Probabilistic RDF

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Probabilistic RDF

• Octavian Udrea1
• V.S. Subrahmanian1
• Zoran Majkic2
• 1University of Maryland College Park
• 2University La Sapienza, Rome, Italy

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Motivation

• Not all information on the Web is easily
  expressible in classic models (i.e.,
  relational)
• RDF extraction from text
• STORY is the first, very successful prototype
• Need to extend RDF with temporal, uncertainty
  components
• Goal build a logical model of RDF with
  uncertainty and provide query algorithms

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The Probabilistic RDF idea

• An RDF theory is a set of triples (subject,
  property, value)
• (USA hasCapital Washington DC),
• (Washington DC hasPopulation 500,000)
• Probabilistic RDF extends this model with
  uncertainty over the set of values.
• (USA hasCapital (Washington DC, 0.95), (State of
  Washington, 0.05))

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Probabilistic RDF example
Extracted based on www.wrongdiagnosis .com
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Probabilistic RDF example
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Probabilistic RDF example
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Probabilistic RDF example
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Probabilistic RDF syntax

• Schema uncertainty
• (c subClassOf (C,d))
• Sd?C d(d) lt 1
• Class-instance uncertainty
• (x rdftype (C,d))
• Sd?C d(d) lt 1
• Instance-based uncertainty
• (x p (Y, d))
• Sy?Y d(y) lt 1

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Probabilistic RDF syntax

• Sanity requirements
• (c subClassOf (C1,d1)), ((c subClassOf (C2,d2))
  gt (C1 C2 and d1 d2) or C1 n C2 Ø
• Same applies for other types of uncertainty
• Transitive properties
• Simple inferential capability
• Examples associatedWith, controlledBy
• P-path
• A set of triples connected by transitive
  properties

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Example p-path
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P-path semantics and t-norms

• We cannot generally assume independence between
  triples on a transitive path
• Flu, AcuteBronchitis, Pneumonia
• T-norms are used to express the users knowledge
  of the relationship between triples
• ? is associative, commutative
• 0 ? x 0, 1 ? x x
• x lt y, z lt w gt x ? z lt y ? w
• P-Path probability t-norm applied to individual
  probabilities on the path

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Example p-path
(Flu, associatedWith, (Pneumonia, 0.455)) w.r.t.
the product t-norm
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pRDF semantics

• A world W is a set of simple triples (with no
  probabilities)
• An interpretation I associates a probability to
  each world
• I satisfies a pRDF theory
• For each (s, p, (V,d)), d(v) lt S I(W), where W
  contains (s,p,v)
• Same applies to paths w.r.t. to a given t-norm

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pRDF semantics

• A theory is consistent iff it has a satisfying
  interpretation
• Every pRDF theory is consistent
• Entailment T entails T iff every satisfying
  interpretation of T satisfies T
• Closure of a theory The entire set of triples
  entailed by the theory
• Maximal w.r.t. the probability values

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pRDF fixpoint semantics

• The closure operator ? adds exactly one entailed
  triple at each step
• (Flu associatedWith, (Acute Bronchitis, .7)) and
• (Acute Bronchitis associatedWith (Pneumonia,
  .65)) yields
• (Flu associatedWith, (Pneumonia, 0.455))
• w.r.t. the product t-norm
• ? has a fixpoint which is the theory closure.

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pRDF query processing

• We will consider only simple queries a triple
  with a variable term
• Example (? associatedWith Pneumonia 4)
• What is associated with Pneumonia with
  probability above .4?
• Simple method
• Compute the closure
• Select any triple in the closure that matches the
  query
• VERY expensive computationally

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pRDF query processing

• Set of algorithms for answering simple queries
  and conjunctions
• pRDF_Subject, pRDF_Property, , pRDF_conjunction
• Central idea
• Apply ? in only those directions that yield
  tuples relevant to the query
• Cut off path computations when the threshold can
  no longer be reached.
• min?(current_probability, threshold)

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Experimental results

• Implementation
• Java, 1700 LOC
• Disk-based storage for pRDF theories
• Synthetically generated datasets
• According to varying underlying distributions
• Datasets extracted from Web sources

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Experimental questions

• Does the underlying distribution affect query
  running time?
• From a practical point of view, which are the
  fastest types of queries?
• How does running time vary with the number of
  atoms in a conjunction?
• What other theory-dependent factors affect
  running time?
• Theory width
• Number of properties

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Query running time (Poisson)
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Query running time (zipf)
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Conjunctive queries running time
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Dependence on property width
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Number of properties
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Take away points

• RDF syntax with uncertainty
• Model-theory and fixpoint semantics for pRDF
• Efficient query algorithms for pRDF

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The end

• http//om.umiacs.umd.edu/
• Thank you!
• Questions comments