REPRES

ENTIN

G AND

QUERYING

CORRELATE

D TUPLE

S

IN PROBABILISTIC

DATABASES

P R I TH V I R

A J SE N A

M O L DE S H P A N D E

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsRepresenting DependenciesQuery evaluationExperimentsConclusions & Work to be done

GENERAL INFOHigh demand for storing uncertain data

Issues with the use of probabilistic databases

1) existent probabilistic databases make simplistic assumptions about the data that make it difficult to use them in applications that naturally produce correlated data2) Most probabilistic databases can only answer a restricted subset of the queries that can be expressed using traditional query languages

A framework that can represent not only probabilistic tuples but also

correlations among them to tackle these limitations

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsProbabilistic graphical models & factored representations

Representing DependenciesQuery evaluationExperimentsConclusions & Work to be done

INTRODUCTION (1/2)

Database research has primarily concentrated on how to store and query exact data

Many real-world applications produce large amounts of uncertain data

Databases need to do more than simply store and retrieve; they have to help the user sift through the uncertainty and find the results most likely to be the answer.

INTRODUCTION (2/2)

Numerous approaches (models) proposed to handle uncertainty.

However, most models make assumptions about data uncertainty that restricts applicability (they cannot easily model or handle dependencies and correlations among tuples)

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsProbabilistic graphical models & factored representations

Representing DependenciesQuery evaluationExperimentsConclusions & Work to be done

INDEPENDENT TUPLES MODEL(1/2) One of the most commonly used tuple-level uncertainty models, associates existence probabilities with individual tuples and assumes that the tuples are independent of each other

INDEPENDENT TUPLES MODEL (2/2)Evaluating a query via the set of possible worlds is clearly intractable as the number of possible worlds is very bigIntensional semantics guarantee results in accordancewith possible words semantics but are computationallyexpensive. Extensional semantics are computationally cheaper but do not guarantee results in accordance with the possible worlds semantics.

o Base tuples are independent of each other, the intermediate tuples that are generated during query evaluation are typically correlated

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsProbabilistic graphical models & factored representations

Representing DependenciesQuery evaluationExperimentsConclusions & Work to be done

TUPLE CORRELATIONS (1/2)

TUPLE CORRELATIONS (2/2)Although the tuple probabilities associated with s1, s2 and t1 are identical, the query results are drastically different across these four databases.

Since both intensional and extensional semantics assume base tuple independence neither can be directly used to do query evaluation in such cases.

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsRepresenting correlationsQuery evaluationExperimentsConclusions & Work to be done

REPRESENTING CORRELATIONS(1/3)

1) Associate every tuple t with a Boolean valued random variable Xt

2) f (X) is a function of a (small) set of random variables X, where 0 <= f (X) <=1

3) Associate with each tuple in the probabilistic database a random variable

4) Define factors on (sub)sets of tuple-based random variables to encode correlations.

5) The probability of an instantiation of the database is given by the product of all the factors.

REPRESENTING CORRELATIONS(2/3)Suppose we want to represent mutual exclusivity between tuples s1 and t1. In particular, let us try to represent the possible worlds:

REPRESENTING CORRELATIONS(3/3)Suppose we want to represent positive correlation between t1 and s1.

In particular, let us try to represent the possible worlds:

PROBABILISTIC GRAPHICAL MODEL REPRESENTATION

A probabilistic graphical model is graph whose nodes represent random variables and edges represent correlations

Complete Ind. Mutual Exclusivity Positive Correlation

Xt1

Xs2

Xs1 Xt1

Xs2

Xs1 Xt1

Xs2

Xs1

PROBABILISTIC GRAPHICAL MODEL REPRESENTATION

X1

X2

X3

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsProbabilistic graphical models & factored representations

Representing DependenciesQuery evaluationExperimentsConclusions & Work to be done

QUERY EVALUATION: BASIC IDEA Treat intermediate tuples as regular tuples. Carefully represent correlations between

intermediate tuples, base tuples and result tuples to construct a probabilistic graphical model.

Cast the probability computations resulting from query evaluation to inference in probabilistic graphical models.

QUERY EVALUATION: EXAMPLE

QUERY EVALUATION :EXAMPLE PROBABILISTIC GRAPHICAL MODEL

Xs1

Xs2Xt

1

Xr1

Xi2Xi1

Query evaluation problem in Prob. Databases: Compute the probability of the result tuple summed over all possible worlds of the database

Equivalent problem in prob. graph. models: marginal probability computation.

use inference algorithms

Xs2Xt

1

Xr1

Xi2Xi1

REPRESENTING PROBABILISTIC RELATIONS

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsProbabilistic graphical models & factored representations

Representing DependenciesQuery evaluationExperimentsConclusions & Work to be done

EXPERIMENTS (1/3)

Database contains 860 publications from CiteSeer [GBL98]. Searched for publications for given (misspelt) author name. Naturally involves mutual exclusivity correlations

EXPERIMENTS (2/3)

Ran experiments on randomly generated TPC-H dataset of size 10MB. The first bar on each query indicates the time it took to run the full query

including all the database operations and the probabilistic computations. The second one indicates the time it took to run only the database

operations using our Java implementation.

EXPERIMENTS(3/3)

The result of running an average query over a synthetically generated dataset containing tuples

OUTLINEGeneral InfoIntroductionIndependent tuples modelTuple correlationsProbabilistic graphical models & factored representations

Representing DependenciesQuery evaluationExperimentsConclusions & Work to be done

CONCLUSIONS There is an increasing need for database

solutions for efficiently managing and querying uncertain data exhibiting complex correlation patterns.

A simple and intuitive framework is presented, based on probabilistic graphical models, for explicitly modeling correlations among tuples in a probabilistic database

WORK TO BE DONEProblem: Although conceptually the approach presented allows for capturing arbitrary tuple correlations, exact query evaluation over large datasets exhibiting complex correlations may not always be feasible.

Future Considerations: Development of approximate query evaluation

techniques that can be used in such cases Develop disk-based query evaluation algorithms so

that their techniques can scale to very large datasets.