Rule Mining and Applications in Social Data

Rule Mining and applications in Social Data

Luis GalárragaTélécom ParisTech

Presented at:International Workshop on Social Media and Culture 2014

Daejeon, KoreaApril 4th, 2014

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Natural Language vs Knowledge Bases (KBs)

Natural Language Knowledge Bases

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Is a performs

born On

Feb 2, 1977

Singer

Hips don't lie

Shakira

Natural Language vs Knowledge Bases (KBs)

Natural Language Knowledge Bases

Understandable forcomputer programs

3

Suitable for humans but difficult

for computers

Some popular KBs

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KBs in action

Some popular KBs

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Social graphs are KBs

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● Sources may be different but they both share: ● Natural graph-like structure likes

Luis Galárraga

Shakira

Hips don't lie

friendOf

Shamiralikes

performs

likes


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● Sources may be different but they both share: ● Natural graph-like structure

● Incompleteness

likes

Luis Galárraga

friendOf

Shamira

likes

Shakira

Hips don't lie

likes

performs

likes

likes


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likes

Luis Galárraga

friendOf

Shamira

likes


● Incompleteness

Shakira

Hips don't lie

likes

performs

Maybe nobody asked me? :(


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likes

Luis Galárraga

friendOf

Shamira


● Incompleteness

● Opportunities for data description and prediction.

Shakira

Hips don't lie

likes

performs

likes


likes

Luis Galárraga

friendOf

Shamira


● Incompleteness

● Opportunities for data description and prediction.

90% of computer scientists like political party X

If you like Shakira you are likely to buy her latest song

Shakira

Hips don't lie

likes

performs

likes

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Rule Mining and KBs

● Data Mining is about finding interesting and non-obvious correlations in data.

● Correlations are rules that hold often.● You probably live in the same city of your spouse.● If you like an artist, you like her songs.

● They can be formulated as logical rules:

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isMarriedTo(x, y) ^ livesIn(x, city) => livesIn(y, city)

likes(x, artist) ^ performs(artist, song) => likes(x, song)

Applications for social data

● Recommendations

likes

Luis Galárraga

friendOf

Shamira

Shakira

Hips don't lie

likes

performs


likes

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● Recommendations

likes

Luis Galárraga

friendOf

Shamira

Shakira

Hips don't lie

likes

performs


likes

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● Recommendations

likes

Luis Galárraga

friendOf

Shamira

Shakira

Hips don't lie

performs


likes

likes

likes

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● Market basket analysis.● People who buy laptops also buy laptop cases.

● Link and event prediction● Two people who attended the same high school the same

year might know each other.● If you registered for this workshop, then you are coming to

Daejeon (and need to book a flight and hotel).

● Dealing with incompleteness● If you like German newspapers, fluency in German is

perhaps missing in your profile.

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Challenges

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Challenges of Rule Mining from KBs

● Scalability● State-of-the-art approaches for rule mining cannot

handle the size of current KBs.– YAGO: 10M entities, 120M facts– Dbpedia 3.8: 24.9M entities, 1.98B facts.– Facebook Graph: 1.2B users

● Rule Mining requires exhaustive search of the data.

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Challenges of Rule Mining from KBs

● Scalability● State-of-the-art approaches cannot handle the size of

current KBs.– YAGO: 10M entities, 120M facts– Dbpedia 3.8: 24.9M entities, 1.98B facts.– Facebook Graph: 1.2B users

● Rule Mining requires exhaustive search of the data.

● Solution:● Language bias.● A set of pruning heuristics.● Optimized storage implementation. 19

AMIE: Association Rule Mining Under Incomplete Evidence

● AMIE is a system that learns Horn rules such as:

● Starting with all possible head relations r(x,y) and a minimum support threshold:– The system explores the search space by means of

carefully designed mining operators.– Search space is restricted to closed Horn rules.– Monotonicity of support helps pruning non-promising paths.– It relies on an optimized in-memory database.– Confidence gain is used to prune the output.

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livesIn(x, city) ^ isMarriedTo(x, y) => livesIn(y, city)

L. Galárraga, C. Teflioudi, K. Hose, and F. M. Suchanek. AMIE: association rule mining under incomplete evidence in ontological knowledge bases. In WWW, 2013.

y citylivesIn

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livesIn(x, city) ^ isMarriedTo(x, y) => livesIn(y, city)

y citylivesIn

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y citylivesIn

Add dangling atom (OD) y city

livesIn?r

isMarriedTolivesIn

….

x

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y citylivesIn


livesIn?r

isMarriedTolivesIn

….

x

y citylivesInmarriedTo

x

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y citylivesIn


livesIn?r

isMarriedTolivesIn

….

x


x

Add closing atom (OC) y city

livesInx

isMarriedTo

?rlivesIndiedIn

…

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y citylivesIn


livesIn?r

isMarriedTolivesIn

….

x


x


livesInx

isMarriedTo

?rlivesIndiedIn

…

livesIn

y citylivesIn

xisMarriedTo

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y citylivesIn


livesIn?r

isMarriedTolivesIn

….

x


x


livesInx

isMarriedTo

?rlivesIndiedIn

…

livesIn

y citylivesIn

xisMarriedTo

27livesIn(x, city) ^ isMarriedTo(x, y) => livesIn(y, city)


Minimum support threshold

RDF KB

k

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Concurrent mining implementation

Tailored In-memory DB

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Facts RulesYAGO2 1M 3.62min 138

1M 17.76min 18K6.7M 2.89min 6.9K

Dataset Runtime

YAGO2 (const)Dbpedia (2 atoms)

AMIE finds rules in medium-size ontologies in a few minutes.

Challenges of Rule Mining on KBs

● Incompleteness● Graph data often contains gaps.

● Open World Assumption (OWA)● Absence of evidence is not evidence of absence

● Problem to estimate the confidence of a rule.





likes

Luis Galárraga

friendOf

ShamiraShakira

likes

citizenOf

likes(x, Shakira) => isCitizenOf(x, Ecuador)

Ecuador





likes(x, Shakira) => isCitizenOf(x, Ecuador) likes

Luis Galárraga

friendOf

ShamiraShakira

likes

citizenOf

Standard confidence uses a CWA and counts Shamira as counterexample. Score = 0.5

Ecuador



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likes

Luis Galárraga

friendOf

ShamiraShakira

likes

Ecuador

AMIE uses the Partial Completeness Assumption (PCA) to estimate the confidence of rules under OWA.

A KB knows all or none of the nationalities of a person.

citizenOf



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likes

Luis Galárraga

friendOf

ShamiraShakira

likes

Ecuador

AMIE uses the Partial Completeness Assumption (PCA) to estimate the confidence of rules under OWA.

A KB knows all or none of the nationalities of a person.

citizenOf

PCA confidence considers as counterexamples only those people whose nationality is known to be different from Ecuador. Score = 1.0

AMIE: Association Rule Mining under Incomplete Evidence

● PCA confidence has better predictive behavior than the standard confidence.

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AMIE: Association Rule Mining under Incomplete Evidence

isMarriedTo(x, y) livesIn(x, z) => livesIn(y, z)∧isCitizenOf(x, y) => livesIn(x, y)hasAdvisor(x, y) graduatedFrom(x, z) => worksAt(y, z)∧hasWonPrize(x, Gottfried Wilhelm Leibniz Prize) => livesIn(x, Germany)

● Some rules mined by AMIE on YAGO:

Research outlook● Mine other types of logical rules for more

applications.● Numerical correlations for data description and

prediction.– If you like Justin Bieber, then you are probably less than

18.● Rules involving temporal information for event

prediction.– If a person bought a laptop today, then she will buy a hard

disk in approximately one month.– If a person traveled for Christmas to the same place in the

last two years, then she will probably do it this year.37