Top-K Query Evaluation on Probabilistic DataChristopher Ré, Nilesh Dalvi and Dan SuciuUniversity of Washington

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High Level Overview

DBMS: Precise answers over clean data Data are often imprecise

Information Integration Information Extraction

Probabilistic DB (PDB) handle imprecisionMany low quality answersTop-K ranked by probability

This talk: Compute Top-K Efficiently

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Overview

Motivating Example Query Processing Background Multisimulation Experimental Results

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Overview

Motivating Example Query Processing Background Multisimulation Experimental Results

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Example Application

IMDB• Lots of interesting data above

movies (e.g. actors, directors)• Well maintained and clean• But no reviews!

On the web there are lots of reviews

How will I know which movie they

are about?

Alice needs to do information extraction and object reconcillation.

Is a movie good or bad?

Alice wants to do sentiment analysis.

A probabilistic database can help Alice store and query her uncertain data.

Find all years where ‘Anthony Hopkins’ starred in a good

movie

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Imprecision is out there…Object Reconciliation

RID Titler124 12 Monkeysr155 Twelve Monkeysr175 2 Monkeyr194 Monk

MID Titlem232 12 Monkeysm143 Monkey Love

Our Approach: Convert scores to probabilities

Data extracted from Reviews

Clean IMDB Data

Output: (RID,MID) pairs

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MatchNo Match

t’ t

Felligi-Sunter Approach: Score (s) each (RID,MID)

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Imprecision is out there…

Object Reconciliation

RID Titler124 12 Monkeysr155 Twelve Monkeysr175 2 Monkeyr194 Monk

MID Titlem232 12 Monkeysm143 Monkey Love

RID MID Probr175 m232 0.8r175 m143 0.2

Felligi-Sunter Approach: Score (s) each (RID,MID)

MatchNo Match

t’ t

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Overview

Motivating Example Query Processing Background Multisimulation Experimental Results

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Query Processing Background

RID MID Probr175 m232 0.8r175 m143 0.2

Query Processing builds event expression

• Intensional Query Processing [FR97]

• Associate to each tuple an event

• Probability event is satisfied = query valueTechnical Point: Projection as last operator implies result is a DNF

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DNF Sampling at a High Level

Estimate p(t),probability DNF sat satisfied Do for each output tuple, t#P-Hard [Valiant79] even if only conjunctive

queries [RDS06,DS04]Randomized Approximation [LK84]

Simulation reduces uncertainty

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Naïve Query Processing

Naïve algorithm (PTIME): Simulate until all small “Epsilon”-small

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Christopher Walken

Harvey Keitel

Samuel L. Jackson

Bruce Willis

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Can we do better?

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Overview

Motivating Example Query Processing Background Multisimulation Experimental Results

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A Better Method: Multisimulation Separate Top-K with few simulations

Concentrate on intervals in Top-K Asymptotically, confidence intervals are nested

Compare against OPT “knows” which intervals to simulate

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The Critical Region

The critical region is the interval (kth-highest min, k+1st higest max) For k = 2

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Three Simple Rules: Rule 1

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Pick a “Double Crosser” OPT must pick this too

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Three Simple Rules: Rule 2

All lower/upper crossers then maximal OPT must pick this too

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Three Simple Rules: Rule 3

Pick an upper and a lower crosser OPT may only pick 1 of these two

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Multisimulation is a 2-Approx

Thm: Multisimulation performs at most twice as many simulations as OPT And, no deterministic algorithm can do better on every

instance. Extensions

Top-K Set (shown) Anytime (produce from 1 to k) Rank (produce top k ranked) All ( rank all intervals )

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Overview

Motivating Example Query Processing Background Multisimulation Experimental Results

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Experiment Details: Uncertain tuples

Table # TuplesStringMatch 339k

ActorMatch 6,758k

DirectorMatch 18k

Table # TuplesReviews 292k

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Running Time

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Running Time

“Find all years in which Anthony Hopkins was in a highly rated movie” (SS)Small Number of Tuples Output (33)

Small DNFs per Output

(Avg. 20.4, Max 63)

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Running Time

“Find all directors who have a highly rated drama but low rated comedy” (LL)Large #Tuples Output (1415)

Large DNFs per Output

(Avg. 234.8, Max. 9088)

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Conclusions

Mystiq is a general purpose probabilistic database

Multisimulation and Logical Optimization key to performance on large data sets

Advert: Demo on my laptop

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Running Time“Find all actors in Pulp Fiction who appeared in two very bad movies in the five years before appearing in Pulp Fiction” (SL)Small Number of Tuples Output (33)

Large DNFs per Output

(Avg. 117.7,Max 685)

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Running Time“Find all directors in the 80s who had a highly rated movie” (LS)Large #Tuples Output (3259)

Small DNFs per Output

(Avg 3.03, Max 30)

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Christopher Walken

Harvey Keitel

Samuel L. Jackson

Bruce Willis

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