Approximate Selection Queries over Imprecise Data

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Approximate Selection Queries over Imprecise Data

• Iosif Lazaridis and Sharad Mehrotra
• University of California, Irvine
• ICDE Conference, March 2004
• Boston, MA, USA

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Talk Outline

• Regular vs. Approximate Selection Queries
• Quality-Aware Queries (QaQs)
• Optimization for QaQs
• Performance Study
• Conclusions

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Regular Selection Queries
Set of precise objects T
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Imprecise Objects

• An imprecise object o corresponds to a precise
  object ?o which can be retrieved (at cost) via a
  probe operation

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Approximate Selection Queries
Set of imprecise objects T
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Formal Problem Setting

• Let T be a set of imprecise objects
• Let ? be a selection predicate which maps an
  imprecise object to set YES, NO, MAYBE
• The exact set is
• E ?o o?T ?? ?(?o)YES
• The goal is to produce an approximate answer A
  with associated quality guarantees
• A will potentially contain both precise and
  imprecise objects

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Prescriptive vs. Diagnostic Quality Measures
Space of all possible approximate answers to a
query q
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Quality Metrics

• Set-based quality
• Precision fraction of objects in A that are also
  in E
• p A?? E / A
• Recall fraction of objects in E that are also in
  A
• r A?? E / E
• Value-Based Quality
• Each imprecise object o has laxity l(o)
• Each precise object ?o has laxity 0
• Answer Laxity
• lmax maxx?Al(x)

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Quality Guarantees
Laxity Guarantee is lmax maxx?Al(x)
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Quality-Aware Query (QaQ)

• Input consists of
• Set T
• Predicate ?
• Quality Requirements pq, rq, lqmax
• Answer A should be such that
• pG? ? pq, rG ? rq and lqmax ? lmax

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QaQ Selection Operator

• Requires O(1) memory/processing per input object
• Each object o is read, and ?(o) is evaluated
• Three choices for each object o
• Forward it to A
• Ignore it
• Probe it, get ?o then Forward or Ignore ?o

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Handling Objects

• Ignore NO objects
• YES objects
• If l(o) gt lqmax Probe or Ignore
• Else Forward
• MAYBE objects
• If l(o) gt lqmax Probe or Ignore
• Else all three choices are feasible

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Ensuring Correctness

• No object with laxity l(o)gtlqmax may be forwarded
• The precision guarantee pG may not be lower than
  pq
• If no other YES objects remain to be seen, then
  pq will be violated
• If A??Y / (Y Ms-A) lt rq then an object o
  cannot be ignored
• If no other YES objects remain to be seen, then
  rq will be violated

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QaQ Evaluation Cost

• R number of objects read (R?? T)
• Y, M number of objects that were YES/MAYBE at
  the input
• Yf, Yp number of YES objects that are
  forwarded/probed (YfYp ? Y)
• Mf, Mp number of MAYBE objects that are
  forwarded/probed (MfMp ? M)
• Mpy number of probed MAYBE objects that become
  YES
• Cost W Rcr (YpMp)cp
  (YfMf)cwi(YpMpy)cwp
• read probe
  write

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The Map
NO MAYBE YES
Probe with probability ppy or Ignore
l(o)
1
2
3
6
Probe
Ignore
s5
s3
4
5
Forward with probability pfm or Ignore
Probe
s(o)0 0lts(o)lt1 s(o)1
s(o) probability MAYBE?YES
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Query Optimization

• Free parameters ppy, s3, s5 , pfm
• Estimate of YES, NO, MAYBE objects
• Estimate of YES, MAYBE objects above lqmax
  laxity requirement
• Requires some knowledge of distribution of l(o)
• Distribution of s(o)
• Minimize cost W subject to pq, rq, lqmax
• 4-parameter optimization problem

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Query Evaluation

• Get selectivity estimates
• Solve optimization problem for ppy, s3, s5 , pfm,
  thus instantiating the Map
• Read one object at a time, handle it according to
  the Map
• Make sure correctness criteria are enforced!
• Finish when rG ? rq

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Performance Study

• Size of input T 10,000
• Laxity ranges in 0,100
• Probe cost 100 x read/write unit cost.
• We vary
• Precision, Recall, Laxity Requirement
• Query selectivity
• Input Uncertainty (ratio of YES/MAYBE objects)
• Costs are normalized by dividing with T

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Competing Algorithms

• We devised two simple heuristics
• STINGY avoids probes it ignores MAYBE objects
  and objects exceeding the lqmax threshold.
• STINGY is conservative, but sometimes it is
  forced to probe to meet the quality guarantees.
• GREEDY forwards all MAYBE objects and probes all
  objects that exceed the lqmax threshold.
• GREEDY tries to produce the result quickly by not
  ignoring objects, but sometimes it uses too many
  probes and forwards too many objects

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Varying Laxity

• Input has 20 YES, 20 MAYBE objects
• 90 Precision and 50 Recall is requested
• As the laxity requirement becomes looser, the
  cost is reduced since imprecise objects can be
  forwarded without a probe

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Varying Precision

• Input has 20 YES, 20 MAYBE objects
• 50 Recall and laxity50 is requested
• Cost increases as Precision requirement
  increases, as objects cant be forwarded unprobed

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Varying Recall

• Input has 20 YES, 20 MAYBE objects
• 90 Precision and laxity50 is requested
• Cost increases as Recall requirement increases
• When Recall requirement is low, only part of the
  input needs to be read
• As Recall requirement tends to 100, all the
  input must be read and no objects can be ignored

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Varying Selectivity

• Input has 20 YES, 20 MAYBE objects
• 90 Precision, 50 Recall, and laxity50 is
  requested
• Cost increases as selectivity increases, since
  more objects need to be output

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Varying Input Uncertainty

• Input has 20 YES, 20 MAYBE objects
• 90 Precision, 50 Recall, and laxity50 is
  requested
• When MAYBE objects are few, no probe cost needs
  to be paid the few MAYBE objects can be ignored
• When MAYBE objects are many, they cannot be
  ignored (Recall might be violated), or forwarded
  (Precision violated). Hence, they are probed,
  increasing the cost

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Conclusions

• Quality-Aware Queries (QaQs)
• Query predicate quality requirement
• Response answer quality guarantee
• Quality Metrics for Set-Based Answers
• On-line algorithm for evaluating QaQs
• Works better than simple heuristics
• Takes into account input characteristics/user
  requirements
• Combines data read/write probing cost
• Future Work
• Indexes, Joins

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Thank You!
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