject? • Part-of-speech tagging • Useful for ranking • For machine translation • Word-Sense Disambiguation • …

  13. Part-of-Speech Tagging • Tag this word. This word is a tag. • He dogs like a flea • The can is in the fridge • The sailor dogs me every day

  14. A Learning Problem • Training set: tagged corpus • Most famous is the Brown Corpus with about 1M words • The goal is to learn a model from the training set, and then perform tagging of untagged text • Performance tested on a test-set

  15. Simple Algorithm • Assign to each word its most popular tag in the training set • Problem: Ignores context • Dogs, tag will always be tagged as a noun… • Can will be tagged as a verb • Still, achieves around 80% correctness for real-life test-sets • Goes up to as high as 90% when combined with some simple rules

  16. (HMM)Hidden Markov Model • Model: sentences are generated by a probabilistic process • In particular, a Markov Chain whose states correspond to Parts-of-Speech • Transitions are probabilistic • In each state a word is outputted • The output word is again chosen probabilistically based on the state

  17. HMM • HMM is: • A set of N states • A set of M symbols (words) • A matrix NXN of transition probabilities Ptrans • A vector of size N of initial state probabilities Pstart • A matrix NXM of emissions probabilities Pout • “Hidden” because we see only the outputs, not the sequence of states traversed

  18. Example

  19. 3 Fundamental Problems 1) Compute the probability of a given observation Sequence (=sentence) 2) Given an observation sequence, find the most likely hidden state sequence This is tagging 3) Given a training set find the model that would make the observations most likely

  20. Tagging • Find the most likely sequence of states that led to an observed output sequence • Problem: exponentially many possible sequences!

  21. Viterbi Algorithm • Dynamic Programming • Vt,k is the probability of the most probable state sequence • Generating the first t + 1 observations (X0,..Xt) • And terminating at state k

  22. Viterbi Algorithm • Dynamic Programming • Vt,k is the probability of the most probable state sequence • Generating the first t + 1 observations (X0,..Xt) • And terminating at state k • V0,k = Pstart(k)*Pout(k,X0) • Vt,k= Pout(k,Xt)*max{Vt-1k’ *Ptrans(k’,k)}

  23. Finding the path • Note that we are interested in the most likely path, not only in its probability • So we need to keep track at each point of the argmax • Combine them to form a sequence • What about top-k?

  24. Complexity • O(T*|S|^2) • Where T is the sequence (=sentence) length, |S| is the number of states (= number of possible tags)

  25. Computing the probability of a sequence • Forward probabilities: αt(k) is the probability of seeing the sequence X1…Xt and terminating at state k • Backward probabilities: βt(k) is the probability of seeing the sequence Xt+1…Xn given that the Markov process is at state k at time t.

  26. Computing the probabilities Forward algorithm α0(k)= Pstart(k)*Pout(k,X0) αt(k)= Pout(k,Xt)*Σk’{αt-1k’ *Ptrans(k’,k)} P(O1,…On)= Σk αn(k) Backward algorithm βt(k) = P(Ot+1…On| state at time t is k) βt(k) = Σk’{Ptrans(k,k’)* Pout(k’,Xt+1)* βt+1(k’)} βn(k) = 1 for all k P(O)= Σk β0(k)* Pstart(k)

  27. Learning the HMM probabilities • Expectation-Maximization Algorithm • Start with initial probabilities • Compute Eij the expected number of transitions from i to j while generating a sequence, for each i,j (see next) • Set the probability of transition from i to j to be Eij/ (ΣkEik) 4. Similarly for omission probability 5. Repeat 2-4 using the new model, until convergence

  28. Estimating the expectancies • By sampling • Re-run a random a execution of the model 100 times • Count transitions • By analysis • Use Bayes rule on the formula for sequence probability • Called the Forward-backward algorithm

  29. Accuracy • Tested experimentally • Exceeds 96% for the Brown corpus • Trained on half and tested on the other half • Compare with the 80-90% by the trivial algorithm • The hard cases are few but are very hard..

  30. NLTK • http://www.nltk.org/ • Natrual Language ToolKit • Open source python modules for NLP tasks • Including stemming, POS tagging and much more

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