1. Max-Planck Institute for Informatics
Efficient and Self-tuning Incremental Query Expansions for Top-k Query Processing
Martin Theobald
Ralf Schenkel
Gerhard Weikum
Max-Planck Institute for Informatics
Saarbrücken
Germany
ACM SigIR ‘05

2. An Initial Example…
TREC Robust Track ’04, hard query no (Aquaint news corpus)
“transportation tunnel disasters”
transportation tunnel disasters
1.0
Increased retrieval robustness
Count only the best match per document and expansion set
Increased efficiency
Top-k-style query evaluations
Open scans on new terms only on demand
No threshold tuning
1.0
1.0
transit
highway
train
truck
metro
“rail car”
car …
0.9
0.8
0.7
0.6
0.5
0.1
tube
underground
“Mont Blanc” …
0.9
0.8
0.7
catastrophe
accident
fire
flood
earthquake
“land slide” …
1.0
0.9
0.7
0.6
0.5 d2 d1
Expansion terms from relevance feedback, thesaurus lookups, Google top-10 snippets, etc.
Term similarities, e.g., Rocchio, Robertson&Sparck-Jones, concept similarities, or other correlation measures
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

3. Computational model & background on top-k algorithms
Outline
Computational model & background on top-k algorithms
Incremental Merge over inverted lists
Probabilistic candidate pruning
Phrase matching
Experiments & Conclusions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

4. Computational Model
Vector space model with a Cartesian product space D1×…×Dm and a data set D  D1×…×Dm   m
Precomputed local scores s(ti,d)∈ Di for all d∈ D
e.g., tf*idf variations, probabilistic models (Okapi BM25), etc.
typically normalized to s(ti,d)∈ [0,1]
Monotonous score aggregation
aggr: (D1×…×Dm )  (D1×…×Dm ) → +
e.g., sum, max, product (using sum over log sij ), cosine (using L2 norm)
Partial-match queries (aka. “andish”)
Non-conjunctive query evaluations
Weak local matches can be compensated
Access model
Disk-resident inverted index over large text corpus
Inverted lists sorted by decreasing local scores
 Inexpensive sequential accesses to per-term lists: “getNextItem()”
 More expensive random accesses: “getItemBy(docid)”
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

5. No-Random-Access (NRA) Algorithm
[Fagin et al., PODS ’01
Balke et al. VLDB ’00
Buckley&Lewit, SigIR ‘85]
Corpus: d1,…,dn
NRA(q,L):
scan all lists Li (i = 1..m) in parallel // e.g., round-robin
< d, s(ti ,d) > = Li.getNextItem()
E(d) = E(d)  {i}
highi = s(ti ,d)
worstscore(d) = ∑E(d) s(t ,d)
bestscore(d) = worstscore(d) + ∑E(d) high
if worstscore(d) > min-k then
add d to top-k
min-k = min{ worstscore(d’) | d’  top-k}
else if bestscore(d) > min-k then
candidates = candidates  {d}
if max {bestscore(d’) | d’ candidates}  min-k then return top-k d1 d1 d1
s(t1,d1) = 0.7 …
s(tm,d1) = 0.2
Query q = (transportation, tunnel disaster)
Inverted Index
Rank
Doc#
Worst-score
Best-score 1
d78
0.9
2.4 2
d64
0.8 3
d10
0.7
k = 1
Rank
Doc#
Worst-score
Best-score 1
d78
1.4
2.0 2
d23
1.9 3
d64
0.8
2.1 4
d10
0.7
Rank
Doc#
Worst-score
Best-score 1
d10
2.1 2
d78
1.4
2.0 3
d23
1.8 4
d64
1.2
d78
0.9
d23
0.8
d10
0.8 d1
0.7
d88
0.2
transport
Scan
depth 1 …
Scan
depth 2
Scan
depth 3
Naive Join-then-Sort
in between
O(mn) and O(mn2) runtime
d64
0.8
d23
0.6
d10
0.6
d10
0.2
d78
0.1
tunnel …
d10
0.7
d78
0.5
d64
0.4
d99
0.2
d34
0.1
STOP!
disaster …
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

6. Computational model & background on top-k algorithms
Outline
Computational model & background on top-k algorithms
Incremental Merge over inverted lists
Probabilistic candidate pruning
Phrase matching
Experiments & Conclusions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

7. Dynamic & Self-tuning Query Expansions
top-k
(transport, tunnel,
~disaster)
Incrementally merge inverted lists Li1…Lim’ in descending order of local scores
Dynamically add lists into set of active expansions exp(ti)
Only touch short prefixes of each list, don’t need to open all lists
Best match score aggregation for combined term similarities and local scores
d42
d11
d92 …
virtual list ~disaster
d42
d11
d92
...
d21
d78
d10 d1
d32
d87
disaster
accident
fire
transport
tunnel
incr. merge
d66
d95
d93
d17
d95
d11
d101
d99
...
...
Increased retrieval robustness & fewer topic drifts
Increased efficiency through fewer active expansions
No threshold tuning of term similarities in the expansions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

8. Incremental Merge Operator
Index list meta data
(e.g., histograms)
Relevance feedback,
Thesaurus lookups,…
Initial high-scores
Expansion terms
~t = {t1,t2,t3}
Correlation measures,
Large corpus statistics …
sim(t, t1 ) = 1.0 t1
...
d78
0.9 d1
0.4
d88
0.3
d23
0.8
d10
0.9
0.4
...
d12
0.2
d78
0.1
d64
0.8
d23
d10
0.7 t2
sim(t, t2 ) = 0.9
Expansion similarities
0.72
0.18
sim(t, t3 ) = 0.5 t3
...
d99
0.7
d34
0.6
d11
0.9
d78
d64
Incremental Merge
iteratively triggered by top-k operator  sequential access “getNextItem()”
0.45
0.35 ~t
d78
0.9
d23
0.8
d10
0.8
d64
0.72
d23
0.72
d10
0.63
d11
0.45
d78
0.45 d1
0.4
d88
0.3
...
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

9. Computational model & background on top-k algorithms
Outline
Computational model & background on top-k algorithms
Incremental Merge over inverted lists
Probabilistic candidate pruning
Phrase matching
Experiments & Conclusions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

10. Probabilistic Candidate Pruning [Theobald, Schenkel & Weikum, VLDB ‘04]
For each physically stored index list Li
Treat each s(ti,d)  [0,1] as a random variable Si and consider
Approximate local score distribution using an
equi-width histogram with n buckets
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

11. Probabilistic Candidate Pruning [Theobald, Schenkel & Weikum, VLDB ‘04]
For each physically stored index list Li
Treat each s(ti,d)  [0,1] as a random variable Si and consider
Approximate local score distribution using an
equi-width histogram with n buckets
For a virtual index list ~Li = Li1…Lim’
Consider the max-distribution (feature independence)
Alternatively, construct meta histogram for the active expansions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

12. Return current top-k list if candidate queue is empty!
Probabilistic Candidate Pruning [Theobald, Schenkel & Weikum, VLDB ‘04]
For each physically stored index list Li
Treat each s(ti,d)  [0,1] as a random variable Si and consider
Approximate local score distribution using an
equi-width histogram with n buckets
For a virtual index list ~Li = Li1…Lim’
Consider the max-distribution (feature independence)
Alternatively, construct meta histogram for the active expansions
For all d in the candidate queue
Consider the convolution over local score distributions to predict aggregated scores
Drop d from candidate queue, if
Return current top-k list if candidate queue is empty!
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

13. Computational model & background on top-k algorithms
Outline
Computational model & background on top-k algorithms
Incremental Merge over inverted lists
Probabilistic candidate pruning
Phrase matching
Experiments & Conclusions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

14. Incremental Merge for Multidimensional Phrases
q = {undersea „fiber optic cable“}
Top-k
Nested Top-k operator iteratively prefetches & joins candidate items for each subquery condition
“getNextItem()”
Propagates candidates in descending order of bestscore(d) values to provide monotonous upper score bounds
Provides [wortscore(d), bestscore(d)] guarantees to superordinate top-k operator
Top-level top-k operator performs phrase tests only for the most promising items (random access)
(Expensive predicates & minimal probes [Chang&Hwang, SIGMOD ‘02] )
Single threshold condition for algorithm termination (candidate pruning at the top-level queue only)
Incr.Merge
sim(„fiber optic cable“,
„fiber optic cable“)
= 1.0
sim(„fiber optic cable“,
„fiber optics“)
= 0.8
Nested
Top-k
Nested
Top-k
undersea …
d14
0.9
d23
0.8
d32
0.7
d18 d1
fiber …
d78
0.9 d1
0.7
d88
0.2
d23
0.8
d10
optic
d34 d7
0.4
0.3
d12
0.6
cable
d41 d2
0.1
d75
0.5
fiber …
d78
0.9 d1
0.7
d88
0.2
d23
0.8
d10
optics d5
0.4
d47
0.1
d17
0.6
random access
term-to-
position
index
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

15. Computational model & background on top-k algorithms
Outline
Computational model & background on top-k algorithms
Incremental Merge over inverted lists
Probabilistic candidate pruning
Phrase matching
Experiments & Conclusions
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

16. Experiments – Aquaint with Fixed Expansions
Aquaint corpus of English news articles (528,155 docs)
50 “hard” queries from TREC 2004 Robust track
WordNet expansions using a simple form of WSD
Okapi-BM25 model for local scores, Dice coefficients as term similarities
Fixed expansion technique (synonyms + first-order hyponyms)
# SA
#CPU sec
MAP
@1000
relPrec
max(m)
max(KB)
# RA
avg(m)
Title-only Baseline
Join&Sort
2.5 4
2,305,637
NRA-Baseline
1,439,815
9.4
432 KB
0.252
0.092
1.000
Static Expansions
Join&Sort 35
118
20,582,764
NRA+Phrases, ε=0.0
18,258,834
210,531
245.0
37,355 KB
0.286
0.105
1.000
NRA+Phrases, ε=0.1
3,622,686
49,783
79.6
5,895 KB
0.238
0.086
0.541
Dynamic Expansions
Incr.Merge, ε=0.0 35
118
7,908,666
53,050
159.1
17,393 KB
0.310
0.118
1.000
Incr.Merge, ε=0.1
5,908,017
48,622
79.4
13,424 KB
0.298
0.110
0.786
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

17. Experiments – Aquaint with Fixed Expansions, cont’d
Probabilistic Pruning Performance Incremental Merge vs. top-k with static expansions Epsilon controls pruning aggressiveness 0 ≤ ε ≤ 1
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

18. Conclusions & Ongoing Work
Increased efficiency
Incremental Merge vs. Join-then-Sort & top-k using static expansions
Very good precision/runtime ratio for probabilistic pruning
Increased retrieval robustness
Largely avoids topic drifts
Modeling of fine grained semantic similarities
(Incremental Merge & Nested Top-k operators)
Scalability (see paper)
Large expansions (m < 876 terms per query) on Aquaint
Expansions for Terabyte collection (~25,000,000 docs)
Efficient support for XML-IR (INEX Benchmark)
Inverted lists for combined tag-term pairs e.g., sec=mining
Efficiently supports child-or-descendant axis e.g., //article//sec//=mining
Vague content & structure queries (VCAS) e.g., //article//~sec=~mining
TopX-Engine, VLDB ’05
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing

19. Thank you!
ACM SigIR ‘05
Efficient & Self-tuning Incremental Query Expansions for Top-k Query Processing