Of Sampling and Smoothing: Approximating Distributions over Linked Open Data

Institute for Web Science & Technologies – WeST

Of Sampling and Smoothing: Approximating Distributions over

Linked Open Data

Thomas Gottron

May 26th, 2014

PROFILES Workshop, Crete

Thomas Gottron PROFILES 26.5.2014, 2Approximating Distributions over LOD

Distributions over Linked Data

Probability to observe a certain pattern k

foaf:knows

Predicates

foaf:Personrdf:type

RDF class types

:follo

?x foaf:knows

rdfs:label

Property Sets

?y foaf:Person

dbpedia:Actor

rdf:type

Type Sets rdf:t

dbpedia:Actor

foaf:knows

foaf:name

Effectively: Estimate a distribution over pattern instances ki

Applications: Query federation Data Mining Schema inferencing

k1 k2 knk3 ...

Using entire LOD cloud becomes less and less feasible Solution:

Operate on a sample

Challenges: How to sample? How to deal with unobserved

instances of a pattern?

k1 k2 knk3 ...

Only an approximation!

Sampling Linked Open Data

Data Format

Linked Data as N-Quads:

triple – what is the information?

context URI – where does it come

( )s op c

Sampling Strategies

Triple (Edge) Based Sampling

Unique Subject URI (Node) Based Sampling

Context Based Sampling

For all sampling approaches: Unbiased sampling based on uniform distribution

Smoothing Distributions

Obtaining a Distribution from an Index

d1,1 d1,2 d1,3 ...

d2,1 d2,2

d3,1 d3,2 d3,3 ...

dn,1 dn,2 dn,3 ...

https://github.com/gottron/lod-index-models

Obtaining a Distribution from an Index

Relative frequencies

Unobserved patterns!

Unobserved pattern instance (e.g. predicate, type sets)

Adjusted relative frequencies

<new> 0

P(<new>) = 0

P(<new>) > 0

Unobserved patterns!

Unobserved pattern instance (e.g. predicate, type sets)

Lidstone-Smoothing with parameter λ Laplace-Smoothing (Add-One) for λ = 1

<new> 0

Evaluation

Experimental Evaluation

Obtain different distributions based on: Sampling:

• Strategy (triple, USU, context)• Rate: (5% - 90%)

Smoothing:• Laplace• Lidstone with λ = 0.5, λ = 0.1 and λ = 0.01

Compare to full data set 10 iterations

Dynamic Linked Data Observatory

Weekly snapshots, 16M triples(only first snapshot used here)

Comparing Distributions

Information theoretic measure for comparing distributions:

Cross-Entropy of P and Q

Kullback-Leibler Divergence

Experimental Setup

Index construction / Estimation of distributions

5% 10% 20% 30% Full (100%)

„dev

10% 20% 30% 100%90%

RDF class typesPredicates

Impact of Sampling Strategy

Property sets Type sets

ECS similar

Impact of SmoothingPredicates, context

samplingPredicates, triple sampling

ECS, context sampling ECS, USU sampling

Conclusion

Summary

Baseline for sampling and smoothing techniques Little difference between classical smoothing techniques Quality of context-based sampling as realistic scenario Other samplings suitable for generating VoID descriptions

Future Work

Smarter smoothing techniques Inspired by Language Modelling Specific for LOD

Thanks!

Contact:Thomas Gottron

WeST – Institute for Web Science and Technologies

Universität Koblenz-Landau

gottron@uni-koblenz.de

Of Sampling and Smoothing: Approximating Distributions over Linked Open Data

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