1. Boolean retrieval http://www-nlp.stanford.edu/IR-book/
Slides from Book: Christopher D. Manning, Prabhakar Raghavan and Hinrich Schütze

2. Information Retrieval
Information Retrieval (IR) is finding material (usually documents) of an unstructured nature (usually text) that satisfies an information need from within large collections (usually stored on computers).
Reference:

3. Unstructured (text) vs. structured (database) data in mid-ninetees

4. Unstructured (text) vs. structured (database) data - Today

5. Basic assumptions of Information Retrieval
Sec. 1.1
Basic assumptions of Information Retrieval
Collection: Fixed set of documents
Goal: Retrieve documents with information that is relevant to the user’s information need and helps the user complete a task

6. The classic search model
TASK
Get rid of mice in a politically correct way
Misconception?
Info Need
Info about removing mice
without killing them
Mistranslation?
Verbal form
How do I trap mice alive?
Misformulation?
Query
mouse trap
SEARCH ENGINE
Query Refinement
Results
Corpus

7. Sec. 1.1
Unstructured data in 1620
Which plays of Shakespeare contain the words Brutus AND Caesar but NOT Calpurnia?
One could grep all of Shakespeare’s plays for Brutus and Caesar, then strip out lines containing Calpurnia?
Why is that not the answer?
Slow (for large corpora)
NOT Calpurnia is non-trivial
Other operations (e.g., find the word Romans near countrymen) not feasible
Ranked retrieval (best documents to return)
Later lectures
Grep is line-oriented; IR is document oriented.

8. Term-document incidence
Sec. 1.1
Term-document incidence
1 if play contains word, 0 otherwise
Brutus AND Caesar BUT NOT Calpurnia

9. Incidence vectors So we have a 0/1 vector for each term.
Sec. 1.1
Incidence vectors
So we have a 0/1 vector for each term.
To answer query: take the vectors for Brutus, Caesar and Calpurnia (complemented)  bitwise AND.
AND AND =

10. Answers to query Antony and Cleopatra, Act III, Scene ii
Sec. 1.1
Answers to query
Antony and Cleopatra, Act III, Scene ii
Agrippa [Aside to DOMITIUS ENOBARBUS]: Why, Enobarbus,
When Antony found Julius Caesar dead,
He cried almost to roaring; and he wept
When at Philippi he found Brutus slain.
Hamlet, Act III, Scene ii
Lord Polonius: I did enact Julius Caesar I was killed i' the
Capitol; Brutus killed me.

11. Evaluation Metrics Relevant Retrieved Irrelevant Retrieved
Irrelevant Rejected
Relevant Rejected
Relevant
Not relevant
Retrieved
Not Retrieved

12. How good are the retrieved docs?
Sec. 1.1
How good are the retrieved docs?
Precision : Fraction of retrieved docs that are relevant to user’s information need
Recall : Fraction of relevant docs in collection that are retrieved

13. Precision P = tp/(tp + fp)
Sec. 8.3
Evaluation Metrics
Precision: fraction of retrieved docs that are relevant = P(relevant|retrieved)
Recall: fraction of relevant docs that are retrieved
= P(retrieved|relevant)
Precision P = tp/(tp + fp)
Recall R = tp/(tp + fn)
Relevant
Nonrelevant
Retrieved tp fp
Not Retrieved fn tn

14. Question: An IR system returns 8 relevant documents, and 10 irrelevant documents. There are a total of 20 relevant documents in the collection. What is the precision of the system on this search, and what is its recall?
Answer
Precision = 8/18 = 0.44
Recall = 8/20 =0.4.

15. Question : For a given query there are 16 relevant documents in the collection. The precision for the query is 0.40, and the recall for the query is How many documents are in the result set?
Answer
Precision = 0.4 = Relevant/Result-Set
Recall = 0.25 = Relevant/16
Relevant = 4
Result-Set = 4/0.4 = 10
10 documents in the result set

16. Explain why both precision and recall metrics are required to measure/evaluate the quality/effectiveness of an IR system than just precision or recall

17. Sec. 8.3
Why not just use recall?
You can get high recall (but low precision) by retrieving all docs for all queries! [Recall = 100%]

18. Why not just use precision?
Sec. 8.3
Why not just use precision?
You can get high precision (but low recall) by retrieving zero docs for all queries! [Precision = 100%]

19. Evaluation Metrics: Example

20. Evaluation Metrics: Example
Recall = 2/6 = 0.33
Precision = 2/3 = 0.67

21. Evaluation Metrics: Example
Recall = 5/6 = 0.83
Precision = 5/6 = 0.83

22. F Measure
Harmonic mean of recall and precision

23. Evaluation Metrics: Example
Recall = 2/6 = 0.33
Precision = 2/3 = 0.67
F = 2*Recall*Precision/(Recall + Precision)
= 2*0.33*0.67/( ) = 0.22

24. Evaluation Metrics: Example
Recall = 5/6 = 0.83
Precision = 5/6 = 0.83
F = 2*Recall*Precision/(Recall + Precision)
= 2*0.83*0.83/( ) = 0.83

25. Sec. 1.1
Bigger collections
Consider N = 1 million documents, each with about 1000 words.
Avg 6 bytes/word including spaces/punctuation
6GB of data in the documents.
Say there are M = 500K distinct terms among these.

26. Sec. 1.1
Can’t build the matrix
500K x 1M matrix has half-a-trillion 0’s and 1’s.
But it has no more than one billion 1’s.
matrix is extremely sparse.
What’s a better representation?
We only record the 1 positions.

27. Sec. 1.2
Inverted index
For each term t, we must store a list of all documents that contain t.
Identify each by a docID, a document serial number
Can we used fixed-size arrays for this?
Brutus 1 2 4 11 31 45
173
174
Caesar 1 2 4 5 6 16 57
132
Calpurnia 2 31 54
101

28. Inverted index We need variable-size postings lists Brutus 1 2 4 11 31
Sec. 1.2
Inverted index
We need variable-size postings lists
Posting
Brutus 1 2 4 11 31 45
173
174
Dictionary
Caesar 1 2 4 5 6 16 57
132
Linked lists generally preferred to arrays
Dynamic space allocation
Insertion of terms into documents easy
Space overhead of pointers
Calpurnia 2 31 54
101
Postings
Sorted by docID (more later on why).

29. Inverted index construction
Sec. 1.2
Inverted index construction
Documents to
be indexed.
Friends, Romans, countrymen.
Tokenizer
Token stream.
Friends
Romans
Countrymen
More on
these later.
Linguistic modules
Modified tokens.
friend
roman
countryman
Indexer
Inverted index.
friend
roman
countryman 2 4 13 16 1

30. Indexer steps: Token sequence
Sec. 1.2
Indexer steps: Token sequence
Sequence of (Modified token, Document ID) pairs.
Doc 1
Doc 2
I did enact Julius
Caesar I was killed
i' the Capitol;
Brutus killed me.
So let it be with
Caesar. The noble
Brutus hath told you
Caesar was ambitious

31. Indexer steps: Sort Sort by terms Core indexing step And then docID
Sec. 1.2
Indexer steps: Sort
Sort by terms
And then docID
Core indexing step

32. Indexer steps: Dictionary & Postings
Sec. 1.2
Indexer steps: Dictionary & Postings
Multiple term entries in a single document are merged.
Split into Dictionary and Postings
Doc. frequency information is added.
Why frequency?
Will discuss later.

33. The index we just built How do we process a query? Today’s focus
Sec. 1.3
The index we just built
How do we process a query?
Later - what kinds of queries can we process?
Today’s focus

34. Query processing: AND Consider processing the query: Brutus AND Caesar
Sec. 1.3
Query processing: AND
Consider processing the query:
Brutus AND Caesar
Locate Brutus in the Dictionary;
Retrieve its postings.
Locate Caesar in the Dictionary;
“Merge” the two postings: 2 4 8 16 32 64
128
Brutus 1 2 3 5 8 13 21 34
Caesar

35. Sec. 1.3
The Merge
Walk through the two postings simultaneously, in time linear in the total number of postings entries 34
128 2 4 8 16 32 64 1 3 5 13 21 2 4 8 16 32 64
128
Brutus
Caesar 2 8 1 2 3 5 8 13 21 34
If the list lengths are x and y, the merge takes O(?)
operations.
Crucial: postings sorted by docID.

36. Sec. 1.3
The Merge
Walk through the two postings simultaneously, in time linear in the total number of postings entries 34
128 2 4 8 16 32 64 1 3 5 13 21 2 4 8 16 32 64
128
Brutus
Caesar 2 8 1 2 3 5 8 13 21 34
If the list lengths are x and y, the merge takes O(x+y)
operations.
Crucial: postings sorted by docID.

37. Intersecting two postings lists (a “merge” algorithm)

38. Question: Write out a postings merge algorithm for an
x OR y query.

39. Question: Write out a postings merge algorithm for an
x OR y query.

40. Question: Write out a postings merge algorithm for an
x AND (NOT y) query.

41. Question Following are two posting lists p1 and p2 that needs to be merged (lists intersection).
How many comparison operations do the list intersection/merge algorithm performs and list all the posting comparisons performed by the merge algorithm in sequential order (trace through the algorithm)

42. Boolean queries: Exact match
Sec. 1.3
Boolean queries: Exact match
Boolean retrieval model: being able to ask a query that is a Boolean expression:
Boolean Queries: using AND, OR and NOT to join query terms
Views each document as a set of words
Is precise: document matches condition or not.
Perhaps the simplest model to build an IR system on
Primary commercial retrieval tool for 3 decades.
Many search systems you still use are Boolean:
, library catalog, Mac OS X Spotlight

43. Query optimization What is the best order for query processing?
Sec. 1.3
Query optimization
What is the best order for query processing?
Consider a query that is an AND of n terms.
For each of the n terms, get its postings, then AND them together.
Brutus 2 4 8 16 32 64
128
Caesar 1 2 3 5 8 16 21 34
Calpurnia 13 16
Query: Brutus AND Calpurnia AND Caesar 43

44. Query optimization example
Sec. 1.3
Query optimization example
Process in order of increasing freq:
start with smallest set, then keep cutting further.
This is why we kept
document freq. in dictionary
Brutus 2 4 8 16 32 64
128
Caesar 1 2 3 5 8 16 21 34
Calpurnia 13 16
Execute the query as (Calpurnia AND Brutus) AND Caesar.

45. More general optimization
Sec. 1.3
More general optimization
e.g., (madding OR crowd) AND (ignoble OR strife)
Get doc. freq.’s for all terms.
Estimate the size of each OR by the sum of its doc. freq.’s (conservative).
Process in increasing order of OR sizes.

46. Exercise (tangerine OR trees) AND (marmalade OR skies) AND
Recommend a query processing order for
(tangerine OR trees) AND
(marmalade OR skies) AND
(kaleidoscope OR eyes)

47. (tangerine OR trees) AND (marmalade OR skies)
AND (kaleidoscope OR eyes)