Probabilistic XML database PRM

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Probabilistic XML database-----PRMBN

• Qihong SHAO

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Motivation

• Uncertain data exist anywhere in the research
• Automated data minging and analysis tools are
  often error-prone
• Data integrated from various sources is often
  uncertain or conflict
• Experiment results are observed in conditions
  which maybe subject to a range of variability in
  natural environment
• Human errors (typos, operation errors, biases, )
• ! Lack of built-in tools to manage data quality
  and uncertain information

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Challenges

• Current research attempts to design probabilistic
  databases and query uncertain data, the node is
  associated with an optinal confidence
• Assumption data tuples are independent
• Fail to capture data dependence relationship,
  result in incorrect confidence computation in
  many applications

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Outline

• What is BN?
• What is PRM?
• Our project

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Bayesian Networks

• A Bayesian network consists of two components.
• a directed acyclic graph G,
• nodes attributes A1,A2,..An
• edges in the graph denote a direct dependence of
  an attribute Ai on its parents Parents(Ai)
• a set of conditional independence assumptions
  each node Ai is conditionally independent of its
  non-descendants given its parents.
• CPD(Conditional Probability Distribution)
• For each attribute, P(AiParents(Ai)) specifies
  the distribution over the values of Ai given any
  possible assignment of values to its parents.

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a) A Bayesian network for the census domain. b)
A tree-structured CPD for the Children node given
its parents Income, Age and Marital-Status.
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Example

• the table contains 12 attributes
• Age, Worker-Class, Education,Marital-Status,
  Industry, Race, Sex, Child-Support, Earner,
  Children, Income, and Employment-Type.
• The domain sizes for the attributes are,
  respectively 18, 9, 17, 7, 24, 5, 2, 3, 3, 42,
  and 4.
• Children attribute depends on other attributes
  only via the attributes
• Income, Age, Marital-Status-gt Children.
• Thus, Children is conditionally independent of
  all other attributes given Income, Age, and
  Marital-Status.

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• With BN, over Children given
• Income?17.5K, Agelt55, and Marital-Statusnever-ma
  rried is (0.19, 0.04, 0.07)
• Income?17.5K, Agelt50, and Marital-Statusmarried
  is (0.26, 0.47, 0.27)
• Income?17.5K, Agelt50, and Marital-Status
  widowed is (0.26, 0.47, 0.27)

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• The conditional independence assumptions
  associated with the BN , together with the CPDs
  associated with the nodes, uniquely determine a
  joint probability distribution over the
  attributes via the chain rule

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BNs for Query Estimation

• A Bayesian network is a compact representation of
  a full joint distribution.
• It implicitly contains the answer to any query
  about the probability of any assignment of values
  to a set of attributes.

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Problem

• Example
• A medical database with two tables
• Patient, containing tuberculosis (TB) patients,
• Contact, containing people with whom a patient
  has had contact, and who may or may not be
  infected with the disease.
• Queries involving a join between these two
  tables.
• // finding all patients whose age is over 60
  who have had contact with a roommate.
• patient.Age 60 and contact. Patient
  patient.Patient-ID
• where contact.Contype roommate,

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• Attributes of different table are often
  correlated.
• In general, foreign keys are often used to
  connect tuples in different tables that are
  semantically related, and hence the attributes of
  tuples related through foreign key joins are
  often correlated.
• For example, there is a clear correlation between
  the age of the patient and the type of contacts
  they have in fact, elderly patients with
  roommates are quite rare, and this naive approach
  would overestimate their number.
• the probability that two tuples join with each
  other can also be correlated with various
  attributes.
• For example, middle-aged patients typically have
  more contacts than older patients.

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PRM

• Probabilistic relational models (PRMs)
• extend Bayesian networks to the relational
  setting.
• allow us to model correlations not only between
  attributes of the same tuple, but also between
  attributes of related tuples in different tables.
  
• a parent of an attribute R.A, an attribute S.B in
  another relation S such that R has a foreign key
  for S .
• allow dependencies on attributes in relations
  that are related to R via a longer chain of joins

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PRM
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• A PRM for our TB domain is shown below, Here, for
  example, we have that the type of the contact
  depends on the age and gender of the patient.

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The key component of PRM

• the annotation of a frame with a probability
  model
• a BN represent a distribution over the possible
  values of the slots in the frame
• Each simple slot in the frame is annotated with a
  local probability model, represent the dependence
  of its value on the values of related slots

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PRM is more expressive than BN

• Allow the probability model of a slot to depend
  on a slot chain
• Allow the properties of one instance depend on
  the properties of other related instances
• Allow inheritance
• Express structure uncertainty,
• express number uncertainty about the set of
  entities in the model(the number of PHD students
  in a department)
• represent relevance uncertainty about relations
  between entities(which of several conferences a
  paper appeared in)

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Our Project

• Modeling uncertain XML data
• Modeling uncertainty using probabilisties
• Considering XFDs in probabilistic XML data
• Defining data dependencies in probabilistic XML
  data
• Effective query evaluation on a probabilistic XML
  database
• Define query languages
• Compute the probability of a node
• Compute the joint probability of the event
• Support different query requirement

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References

• Learning Probabilistic Models of Link
  Structure, L. Getoor, N. Friedman, D. Koller
  and B. Taskar, JMLR 2002.
• Probabilistic Models of Text and Link Structure
  for Hypertext Classification, L. Getoor, E.
  Segal, B. Taskar and D. Koller, IJCAI WS Text
  Learning Beyond Classification, 2001.
• Selectivity Estimation using Probabilistic
  Models, L. Getoor, B. Taskar and D. Koller,
  SIGMOD-01.
• Learning Probabilistic Relational Models, L.
  Getoor, N. Friedman, D. Koller, and A. Pfeffer,
  chapter in Relation Data Mining, eds. S. Dzeroski
  and N. Lavrac, 2001.
• see also N. Friedman, L. Getoor, D. Koller, and
  A. Pfeffer, IJCAI-99.
• Learning Probabilistic Models of Relational
  Structure, L. Getoor, N. Friedman, D. Koller,
  and B. Taskar, ICML-01.
• From Instances to Classes in Probabilistic
  Relational Models, L. Getoor, D. Koller and N.
  Friedman, ICML Workshop on Attribute-Value and
  Relational Learning Crossing the Boundaries,
  2000.
• Notes from AAAI Workshop on Learning Statistical
  Models from Relational Data, eds. L.Getoor and D.
  Jensen, 2000.
• Notes from IJCAI Workshop on Learning Statistical
  Models from Relational Data, eds. L.Getoor and D.
  Jensen, 2003.

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• Thank you!