Download pdf - Exception-enrcihed Rule Learning from Knowledge Graphs

Transcript
Page 1: Exception-enrcihed Rule Learning from Knowledge Graphs

Exception-enriched Rule Learning from Knowledge

Graphs

Mohamed Gad-Elrab1, Daria Stepanova1, Jacopo Urbani 2, Gerhard Weikum1

1Max-Planck-Institut fΓΌr Informatik, Saarland Informatics Campus, Germany

2 Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

21st October 2016

Page 2: Exception-enrcihed Rule Learning from Knowledge Graphs

Knowledge Graphs (KGs)

2

β€’ Huge collection of < 𝑠𝑒𝑏𝑗𝑒𝑐𝑑, π‘π‘Ÿπ‘’π‘‘π‘–π‘π‘Žπ‘‘π‘’, π‘œπ‘π‘—π‘’π‘π‘‘ > triples

β€’ Positive facts under Open World Assumption (OWA)

β€’ Possibly incomplete and/or inaccurate

Page 3: Exception-enrcihed Rule Learning from Knowledge Graphs

Mining Rules from KGs

3

Amsterdam

isMarriedToJohn Kate

Chicago

isMarriedToBrad Anna

Berlin

hasBrother

isMarriedToDave ClaraisMarriedToBob Alice

Researcher

Berlin Football

Page 4: Exception-enrcihed Rule Learning from Knowledge Graphs

Mining Rules from KGs

4

π‘Ÿ: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 𝑍 ← π‘–π‘ π‘€π‘Žπ‘Ÿπ‘Ÿπ‘–π‘’π‘‘π‘‡π‘œ 𝑋, π‘Œ , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛(π‘Œ, 𝑍)

Amsterdam

isMarriedToJohn Kate

Chicago

isMarriedToBrad Anna

Berlin

hasBrother

isMarriedToDave ClaraisMarriedToBob Alice

Researcher

Berlin Football

[GalΓ‘rraga et al., 2015]

Page 5: Exception-enrcihed Rule Learning from Knowledge Graphs

Mining Rules from KGs

5

π‘Ÿ: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 𝑍 ← π‘–π‘ π‘€π‘Žπ‘Ÿπ‘Ÿπ‘–π‘’π‘‘π‘‡π‘œ 𝑋, π‘Œ , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛(π‘Œ, 𝑍)

Amsterdam

isMarriedToJohn Kate

Chicago

isMarriedToBrad Anna

Berlin

hasBrother

isMarriedToDave ClaraisMarriedToBob Alice

Researcher

Berlin Football

1 2

Page 6: Exception-enrcihed Rule Learning from Knowledge Graphs

Our Goal

6

π‘Ÿ: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 𝑍 ← π‘–π‘ π‘€π‘Žπ‘Ÿπ‘Ÿπ‘–π‘’π‘‘π‘‡π‘œ 𝑋, π‘Œ , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 π‘Œ, 𝑍 , π‘›π‘œπ‘‘ 𝑖𝑠𝐴(𝑋, π‘Ÿπ‘’π‘ )

Amsterdam

isMarriedToJohn Kate

Chicago

isMarriedToBrad Anna

Berlin

hasBrother

isMarriedToDave ClaraisMarriedToBob Alice

Researcher

Berlin Football

1 2

Page 7: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement

β€’ Quality-based theory revision problem

β€’ Givenβ€’ Knowledge graph 𝐾𝐺

β€’ Set of Horn rules 𝑅𝐻

β€’ Find the nonmonotonic revision 𝑅𝑁𝑀 of 𝑅𝐻

β€’ Maximize top-k avg. confidence

β€’ Minimize conflicting prediction

7

Page 8: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement

β€’ Quality-based theory revision problem

β€’ Givenβ€’ Knowledge graph 𝐾𝐺

β€’ Set of Horn rules 𝑅𝐻

β€’ Find the nonmonotonic revision 𝑅𝑁𝑀 of 𝑅𝐻

β€’ Maximize top-k avg. confidence

β€’ Minimize conflicting prediction

8

Unknown

Page 9: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement: Conflicting Predictions

β€’ Defining conflicts

β€’ Measuring conflicts (auxiliary rules)

9

π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

π‘Ÿ2π‘Žπ‘’π‘₯: π‘›π‘œπ‘‘_π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

𝑅 = π‘Ÿ1: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← π‘–π‘ πΊπ‘Žπ‘šπ‘’ 𝑋 , π‘–π‘ π΅π‘Žπ‘ π‘’π‘‘π‘‚π‘›π½π‘ƒπ΄π‘›π‘–π‘šπ‘’ (𝑋)π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

{π‘–π‘ πΊπ‘Žπ‘šπ‘’ π‘Ž , π‘–π‘ π΅π‘Žπ‘ π‘’π‘‘π‘‚π‘›π½π‘ƒπ΄π‘›π‘–π‘šπ‘’ π‘Ž , β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ π‘Ž , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄ π‘Ž }

Output: {(π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ π‘Ž , π‘Ÿ2: π‘›π‘œπ‘‘ π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ π‘Ž )}

π‘Ž =

Page 10: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement: Conflicting Predictions

β€’ Defining conflicts

β€’ Measuring conflicts (auxiliary rules)

10

π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

π‘Ÿ2π‘Žπ‘’π‘₯: π‘›π‘œπ‘‘_π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

𝑅 = π‘Ÿ1: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← π‘–π‘ πΊπ‘Žπ‘šπ‘’ 𝑋 , π‘–π‘ π΅π‘Žπ‘ π‘’π‘‘π‘‚π‘›π½π‘ƒπ΄π‘›π‘–π‘šπ‘’ (𝑋)π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

{π‘–π‘ πΊπ‘Žπ‘šπ‘’ π‘Ž , π‘–π‘ π΅π‘Žπ‘ π‘’π‘‘π‘‚π‘›π½π‘ƒπ΄π‘›π‘–π‘šπ‘’ π‘Ž , β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ π‘Ž , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄ π‘Ž }

Output: {(π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ π‘Ž , π‘Ÿ2: π‘›π‘œπ‘‘ π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ π‘Ž )}

π‘Ž =

Page 11: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement: Conflicting Predictions

β€’ Defining conflicts

β€’ Measuring conflicts (auxiliary rules)

11

π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

π‘Ÿ2π‘Žπ‘’π‘₯: π‘›π‘œπ‘‘_π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

𝑅 = π‘Ÿ1: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← π‘–π‘ πΊπ‘Žπ‘šπ‘’ 𝑋 , π‘–π‘ π΅π‘Žπ‘ π‘’π‘‘π‘‚π‘›π½π‘ƒπ΄π‘›π‘–π‘šπ‘’ (𝑋)π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

{π‘–π‘ πΊπ‘Žπ‘šπ‘’ π‘Ž , π‘–π‘ π΅π‘Žπ‘ π‘’π‘‘π‘‚π‘›π½π‘ƒπ΄π‘›π‘–π‘šπ‘’ π‘Ž , β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ π‘Ž , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄ π‘Ž }

(π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ π‘Ž , π‘›π‘œπ‘‘_π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ π‘Ž )

π‘Ž =

Page 12: Exception-enrcihed Rule Learning from Knowledge Graphs

Approach Overview

Step 1β€’ Mining Horn Rules

Step 2β€’ Extracting Exception Witness Set (EWS)

Step 3β€’ Constructing Candidate Revisions

Step 4β€’ Selecting the Best Revision

12

Page 13: Exception-enrcihed Rule Learning from Knowledge Graphs

bornInUSA livesInUSA stateless emigrant singer poet

p1 βœ“ βœ“

p2 βœ“ βœ“

p3 βœ“ βœ“

p4 βœ“ βœ“ βœ“

p5 βœ“ βœ“ βœ“

p6 βœ“ βœ“

p7 βœ“ βœ“

p8 βœ“ βœ“ βœ“ βœ“

p9 βœ“ βœ“ βœ“

p10 βœ“ βœ“ βœ“ βœ“

p11 βœ“ βœ“ βœ“

Step 1: Mining Horn Rules

13

π’“π’Š: π’π’Šπ’—π’†π’”π‘°π’π‘Όπ‘Ίπ‘¨ 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)

No

rmal

Ab

-no

rmal

Page 14: Exception-enrcihed Rule Learning from Knowledge Graphs

bornInUSA livesInUSA stateless emigrant singer poet

p1 βœ“ βœ“

p2 βœ“ βœ“

p3 βœ“ βœ“

p4 βœ“ βœ“ βœ“

p5 βœ“ βœ“ βœ“

p6 βœ“ βœ“

p7 βœ“ βœ“

p8 βœ“ βœ“ βœ“ βœ“

p9 βœ“ βœ“ βœ“

p10 βœ“ βœ“ βœ“ βœ“

p11 βœ“ βœ“ βœ“

π’“π’Š: π’π’Šπ’—π’†π’”π‘°π’π‘Όπ‘Ίπ‘¨ 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)

No

rmal

Ab

-no

rmal

Step 2: Extracting Exception Witness Set (EWS)

14πΈπ‘Šπ‘†π‘– = {π‘’π‘šπ‘–π‘”π‘Ÿπ‘Žπ‘›π‘‘ 𝑋 , π‘π‘œπ‘’π‘‘ 𝑋 }

Page 15: Exception-enrcihed Rule Learning from Knowledge Graphs

Step 3: Constructing Candidate Revisions

β€’ Horn rules

β€’ Rule revisions

15

π‘Ÿ1: π‘™π‘–π‘£π‘’π‘ πΌπ‘›π‘ˆπ‘†π΄ 𝑋 ← π‘π‘œπ‘Ÿπ‘›πΌπ‘›π‘ˆπ‘†π΄ 𝑋 , π‘›π‘œπ‘‘ π‘π‘œπ‘’π‘‘ π‘‹π‘Ÿ1: π‘™π‘–π‘£π‘’π‘ πΌπ‘›π‘ˆπ‘†π΄ 𝑋 ← π‘π‘œπ‘Ÿπ‘›πΌπ‘›π‘ˆπ‘†π΄ 𝑋 , π‘›π‘œπ‘‘ π‘’π‘šπ‘–π‘”π‘Ÿπ‘Žπ‘›π‘‘ 𝑋…

𝑅 = π‘Ÿ1: π‘™π‘–π‘£π‘’π‘ πΌπ‘›π‘ˆπ‘†π΄ 𝑋 ← π‘π‘œπ‘Ÿπ‘›πΌπ‘›π‘ˆπ‘†π΄(𝑋)π‘Ÿ2: π‘’π‘šπ‘–π‘”π‘Ÿπ‘Žπ‘›π‘‘ 𝑋 ← π‘ π‘‘π‘Žπ‘‘π‘’π‘™π‘’π‘ π‘ (𝑋)

πΈπ‘Šπ‘† = {π‘π‘œπ‘’π‘‘ 𝑋 , π‘’π‘šπ‘–π‘”π‘Ÿπ‘Žπ‘›π‘‘ 𝑋 ,… }πΈπ‘Šπ‘† = {𝑒1 𝑋 , 𝑒2(𝑋), … }

Page 16: Exception-enrcihed Rule Learning from Knowledge Graphs

Step 4: Selecting the Best Revision

Finding globally best revision is expensive!

β€’ NaΓ―ve rankerβ€’ For each rule, pick the revision that maximizes confidence

β€’ Works in isolation from other rules

β€’ Partial materialization rankerβ€’ 𝐾𝐺s are incomplete!

β€’ Augment the original 𝐾𝐺 with predictions of other rules

β€’ Rank revisions on avg. confidence of the rule and its auxiliary.

16

Page 17: Exception-enrcihed Rule Learning from Knowledge Graphs

β€’ Partial materialization

Ranking Rule’s Revisions

17

bornInUSA livesInUSA stateless emigrant singer poet

p1 βœ“ βœ“

p2 βœ“ βœ“

p3 βœ“ βœ“

p4 βœ“ βœ“ βœ“

p5 βœ“ βœ“ βœ“

p6 βœ“ βœ“

p7 βœ“ βœ“

p8 βœ“ βœ“ βœ“ βœ“

p9 βœ“ βœ“ βœ“

p10 βœ“ βœ“ βœ“ βœ“

p11 βœ“ βœ“ βœ“

π’“π’Š: π’π’Šπ’—π’†π’”π‘°π’π‘Όπ‘Ίπ‘¨ 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)

No

rmal

Ab

-no

rmal

Page 18: Exception-enrcihed Rule Learning from Knowledge Graphs

β€’ Partial materialization

bornInUSA livesInUSA stateless emigrant singer poet

p1 βœ“ βœ“

p2 βœ“ βœ“

p3 βœ“ βœ“

p4 βœ“ βœ“ βœ“ βœ“

p5 βœ“ βœ“ βœ“ βœ“

p6 βœ“ βœ“ βœ“

p7 βœ“ βœ“ βœ“

p8 βœ“ βœ“ βœ“ βœ“

p9 βœ“ βœ“ βœ“ βœ“ βœ“

p10 βœ“ βœ“ βœ“ βœ“

p11 βœ“ βœ“ βœ“ βœ“

π’“π’Š: π’π’Šπ’—π’†π’”π‘°π’π‘Όπ‘Ίπ‘¨ 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)

No

rmal

Ab

-no

rmal

Ranking Rule’s Revisions

18

Page 19: Exception-enrcihed Rule Learning from Knowledge Graphs

Ranking Rule’s Revisions

β€’ Ordered partial materialization rankerβ€’ Only rules with higher quality

β€’ Ordered weighted partial materialization rankerβ€’ KG fact weight = 1

β€’ Predicted facts inherit their weights from the rules

19

Page 20: Exception-enrcihed Rule Learning from Knowledge Graphs

Experiments

β€’ Ruleset quality

20*Higher is better

0.60

0.65

0.70

0.75

0.80

20 40 60 80 100

Avg

. Co

nfi

den

ce

Top-K (%) Rules

YAGO3

Horn Naive Ordered & Weighted PM

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

20 40 60 80 100A

vg. C

on

fid

ence

Top-K (%) Rules

IMDB

Horn Naive Ordered & Weighted PM

Facts 10M 2MRules 10K 25K

Page 21: Exception-enrcihed Rule Learning from Knowledge Graphs

Experiments

β€’ Predictions consistency

21*Lower is better

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

200 400 600 800 1000

Co

nfl

ict

Rat

io

Top-K Rules

YAGO3

Naive Ordered & Weighted PM

0

0.1

0.2

0.3

0.4

0.5

200 400 600 800 1000C

on

flic

t R

atio

Top-K Rules

IMDB

Naive Ordered & Weighted PM

Page 22: Exception-enrcihed Rule Learning from Knowledge Graphs

Experiments

β€’ Examples

22

π‘–π‘ π‘€π‘œπ‘’π‘›π‘‘π‘Žπ‘–π‘›(𝑋) ← π‘–π‘ πΌπ‘›π΄π‘’π‘ π‘‘π‘Ÿπ‘–π‘Ž(𝑋), π‘–π‘ πΌπ‘›πΌπ‘‘π‘Žπ‘™π‘¦ 𝑋 , π‘›π‘œπ‘‘ π‘–π‘ π‘…π‘–π‘£π‘’π‘Ÿ (𝑋)

π‘–π‘ π‘ƒπ‘œπ‘™π‘–π‘‘π‘‚π‘“π‘ˆπ‘†π΄ 𝑋 ← π‘π‘œπ‘Ÿπ‘›πΌπ‘›π‘ˆπ‘†π΄ 𝑋 , π‘–π‘ πΊπ‘œπ‘£ 𝑋 , π‘›π‘œπ‘‘ π‘–π‘ π‘ƒπ‘œπ‘™π‘–π‘‘π‘ƒπ‘’π‘’π‘Ÿπ‘‘π‘œπ‘…π‘–π‘π‘œ(𝑋)

π‘π‘œπ‘Ÿπ‘›πΌπ‘›π‘ˆπ‘†π΄ 𝑋 ← π‘Žπ‘π‘‘π‘’π‘‘πΌπ‘›π‘€π‘œπ‘£π‘–π‘’ 𝑋 , π‘π‘Ÿπ‘’π‘Žπ‘‘π‘’π‘‘π‘€π‘œπ‘£π‘–π‘’ 𝑋 , π‘›π‘œπ‘‘ π‘€π‘œπ‘›πΉπ‘–π‘™π‘šπ‘“π‘Žπ‘Ÿπ‘’(𝑋)

Page 23: Exception-enrcihed Rule Learning from Knowledge Graphs

Summary

β€’ Conclusionβ€’ Quality-based theory revision under OWA

β€’ Partial materialization for ranking revisions

β€’ Comparison of ranking methods on real life KGs

β€’ Outlookβ€’ Extending to higher arity predicates

β€’ Binary predicates [Tran et al., to appear ILP2016]

β€’ Evidence from text corpora

β€’ Exploiting partial completeness

23

Page 24: Exception-enrcihed Rule Learning from Knowledge Graphs

References

β€’ [Angiulli and Fassetti, 2014] Fabrizio Angiulli and Fabio Fassetti. Exploiting domain knowledge to detect outliers. Data Min. Knowl. Discov., 28(2):519–568, 2014.

β€’ [Dimopoulos and Kakas, 1995] Yannis Dimopoulos and Antonis C. Kakas. Learning non-monotonic logic programs: Learning exceptions. In Machine Learning: ECML-95, 8th European Conference on Machine Learning, Heraclion, Crete, Greece, April 25-27, 1995, Proceedings, pages 122–137, 1995.

β€’ [Galarraga et al., 2015] Luis Galarraga, Christina Teflioudi, Katja Hose, and Fabian M. Suchanek. Fast Rule Mining in Ontological Knowledge Bases with AMIE+. In VLDB Journal, 2015.

β€’ [Law et al., 2015] Mark Law, Alessandra Russo, and Krysia Broda. The ILASP system for learning answer set programs, 2015.

β€’ [Leone et al., 2006] Nicola Leone, Gerald Pfeifer, Wolfgang Faber, Thomas Eiter, Georg Gottlob, Simona Perri, and Francesco Scarcello. 2006. The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Logic 7, 3 (July 2006), 499-562.

β€’ [Suzuki, 2006] Einoshin Suzuki. Data mining methods for discovering interesting exceptions from an unsupervised table. J. UCS, 12(6):627–653, 2006.

β€’ [Tran et al., 2016] Hai Dang Tran, Daria Stepanova, Mohamed H. Gad-Elrab, Francesca A. Lisi, Gerhard Weikum. Towards Nonmonotonic Relational Learning from Knowledge Graphs. ILP2016, London, UK, to appear.

β€’ [Katzouris et al., 2015] Nikos Katzouris, Alexander Artikis, and Georgios Paliouras. Incremental learning of event definitions with inductive logic programming. Machine Learning, 100(2-3):555–585, 2015.

24

Page 25: Exception-enrcihed Rule Learning from Knowledge Graphs

Related Work

β€’ Learning nonmonotonic programsβ€’ E.g., [Dimopoulos and Kakas, 1995], ILASP [Law et al., 2015],

ILED [Katzouris et al., 2015], etc.

β€’ Outlier detection in logic programsβ€’ E.g., [Angiulli and Fassetti, 2014], etc.

β€’ Mining exception rulesβ€’ E.g., [Suzuki, 2006], etc.

25

Page 26: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement: Ruleset Quality

β€’ Independent Rule Measure (π‘Ÿπ‘š)β€’ Support: 𝑠𝑒𝑝𝑝 𝐻 ← 𝐡 = 𝑠𝑒𝑝𝑝(𝐻 βˆͺ 𝐡)

β€’ Coverage: cπ‘œπ‘£ 𝐻 ← 𝐡 = 𝑠𝑒𝑝𝑝(𝐡)

β€’ Confidence: cπ‘œπ‘›π‘“ 𝐻 ← 𝐡 =𝑠𝑒𝑝𝑝(𝐻βˆͺ𝐡)

𝑠𝑒𝑝𝑝(𝐡)

β€’ Lift: 𝑙𝑖𝑓𝑑 𝐻 ← 𝐡 =π‘π‘œπ‘›π‘“(𝐻←𝐡)

𝑠𝑒𝑝𝑝(𝐻)

β€’ …

β€’ Average Ruleset Quality

26

π‘žπ‘Ÿπ‘š 𝑅𝑁𝑀, 𝐺 =

π‘Ÿ βˆˆπ‘…π‘π‘€

π‘Ÿπ‘š(π‘Ÿ, 𝐺)

𝑅𝑁𝑀

Page 27: Exception-enrcihed Rule Learning from Knowledge Graphs

Problem Statement: Conflicting Predictions

β€’ Measuring conflicts (auxiliary rules)

27

π‘Ÿ2: π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘›π‘œπ‘‘ π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

π‘Ÿ2π‘Žπ‘’π‘₯: π‘›π‘œπ‘‘_π‘Ÿπ‘’π‘™π‘’π‘Žπ‘ π‘’π‘‘πΌπ‘›π½π‘ƒ 𝑋 ← β„Žπ‘Žπ‘ π½π‘ƒπΆπ‘œπ‘šπ‘π‘œπ‘ π‘’π‘Ÿ 𝑋 , π‘π‘’π‘π‘™π‘–π‘ β„Žπ‘’π‘Ÿπ‘ˆπ‘†π΄(𝑋)

π‘žπ‘π‘œπ‘›π‘“π‘™π‘–π‘π‘‘ 𝑅𝑁𝑀, 𝐺 =|{(𝑝 π‘Ž , π‘›π‘œπ‘‘_𝑝 π‘Ž ), … }|

{π‘›π‘œπ‘‘_𝑝 π‘Ž , … }

Page 28: Exception-enrcihed Rule Learning from Knowledge Graphs

Propositionalization

β€’ Unary predicates

28

Binary Predicates

β€’ hasType(enstein, scientist)

β€’ isMarriedTo(elsa, einstein)

β€’ bornIn(einstein, um)

Unary

β€’ isAScientist(einstein)

β€’ isMarriedToEinstein(elsa)

β€’ bornInUlm(einstein)

Abstraction

β€’ isAScientist(einstein)

β€’ isMarriedToScientist(elsa)

β€’ bornInGermany(einstein)

Page 29: Exception-enrcihed Rule Learning from Knowledge Graphs

Experiments

β€’ Input

β€’ Experiment statistics

29

YAGO3 IMDB

Input Facts 10M 2M

Horn Rules 10K 25K

Revised Rules 6K 22K

General-purpose KG Domain-specific KG (Movies)

Page 30: Exception-enrcihed Rule Learning from Knowledge Graphs

Experiments

β€’ Predictions assessmentβ€’ Run DLV on YAGO and 𝑅𝐻 then 𝑅𝑁𝑀 seperately

β€’ Sample facts such that fact 𝑓 ∈ π‘Œπ΄πΊπ‘‚π»\π‘Œπ΄πΊπ‘‚π‘π‘€

β€’ 73% of the sampled facts were found to be erroneous

30

checked predictions

Page 31: Exception-enrcihed Rule Learning from Knowledge Graphs

Ranking Rule’s Revisions

β€’ Partial materialization rankerβ€’ Augment the original 𝐾𝐺 with predictions of other rules

β€’ Rank revisions on Avg. confidence of the π‘Ÿ and π‘Ÿπ‘Žπ‘’π‘₯

31

π‘ π‘π‘œπ‘Ÿπ‘’ π‘Ÿπ‘’ , πΎπΊβˆ— =

π‘π‘œπ‘›π‘“ π‘Ÿπ‘’ , πΎπΊβˆ— + π‘π‘œπ‘›π‘“(π‘Ÿπ‘’

π‘Žπ‘’π‘₯ , πΎπΊβˆ—)

2

where π‘Ÿπ‘’ is the rule π‘Ÿ with exception 𝑒 & πΎπΊβˆ—is the augmented 𝐾𝐺.


Recommended

Python Graphs
Python Graphs Documents
The former testimony exception to the hearsay rule former testimony exception to the hearsay rule ... the hearsay rule if the declarant is unavailable as a ... β€œHearsay Exceptions
The former testimony exception to the hearsay rule former testimony exception to the hearsay rule ... the hearsay rule if the declarant is unavailable as a ... β€œHearsay Exceptions Documents
Exception Handling
Exception Handling Documents
Exception HandlingΒ Β· 2018. 11. 28.Β Β· membuat objek exception dan melemparkannya –sebagai tanda bahwa error telah terjadi Jika objek exception tidak ditangkap dan ditangani secara
Exception HandlingΒ Β· 2018. 11. 28.Β Β· membuat objek exception dan melemparkannya –sebagai tanda bahwa error telah terjadi Jika objek exception tidak ditangkap dan ditangani secara Documents
Chapter 5 Graphs
Chapter 5 Graphs Documents
Pemrograman Berorientasi Object - Gunadarmamiftah.staff.gunadarma.ac.id/Downloads/files/29161/8.+exception+handling.pdfMenangani Exception Untuk menangani exception dalam Java, kita
Pemrograman Berorientasi Object - Gunadarmamiftah.staff.gunadarma.ac.id/Downloads/files/29161/8.+exception+handling.pdfMenangani Exception Untuk menangani exception dalam Java, kita Documents
Fabbrica della ConoscenzaEnzo Siviero’s ten-year route, 1999/2009 Norma dell’eccezione ed eccezione nella norma, ovvero i ponti di Enzo Siviero Rule of the exception or exception
Fabbrica della ConoscenzaEnzo Siviero’s ten-year route, 1999/2009 Norma dell’eccezione ed eccezione nella norma, ovvero i ponti di Enzo Siviero Rule of the exception or exception Documents
La2_Modul Exception & Assertions
La2_Modul Exception & Assertions Documents
Extremal 1-codes in distance-regular graphs of diameter 3Β Β· Distance-regular graphs Codes in distance-regular graphs Triple intersection numbers Codes in distance-regular graphs
Extremal 1-codes in distance-regular graphs of diameter 3Β Β· Distance-regular graphs Codes in distance-regular graphs Triple intersection numbers Codes in distance-regular graphs Documents
Flow Control & Exception Handling
Flow Control & Exception Handling Documents
Java'da Exception Anti-Pattern'leri
Java'da Exception Anti-Pattern'leri Software
Exception Dan Jenisnya
Exception Dan Jenisnya Documents
Misleading graphs
Misleading graphs Documents
Last lesson Graphs Today Graphs (Implementation, Traversal)
Last lesson Graphs Today Graphs (Implementation, Traversal) Documents
Parsimonious Graphs
Parsimonious Graphs Documents
[Exploit]Exception Handler
[Exploit]Exception Handler Documents
κ°•μ—°μ†Œκ°œ Exception Handler λ₯Όν†΅ν•œ μ—λŸ¬κ²€μΆœλ°μˆ˜μ • fileκ°•μ—°μ†Œκ°œβ€“ Exception Handler λ₯Όν†΅ν•œ μ—λŸ¬κ²€μΆœλ°μˆ˜μ • zλ””λ²„κΉ…μ„μ¦κ²¨ν•˜μ‹­λ‹ˆκΉŒ..? zμ—λŸ¬λ₯Όλ§Œλ‚˜λ©΄λ°˜κ°‘μŠ΅λ‹ˆκΉŒ..?
κ°•μ—°μ†Œκ°œ Exception Handler λ₯Όν†΅ν•œ μ—λŸ¬κ²€μΆœλ°μˆ˜μ • fileκ°•μ—°μ†Œκ°œβ€“ Exception Handler λ₯Όν†΅ν•œ μ—λŸ¬κ²€μΆœλ°μˆ˜μ • zλ””λ²„κΉ…μ„μ¦κ²¨ν•˜μ‹­λ‹ˆκΉŒ..? zμ—λŸ¬λ₯Όλ§Œλ‚˜λ©΄λ°˜κ°‘μŠ΅λ‹ˆκΉŒ..? Documents
ภาษาจาวา – Exception & Assertionsomchai/spj/slides/...Β Β· ภาษาจาวา – Exception & Assertion ΰΈͺฑชาฒ ΰΈ›ΰΈ£ΰΈ°ΰΈͺΰΈ΄ΰΈ—ΰΈ˜ΰΈ΄ΰΉŒΰΈˆΰΈΉΰΈ•ΰΈ£ΰΈ°ΰΈ
ภาษาจาวา – Exception & Assertionsomchai/spj/slides/...Β Β· ภาษาจาวา – Exception & Assertion ΰΈͺฑชาฒ ΰΈ›ΰΈ£ΰΈ°ΰΈͺΰΈ΄ΰΈ—ΰΈ˜ΰΈ΄ΰΉŒΰΈˆΰΈΉΰΈ•ΰΈ£ΰΈ°ΰΈ Documents