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

sioc

:follo

ws

?x foaf:knows

rdfs:label

Property Sets

rdf:t

ype

?y foaf:Person

dbpedia:Actor

rdf:type

Type Sets rdf:t

ype

?z

dbpedia:Actor

foaf:knows

foaf:name

ECS



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

from?

s op

c

( )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

s op

s

c


Smoothing Distributions


Obtaining a Distribution from an Index

k1

k2

k3

...

kn

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

k1

k2

k3

...

kn

4

2

10

8

Relative frequencies

...


Unobserved patterns!

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

Adjusted relative frequencies

k1

k2

k3

...

kn

4

2

10

8

<new> 0

...

+ λ

+ λ

+ λ

+ λ

+ λ

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

k1

k2

k3

...

kn

4

2

10

8

<new> 0

...

+ λ

+ λ

+ λ

+ λ

+ λ


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%)

...

90%

5%

„dev

iatio

n“

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

[email protected]

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