程序代写代做代考 C algorithm COMP6714: Informa2on Retrieval & Web Search

COMP6714: Informa2on Retrieval & Web Search
Introduc)on to
Informa(on Retrieval
Lecture 1: Boolean retrieval

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Unstructured data in 1680
 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 opera)ons (e.g., find the word Romans near countrymen) not feasible
 Ranked retrieval (best documents to return)  Later lectures
2

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Term‐document incidence
1 if play contains word, 0 otherwise
Brutus AND Caesar BUT NOT Calpurnia

COMP6714: Informa2on Retrieval & Web Search
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.
 110100 AND 110111 AND 101111 = 100100.
4

COMP6714: Informa2on Retrieval & Web Search
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.
5

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Basic assump)ons of Informa)on Retrieval  Collec)on: Fixed set of documents
 Goal: Retrieve documents with informa)on that is relevant to the user’s informa)on need and helps the user complete a task
6

COMP6714: Informa2on Retrieval & Web Search
The classic search model
TASK
Info Need
Verbal form
Query
mouse trap
Misconception?
Info about removing mice without killing them
Mistranslation?
Misformulation?
SEARCH ENGINE
Query Refinement
Results
Corpus

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
How good are the retrieved docs?
 Precision : Frac)on of retrieved docs that are relevant to user’s informa)on need
 Recall : Frac)on of relevant docs in collec)on that are retrieved
 More precise defini)ons and measurements to follow in later lectures
8

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.1
Bigger collec)ons
 Consider N = 1 million documents, each with about 1000 words.
 Avg 6 bytes/word including spaces/punctua)on  6GB of data in the documents.
 Say there are M = 500K dis2nct terms among these.
9

COMP6714: Informa2on Retrieval & Web Search
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 be^er representa)on?  We only record the 1 posi)ons.
Why?
10

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Inverted index
 For each term t, we must store a list of all documents that contain t.
 Iden)fy 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
What happens if the word Caesar is added to document 14?
11

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Inverted index
 We need variable‐size pos)ngs lists
 On disk, a con)nuous run of pos)ngs is normal and best
 In memory, can use linked lists or variable length arrays
 Some tradeoffs in size/ease of inser)on
Dictionary
Pos2ng
Brutus
1
2
4
11
31
45
173
174
Caesar
1
2
4
5
6
16
57
132
Calpurnia
2
31
54
101
Postings
Sorted by docID (more later on why).
12

COMP6714: Informa2on Retrieval & Web Search
Inverted index construc)on
Sec. 1.2
Documents to be indexed.
Token stream.
Modified tokens.
Inverted index.
Tokenizer
Linguistic modules
Indexer
More on these later.
Friends, Romans, countrymen.
Friends
Romans
Countrymen
friend
roman
countryman
friend
roman
1
13
4
2
16
countryman
2

COMP6714: Informa2on Retrieval & Web Search
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

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Indexer steps: Sort  Sort by terms
 And then docID
Core indexing step

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Indexer steps: Dic)onary & Pos)ngs
 Mul)ple term entries in a single document are merged.
 Split into Dic)onary and Pos)ngs
 Doc. frequency informa)on is added.
Why frequency? Will discuss later.

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.2
Where do we pay in storage?
Lists of docIDs
Terms and counts
Pointers
17
Later in the course:
• How do we index
efficiently?
• How much storage do we need?

COMP6714: Informa2on Retrieval & Web Search
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
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Query processing: AND
 Consider processing the query:
Brutus AND Caesar
 Locate Brutus in the Dic)onary;  Retrieve its pos)ngs.
 Locate Caesar in the Dic)onary;  Retrieve its pos)ngs.
 “Merge” the two pos)ngs:
2

4

8

16

32

64

128

Brutus
 Caesar

1

2

3

5

8

13

21

34

19

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
The merge
 Walk through the two pos)ngs simultaneously, in )me linear in the total number of pos)ngs entries
Brutus
 Caesar

If the list lengths are x and y, the merge takes O(x+y) operations.
Crucial: postings sorted by docID.
2

4

8

16

32

64

128

2

8

1

2

3

5

8

13

21

34

20

COMP6714: Informa2on Retrieval & Web Search
Intersec)ng two pos)ngs lists (a “merge” algorithm)
21

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Boolean queries: Exact match
 The Boolean retrieval model is being able to ask a query that is a Boolean expression:
 Boolean Queries are queries using AND, OR and NOT to join query terms
 Views each document as a set of words
 Is precise: document matches condi)on or not.
 Perhaps the simplest model to build an IR system on
 Primary commercial retrieval tool for 3 decades.
 Many search systems you s)ll use are Boolean:  Email, library catalog, Mac OS X Spotlight
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.4
Example: WestLaw http://www.westlaw.com/
 Largest commercial (paying subscribers) legal search service (started 1975; ranking added 1992)
 Tens of terabytes of data; 700,000 users
 Majority of users still use boolean queries
 Example query:
 What is the statute of limitations in cases involving
the federal tort claims act?
 LIMIT! /3 STATUTE ACTION /S FEDERAL /2 TORT /3 CLAIM
 foo! = foo*, /3 = within 3 words, /S = in same sentence
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COMP6714: Informa2on Retrieval & Web Search
Sec. 1.4
Example: WestLaw http://www.westlaw.com/
 Another example query:
 Requirements for disabled people to be able to access a workplace
 disabl! /p access! /s work‐site work‐place (employment /3 place
 Note that SPACE is disjunc)on, not conjunc)on!
 Long, precise queries; proximity operators;
incrementally developed; not like web search
 Many professional searchers s)ll like Boolean search
 You know exactly what you are geqng
 But that doesn’t mean it actually works be^er….

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Boolean queries: More general merges
 Exercise: Adapt the merge for the queries: Brutus AND NOT Caesar
Brutus OR NOT Caesar
Can we s)ll run through the merge in )me O(x+y)? What can we achieve?
25

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Merging
What about an arbitrary Boolean formula?
(Brutus OR Caesar) AND NOT
(Antony OR Cleopatra)
 Can we always merge in “linear” )me?  Linear in what?
 Can we do be^er?
26

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Query op)miza)on
 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 pos)ngs, then AND them together.
21 34
27

Brutus
2
4
8
16
32
64
128
Caesar
1
2
3
5
8
16
Calpurnia
13
16
Query: Brutus AND Calpurnia AND Caesar

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
Query op)miza)on example  Process in order of increasing freq:
 start with the smallest set, then keep cuNng further. This is why we kept
document freq. in dictionary
Brutus
2
4
8
16
32
64
128
Caesar
21 34
1
2
3
5
8
16
Calpurnia
13
16
Execute the query as (Calpurnia AND Brutus) AND Caesar.
28

COMP6714: Informa2on Retrieval & Web Search
Sec. 1.3
More general op)miza)on
 e.g., (madding OR crowd) AND (ignoble OR
strife) AND (light OR lord)
 Get doc. freq.’s for all terms.
 Es)mate the size of each OR by the sum of its doc. freq.’s (conserva)ve).
 Process in increasing order of OR sizes.
29

COMP6714: Informa2on Retrieval & Web Search
Exercise
 Recommend a query processing order for
(tangerine OR trees) AND (marmalade OR skies) AND (kaleidoscope OR eyes)
Q: Any more accurate way to es)mate the cardinality of intermediate results? Q: Can we merge mul)ple lists (>2) simultaneously?
30

COMP6714: Informa2on Retrieval & Web Search
Problema)c Cases

COMP6714: Informa2on Retrieval & Web Search
Query processing exercises
 Exercise: If the query is friends AND romans AND (NOT countrymen), how could we use the freq of countrymen?
 Exercise: Extend the merge to an arbitrary Boolean query. Can we always guarantee execu)on in )me linear in the total pos)ngs size?
 Hint: Begin with the case of a Boolean formula query: in this, each query term appears only once in the query.
32

COMP6714: Informa2on Retrieval & Web Search
Exercise
 Try the search feature at
h^p://www.rhymezone.com/shakespeare/
 Write down five search features you think it could do be^er
33

COMP6714: Informa2on Retrieval & Web Search
FASTER POSTINGS MERGES: SKIP POINTERS/SKIP LISTS

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Recall basic merge
 Walk through the two pos)ngs simultaneously, in )me linear in the total number of pos)ngs entries
Brutus Caesar
If the list lengths are m and n, the merge takes O(m+n) operations.
Can we do better?
Yes (if index isn’t changing too fast).
2
4
8
41
48
64
128
2
8
1
2
3
8
11
17
21
31

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Augment pos)ngs with skip pointers (at indexing )me)
41
11
128
31
2
4
8
41
48
64
128
1
2
3
8
11
17
21
31
 Why?
 To skip pos)ngs that will not figure in the search
results.
 How?
 Where do we place skip pointers?

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Query processing with skip pointers
41
11
128
31
2
4
8
41
48
64
128
1
2
3
8
11
17 21 31
Suppose we’ve stepped through the lists until we process 8 on each list. We match it and advance.
We then have 41 and 11 on the lower. 11 is smaller.
But the skip successor of 11 on the lower list is 31, so we can skip ahead past the intervening postings.

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Where do we place skips?  Tradeoff:
 More skips → shorter skip spans ⇒ more likely to skip. But lots of comparisons to skip pointers.
 Fewer skips → few pointer comparison, but then long skip spans ⇒ few successful skips.
Can we skip w/o skip pointers?

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.3
Placing skips
 Simple heuris)c: for pos)ngs of length L, use L1/2 evenly‐spaced skip pointers.
 This ignores the distribu)on of query terms.
 Easy if the index is rela)vely sta)c; harder if L keeps
changing because of updates.
 This definitely used to help; with modern hardware it may not (Bahle et al. 2002) unless you’re memory‐ based
 The I/O cost of loading a bigger pos)ngs list can outweigh the gains from quicker in memory merging!

COMP6714: Informa2on Retrieval & Web Search
Skip Pointers
 A skip pointer (d, p) contains a document number d and a byte (or bit) posi)on p
 Means there is an inverted list pos)ng that starts at posi)on p, and the pos)ng before it was for document d
CMS09::Chap5
skip pointers
Inverted list

COMP6714: Informa2on Retrieval & Web Search
Skip Pointers  Example
 Inverted list  D‐gaps
 Skip pointers

COMP6714: Informa2on Retrieval & Web Search
PHRASE QUERIES AND POSITIONAL INDEXES

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4
Phrase queries
 Want to be able to answer queries such as “stanford
university” – as a phrase
 Thus the sentence “I went to university at Stanford” is not a match.
 The concept of phrase queries has proven easily understood by users; one of the few “advanced search” ideas that works
 Many more queries are implicit phrase queries  For this, it no longer suffices to store only
entries

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Solu)on 1: Biword indexes
 Index every consecu)ve pair of terms in the text as a
phrase
 For example the text “Friends, Romans, Countrymen” would generate the biwords
 friends romans
 romans countrymen
 Each of these biwords is now a dic)onary term
 Two‐word phrase query‐processing is now immediate.

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Longer phrase queries
 Longer phrases are processed as we did with wild‐ cards:
 stanford university palo alto can be broken into the Boolean query on biwords:
stanford university AND university palo AND palo alto
Without the docs, we cannot verify that the docs matching the above Boolean query do contain the phrase.
Can have false positives!

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Extended biwords
 Parse the indexed text and perform part‐of‐speech‐tagging (POST).
 Bucket the terms into (say) Nouns (N) and ar)cles/ preposi)ons (X).
 Call any string of terms of the form NX*N an extended biword.
 Each such extended biword is now made a term in the dic)onary.
 Example: catcher in the rye NXXN
 Query processing: parse it into N’s and X’s  Segment query into enhanced biwords  Look up in index: catcher rye

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.1
Issues for biword indexes  False posi)ves, as noted before
 Index blowup due to bigger dic)onary
 Infeasible for more than biwords, big even for them
 Biword indexes are not the standard solu)on (for all biwords) but can be part of a compound strategy

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Solu)on 2: Posi)onal indexes
 In the pos)ngs, store, for each term the posi)on(s) in
which tokens of it appear:

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Posi)onal index example

Which of docs 1,2,4,5 could contain “to be
or not to be”?  For phrase queries, we use a merge algorithm
recursively at the document level
 But we now need to deal with more than just equality

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Processing a phrase query
 Extract inverted index entries for each dis)nct term:
to, be, or, not.
 Merge their doc:posi2on lists to enumerate all posi)ons with “to be or not to be”.
 to:
 2:1,17,74,222,551; 4:8,16,190,429,433; 7:13,23,191; …
 be:
 1:17,19; 4:17,191,291,430,434; 5:14,19,101; …
 Same general method for proximity searches

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Proximity queries
 LIMIT! /3 STATUTE /3 FEDERAL /2 TORT  Again, here, /k means “within k words of”.
 Clearly, posi)onal indexes can be used for such queries; biword indexes cannot.
 Exercise: Adapt the linear merge of pos)ngs to handle proximity queries. Can you make it work for any value of k?
 This is a li^le tricky to do correctly and efficiently  See Figure 2.12 of IIR (Page 39)
 There’s likely to be a problem on it!

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Posi)onal index size
 You can compress posi)on values/offsets: we’ll talk about that in lecture 5
 Nevertheless, a posi)onal index expands pos)ngs storage substan2ally
 Nevertheless, a posi)onal index is now standardly used because of the power and usefulness of phrase and proximity queries … whether used explicitly or implicitly in a ranking retrieval system.

COMP6714: Informa2on Retrieval & Web Search
Sec. 2.4.2
Posi)onal index size
 Need an entry for each occurrence, not just once per document
 Index size depends on average document size  Average web page has <1000 terms Why?  SEC filings, books, even some epic poems ... easily 100,000 terms  Consider a term with frequency 0.1% Document size Postings Positional postings 1000 1 1 100,000 1 100 COMP6714: Informa2on Retrieval & Web Search Sec. 2.4.2 Rules of thumb  A posi)onal index is 2–4 as large as a non‐posi)onal index  Posi)onal index size 35–50% of volume of original text  Caveat: all of this holds for “English‐like” languages COMP6714: Informa2on Retrieval & Web Search Sec. 2.4.3 Combina)on schemes  These two approaches can be profitably combined  For par)cular phrases (“Michael Jackson”, “Britney Spears”) it is inefficient to keep on merging posi)onal pos)ngs lists  Even more so for phrases like “The Who”  Williams et al. (2004) evaluate a more sophis)cated mixed indexing scheme  A typical web query mixture was executed in 1⁄4 of the )me of using just a posi)onal index  It required 26% more space than having a posi)onal index alone COMP6714: Informa2on Retrieval & Web Search Sec. 2.4.3 Solu)on 3: Suffix Tree/Array  BANANA$             BANANA$ ANANA$ NANA$ ANA$ NA$ A$ A$ ANA$ ANANA$ BANANA$ NA$ NANA$ pos:0 pos:1 pos:2 pos:3 pos:4 pos:5 pos:5 pos:3 pos:1 pos:0 pos:4 pos:2 Sort on the strings COMP6714: Informa2on Retrieval & Web Search Sec. 2.4.3 Suffix Array  BANANA$  If the original string is available, each suffix can be completely specified by the index of its first character             BANANA$ ANANA$ NANA$ ANA$ NA$ A$ A$ ANA$ ANANA$ BANANA$ NA$ NANA$ pos:0 pos:1 pos:2 pos:3 pos:4 pos:5 pos:5 pos:3 pos:1 pos:0 pos:4 pos:2 Sort on the strings B A N A N A $ 4 3 6 2 5 1 7 COMP6714: Informa2on Retrieval & Web Search Resources for today’s lecture  Introduc2on to Informa2on Retrieval, chapter 1  Shakespeare:  h^p://www.rhymezone.com/shakespeare/  Try the neat browse by keyword sequence feature!  Managing Gigabytes, chapter 3.2  Modern Informa2on Retrieval, chapter 8.2 58 COMP6714: Informa2on Retrieval & Web Search Resources for today’s lecture    Skip Lists theory: Pugh (1990)  Mul)level skip lists give same O(log n) efficiency as trees H.E. Williams, J. Zobel, and D. Bahle. 2004. “Fast Phrase Querying with Combined Indexes”, ACM Transactions on Information Systems. h^p://www.seg.rmit.edu.au/research/research.php?author=4 D. Bahle, H. Williams, and J. Zobel. Efficient phrase querying with an auxiliary index. SIGIR 2002, pp. 215‐221. COMP6714: Informa2on Retrieval & Web Search Es)ma)ng Result Set Size  How many pages contain all of the query terms?  For the query “a b c”: fabc = N ∙ fa/N ∙ fb/N ∙ fc/N = (fa ∙ fb ∙ fc)/N2  Assuming that terms occur independently  fabc is the es)mated size of the result set  fa, fb, fc are the number of documents that terms a, b, and c occur in  N is the number of documents in the collec)on CMS09::Chap4 COMP6714: Informa2on Retrieval & Web Search GOV2 Example Collection size (N) is 25,205,179 COMP6714: Informa2on Retrieval & Web Search Inconsistent Es)mate by Google circa 2007 iterative proportional scaling 62 COMP6714: Informa2on Retrieval & Web Search Result Set Size Es)ma)on  Poor es)mates because words are not independent  Be^er es)mates possible if co‐occurrence informa)on available P(a ∩ b ∩ c) = P(a ∩ c) ∙ P(b|(a ∩ c)) ≈ P(a ∩ c) ∙ P(b|c) = P(a ∩ c) ∙ P(b ∩ c) / P(c) ftropical∩fish∩aquarium = ftropical∩aquarium ∙ ffish∩aquarium/faquarium = 1921 ∙ 9722/26480 = 705 vs. 1529 ftropical∩fish∩breeding = ftropical∩breeding ∙ ffish∩breeeding/fbreeding = 5510 ∙ 36427/81885 = 2451 vs. 3629 COMP6714: Informa2on Retrieval & Web Search Result Set Es)ma)on  Even be^er es)mates using ini)al result set  Es)mate is simply C/s  where s is the propor)on of the total documents that have been ranked, and C is the number of documents found that contain all the query words  E.g., “tropical fish aquarium” in GOV2  aÄer processing 3,000 out of the 26,480 documents that contain “aquarium”, C = 258 ftropical∩fish∩aquarium = 258/(3000÷26480) = 2,277  AÄer processing 20% of the documents, ftropical∩fish∩aquarium = 1,778 (1,529 is real value) COMP6714: Informa2on Retrieval & Web Search Mo)va)on into a Be^er Es)mator  Example 1. N = 100, fA = 10, fB = 20 2. 1 sec into the intersec)on query processing, the current cursors points to docID = 20 and 30 on A and B’s inverted lists, respec)vely; and there are 1 documents in the intersec)on. (Assuming docIDs are randomly assigned)  Es)ma)on 1. Based on independence: fAB = (10/100)*(20/100)*100 = 2 2. Based on “sampling”: fAB = 1 * (100/min(20, 30)) = 5  Can we combine the “strength” of both es)mators?  Condi)onal random sampling [Li & Church, A Sketch Algorithm for Es)ma)ng Two‐Way and Mul)‐Way Associa)ons]