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![Mining Rules from KGs
4
𝑟: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 𝑍 ← 𝑖𝑠𝑀𝑎𝑟𝑟𝑖𝑒𝑑𝑇𝑜 𝑋, 𝑌 , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛(𝑌, 𝑍)
Amsterdam
isMarriedToJohn Kate
Chicago
isMarriedToBrad Anna
Berlin
hasBrother
isMarriedToDave ClaraisMarriedToBob Alice
Researcher
Berlin Football
[Galárraga et al., 2015]](https://image.slidesharecdn.com/pkwebjzdq9ao0xoud3sq-signature-85211fc9d1cb6a868799192dc03b747dd4e366e70af6d5aac30914fe20b4a92c-poli-161026083937/75/Exception-enrcihed-Rule-Learning-from-Knowledge-Graphs-4-2048.jpg)
![Summary
• Conclusion
• Quality-based theory revision under OWA
• Partial materialization for ranking revisions
• Comparison of ranking methods on real life KGs
• Outlook
• Extending to higher arity predicates
• Binary predicates [Tran et al., to appear ILP2016]
• Evidence from text corpora
• Exploiting partial completeness
23](https://image.slidesharecdn.com/pkwebjzdq9ao0xoud3sq-signature-85211fc9d1cb6a868799192dc03b747dd4e366e70af6d5aac30914fe20b4a92c-poli-161026083937/75/Exception-enrcihed-Rule-Learning-from-Knowledge-Graphs-23-2048.jpg)
![References
• [Angiulli and Fassetti, 2014] Fabrizio Angiulli and Fabio Fassetti. Exploiting domain knowledge to
detect outliers. Data Min. Knowl. Discov., 28(2):519–568, 2014.
• [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.
• [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.
• [Law et al., 2015] Mark Law, Alessandra Russo, and Krysia Broda. The ILASP system for learning
answer set programs, 2015.
• [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.
• [Suzuki, 2006] Einoshin Suzuki. Data mining methods for discovering interesting exceptions from
an unsupervised table. J. UCS, 12(6):627–653, 2006.
• [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.
• [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](https://image.slidesharecdn.com/pkwebjzdq9ao0xoud3sq-signature-85211fc9d1cb6a868799192dc03b747dd4e366e70af6d5aac30914fe20b4a92c-poli-161026083937/75/Exception-enrcihed-Rule-Learning-from-Knowledge-Graphs-24-2048.jpg)
![Related Work
• Learning nonmonotonic programs
• E.g., [Dimopoulos and Kakas, 1995], ILASP [Law et al., 2015],
ILED [Katzouris et al., 2015], etc.
• Outlier detection in logic programs
• E.g., [Angiulli and Fassetti, 2014], etc.
• Mining exception rules
• E.g., [Suzuki, 2006], etc.
25](https://image.slidesharecdn.com/pkwebjzdq9ao0xoud3sq-signature-85211fc9d1cb6a868799192dc03b747dd4e366e70af6d5aac30914fe20b4a92c-poli-161026083937/75/Exception-enrcihed-Rule-Learning-from-Knowledge-Graphs-25-2048.jpg)
Uploaded byMohamed Gad-elrab
Exception-enrcihed Rule Learning from Knowledge Graphs
This document presents an approach for exception-enriched rule learning from knowledge graphs. It aims to mine rules from knowledge graphs while accounting for exceptions to the rules. The approach involves: 1) Mining Horn rules (if-then rules) from a knowledge graph 2) Extracting an exception witness set (EWS) of entities that violate the mined rules 3) Constructing candidate rule revisions by adding exceptions to the rules 4) Selecting the best rule revision by maximizing prediction accuracy while minimizing conflicting predictions against the knowledge graph. The goal is to learn more accurate rules from knowledge graphs by incorporating known exceptions.
Exception-enrcihed Rule Learning from Knowledge Graphs
- 1. Exception-enriched Rule Learning fromKnowledge Graphs Mohamed Gad-Elrab1, Daria Stepanova1, Jacopo Urbani 2, Gerhard Weikum1 1Max-Planck-Institut für Informatik, Saarland Informatics Campus, Germany 2 Vrije Universiteit Amsterdam, Amsterdam, The Netherlands 21st October 2016
- 2. Knowledge Graphs (KGs) 2 •Huge collection of < 𝑠𝑢𝑏𝑗𝑒𝑐𝑡, 𝑝𝑟𝑒𝑑𝑖𝑐𝑎𝑡𝑒, 𝑜𝑏𝑗𝑒𝑐𝑡 > triples • Positive facts under Open World Assumption (OWA) • Possibly incomplete and/or inaccurate
- 3. Mining Rules fromKGs 3 Amsterdam isMarriedToJohn Kate Chicago isMarriedToBrad Anna Berlin hasBrother isMarriedToDave ClaraisMarriedToBob Alice Researcher Berlin Football
- 4. Mining Rules fromKGs 4 𝑟: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 𝑍 ← 𝑖𝑠𝑀𝑎𝑟𝑟𝑖𝑒𝑑𝑇𝑜 𝑋, 𝑌 , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛(𝑌, 𝑍) Amsterdam isMarriedToJohn Kate Chicago isMarriedToBrad Anna Berlin hasBrother isMarriedToDave ClaraisMarriedToBob Alice Researcher Berlin Football [Galárraga et al., 2015]
- 5. Mining Rules fromKGs 5 𝑟: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 𝑍 ← 𝑖𝑠𝑀𝑎𝑟𝑟𝑖𝑒𝑑𝑇𝑜 𝑋, 𝑌 , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛(𝑌, 𝑍) Amsterdam isMarriedToJohn Kate Chicago isMarriedToBrad Anna Berlin hasBrother isMarriedToDave ClaraisMarriedToBob Alice Researcher Berlin Football 1 2
- 6. Our Goal 6 𝑟: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛𝑋, 𝑍 ← 𝑖𝑠𝑀𝑎𝑟𝑟𝑖𝑒𝑑𝑇𝑜 𝑋, 𝑌 , 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑌, 𝑍 , 𝑛𝑜𝑡 𝑖𝑠𝐴(𝑋, 𝑟𝑒𝑠) Amsterdam isMarriedToJohn Kate Chicago isMarriedToBrad Anna Berlin hasBrother isMarriedToDave ClaraisMarriedToBob Alice Researcher Berlin Football 1 2
- 7. Problem Statement • Quality-basedtheory revision problem • Given • Knowledge graph 𝐾𝐺 • Set of Horn rules 𝑅 𝐻 • Find the nonmonotonic revision 𝑅 𝑁𝑀 of 𝑅 𝐻 • Maximize top-k avg. confidence • Minimize conflicting prediction 7
- 8. Problem Statement • Quality-basedtheory revision problem • Given • Knowledge graph 𝐾𝐺 • Set of Horn rules 𝑅 𝐻 • Find the nonmonotonic revision 𝑅 𝑁𝑀 of 𝑅 𝐻 • Maximize top-k avg. confidence • Minimize conflicting prediction 8 Unknown
- 9. Problem Statement: ConflictingPredictions • Defining conflicts • Measuring conflicts (auxiliary rules) 9 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑟2 𝑎𝑢𝑥 : 𝑛𝑜𝑡_𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑅 = 𝑟1: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← 𝑖𝑠𝐺𝑎𝑚𝑒 𝑋 , 𝑖𝑠𝐵𝑎𝑠𝑒𝑑𝑂𝑛𝐽𝑃𝐴𝑛𝑖𝑚𝑒 (𝑋) 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) {𝑖𝑠𝐺𝑎𝑚𝑒 𝑎 , 𝑖𝑠𝐵𝑎𝑠𝑒𝑑𝑂𝑛𝐽𝑃𝐴𝑛𝑖𝑚𝑒 𝑎 , ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑎 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴 𝑎 } Output: {(𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑎 , 𝑟2: 𝑛𝑜𝑡 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑎 )} 𝑎 =
- 10. Problem Statement: ConflictingPredictions • Defining conflicts • Measuring conflicts (auxiliary rules) 10 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑟2 𝑎𝑢𝑥 : 𝑛𝑜𝑡_𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑅 = 𝑟1: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← 𝑖𝑠𝐺𝑎𝑚𝑒 𝑋 , 𝑖𝑠𝐵𝑎𝑠𝑒𝑑𝑂𝑛𝐽𝑃𝐴𝑛𝑖𝑚𝑒 (𝑋) 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) {𝑖𝑠𝐺𝑎𝑚𝑒 𝑎 , 𝑖𝑠𝐵𝑎𝑠𝑒𝑑𝑂𝑛𝐽𝑃𝐴𝑛𝑖𝑚𝑒 𝑎 , ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑎 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴 𝑎 } Output: {(𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑎 , 𝑟2: 𝑛𝑜𝑡 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑎 )} 𝑎 =
- 11. Problem Statement: ConflictingPredictions • Defining conflicts • Measuring conflicts (auxiliary rules) 11 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑟2 𝑎𝑢𝑥 : 𝑛𝑜𝑡_𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑅 = 𝑟1: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← 𝑖𝑠𝐺𝑎𝑚𝑒 𝑋 , 𝑖𝑠𝐵𝑎𝑠𝑒𝑑𝑂𝑛𝐽𝑃𝐴𝑛𝑖𝑚𝑒 (𝑋) 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) {𝑖𝑠𝐺𝑎𝑚𝑒 𝑎 , 𝑖𝑠𝐵𝑎𝑠𝑒𝑑𝑂𝑛𝐽𝑃𝐴𝑛𝑖𝑚𝑒 𝑎 , ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑎 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴 𝑎 } (𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑎 , 𝑛𝑜𝑡_𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑎 ) 𝑎 =
- 12. Approach Overview Step 1 •Mining Horn Rules Step 2 • Extracting Exception Witness Set (EWS) Step 3 • Constructing Candidate Revisions Step 4 • Selecting the Best Revision 12
- 13. bornInUSA livesInUSA statelessemigrant singer poet p1 ✓ ✓ p2 ✓ ✓ p3 ✓ ✓ p4 ✓ ✓ ✓ p5 ✓ ✓ ✓ p6 ✓ ✓ p7 ✓ ✓ p8 ✓ ✓ ✓ ✓ p9 ✓ ✓ ✓ p10 ✓ ✓ ✓ ✓ p11 ✓ ✓ ✓ Step 1: Mining Horn Rules 13 𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿) NormalAb-normal
- 14. bornInUSA livesInUSA statelessemigrant singer poet p1 ✓ ✓ p2 ✓ ✓ p3 ✓ ✓ p4 ✓ ✓ ✓ p5 ✓ ✓ ✓ p6 ✓ ✓ p7 ✓ ✓ p8 ✓ ✓ ✓ ✓ p9 ✓ ✓ ✓ p10 ✓ ✓ ✓ ✓ p11 ✓ ✓ ✓ 𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿) NormalAb-normalStep 2: Extracting Exception Witness Set (EWS) 14 𝐸𝑊𝑆𝑖 = {𝑒𝑚𝑖𝑔𝑟𝑎𝑛𝑡 𝑋 , 𝑝𝑜𝑒𝑡 𝑋 }
- 15. Step 3: ConstructingCandidate Revisions • Horn rules • Rule revisions 15 𝑟1: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛𝑈𝑆𝐴 𝑋 ← 𝑏𝑜𝑟𝑛𝐼𝑛𝑈𝑆𝐴 𝑋 , 𝑛𝑜𝑡 𝑝𝑜𝑒𝑡 𝑋 𝑟1: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛𝑈𝑆𝐴 𝑋 ← 𝑏𝑜𝑟𝑛𝐼𝑛𝑈𝑆𝐴 𝑋 , 𝑛𝑜𝑡 𝑒𝑚𝑖𝑔𝑟𝑎𝑛𝑡 𝑋 … 𝑅 = 𝑟1: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛𝑈𝑆𝐴 𝑋 ← 𝑏𝑜𝑟𝑛𝐼𝑛𝑈𝑆𝐴(𝑋) 𝑟2: 𝑒𝑚𝑖𝑔𝑟𝑎𝑛𝑡 𝑋 ← 𝑠𝑡𝑎𝑡𝑒𝑙𝑒𝑠𝑠(𝑋) 𝐸𝑊𝑆 = {𝑝𝑜𝑒𝑡 𝑋 , 𝑒𝑚𝑖𝑔𝑟𝑎𝑛𝑡 𝑋 , … } 𝐸𝑊𝑆 = {𝑒1 𝑋 , 𝑒2(𝑋), … }
- 16. Step 4: Selectingthe Best Revision Finding globally best revision is expensive! • Naïve ranker • For each rule, pick the revision that maximizes confidence • Works in isolation from other rules • Partial materialization ranker • 𝐾𝐺s are incomplete! • Augment the original 𝐾𝐺 with predictions of other rules • Rank revisions on avg. confidence of the rule and its auxiliary. 16
- 17. • Partial materialization RankingRule’s Revisions 17 bornInUSA livesInUSA stateless emigrant singer poet p1 ✓ ✓ p2 ✓ ✓ p3 ✓ ✓ p4 ✓ ✓ ✓ p5 ✓ ✓ ✓ p6 ✓ ✓ p7 ✓ ✓ p8 ✓ ✓ ✓ ✓ p9 ✓ ✓ ✓ p10 ✓ ✓ ✓ ✓ p11 ✓ ✓ ✓ 𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿) NormalAb-normal
- 18. • Partial materialization bornInUSAlivesInUSA stateless emigrant singer poet p1 ✓ ✓ p2 ✓ ✓ p3 ✓ ✓ p4 ✓ ✓ ✓ ✓ p5 ✓ ✓ ✓ ✓ p6 ✓ ✓ ✓ p7 ✓ ✓ ✓ p8 ✓ ✓ ✓ ✓ p9 ✓ ✓ ✓ ✓ ✓ p10 ✓ ✓ ✓ ✓ p11 ✓ ✓ ✓ ✓ 𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿) NormalAb-normalRanking Rule’s Revisions 18
- 19. Ranking Rule’s Revisions •Ordered partial materialization ranker • Only rules with higher quality • Ordered weighted partial materialization ranker • KG fact weight = 1 • Predicted facts inherit their weights from the rules 19
- 20. Experiments • Ruleset quality 20 *Higheris better 0.60 0.65 0.70 0.75 0.80 20 40 60 80 100 Avg.Confidence 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 100Avg.Confidence Top-K (%) Rules IMDB Horn Naive Ordered & Weighted PM Facts 10M 2M Rules 10K 25K
- 21. Experiments • Predictions consistency 21*Loweris better 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 200 400 600 800 1000 ConflictRatio Top-K Rules YAGO3 Naive Ordered & Weighted PM 0 0.1 0.2 0.3 0.4 0.5 200 400 600 800 1000ConflictRatio Top-K Rules IMDB Naive Ordered & Weighted PM
- 22. Experiments • Examples 22 𝑖𝑠𝑀𝑜𝑢𝑛𝑡𝑎𝑖𝑛(𝑋) ←𝑖𝑠𝐼𝑛𝐴𝑢𝑠𝑡𝑟𝑖𝑎(𝑋), 𝑖𝑠𝐼𝑛𝐼𝑡𝑎𝑙𝑦 𝑋 , 𝑛𝑜𝑡 𝑖𝑠𝑅𝑖𝑣𝑒𝑟 (𝑋) 𝑖𝑠𝑃𝑜𝑙𝑖𝑡𝑂𝑓𝑈𝑆𝐴 𝑋 ← 𝑏𝑜𝑟𝑛𝐼𝑛𝑈𝑆𝐴 𝑋 , 𝑖𝑠𝐺𝑜𝑣 𝑋 , 𝑛𝑜𝑡 𝑖𝑠𝑃𝑜𝑙𝑖𝑡𝑃𝑢𝑒𝑟𝑡𝑜𝑅𝑖𝑐𝑜(𝑋) 𝑏𝑜𝑟𝑛𝐼𝑛𝑈𝑆𝐴 𝑋 ← 𝑎𝑐𝑡𝑒𝑑𝐼𝑛𝑀𝑜𝑣𝑖𝑒 𝑋 , 𝑐𝑟𝑒𝑎𝑡𝑒𝑑𝑀𝑜𝑣𝑖𝑒 𝑋 , 𝑛𝑜𝑡 𝑤𝑜𝑛𝐹𝑖𝑙𝑚𝑓𝑎𝑟𝑒(𝑋)
- 23. Summary • Conclusion • Quality-basedtheory revision under OWA • Partial materialization for ranking revisions • Comparison of ranking methods on real life KGs • Outlook • Extending to higher arity predicates • Binary predicates [Tran et al., to appear ILP2016] • Evidence from text corpora • Exploiting partial completeness 23
- 24. References • [Angiulli andFassetti, 2014] Fabrizio Angiulli and Fabio Fassetti. Exploiting domain knowledge to detect outliers. Data Min. Knowl. Discov., 28(2):519–568, 2014. • [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. • [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. • [Law et al., 2015] Mark Law, Alessandra Russo, and Krysia Broda. The ILASP system for learning answer set programs, 2015. • [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. • [Suzuki, 2006] Einoshin Suzuki. Data mining methods for discovering interesting exceptions from an unsupervised table. J. UCS, 12(6):627–653, 2006. • [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. • [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
- 25. Related Work • Learningnonmonotonic programs • E.g., [Dimopoulos and Kakas, 1995], ILASP [Law et al., 2015], ILED [Katzouris et al., 2015], etc. • Outlier detection in logic programs • E.g., [Angiulli and Fassetti, 2014], etc. • Mining exception rules • E.g., [Suzuki, 2006], etc. 25
- 26. Problem Statement: RulesetQuality • Independent Rule Measure (𝑟𝑚) • Support: 𝑠𝑢𝑝𝑝 𝐻 ← 𝐵 = 𝑠𝑢𝑝𝑝(𝐻 ∪ 𝐵) • Coverage: c𝑜𝑣 𝐻 ← 𝐵 = 𝑠𝑢𝑝𝑝(𝐵) • Confidence: c𝑜𝑛𝑓 𝐻 ← 𝐵 = 𝑠𝑢𝑝𝑝(𝐻∪𝐵) 𝑠𝑢𝑝𝑝(𝐵) • Lift: 𝑙𝑖𝑓𝑡 𝐻 ← 𝐵 = 𝑐𝑜𝑛𝑓(𝐻←𝐵) 𝑠𝑢𝑝𝑝(𝐻) • … • Average Ruleset Quality 26 𝑞 𝑟𝑚 𝑅 𝑁𝑀, 𝐺 = 𝑟 ∈𝑅 𝑁𝑀 𝑟𝑚(𝑟, 𝐺) 𝑅 𝑁𝑀
- 27. Problem Statement: ConflictingPredictions • Measuring conflicts (auxiliary rules) 27 𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑟2 𝑎𝑢𝑥 : 𝑛𝑜𝑡_𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋) 𝑞 𝑐𝑜𝑛𝑓𝑙𝑖𝑐𝑡 𝑅 𝑁𝑀, 𝐺 = |{(𝑝 𝑎 , 𝑛𝑜𝑡_𝑝 𝑎 ), … }| {𝑛𝑜𝑡_𝑝 𝑎 , … }
- 28. Propositionalization • Unary predicates 28 BinaryPredicates • hasType(enstein, scientist) • isMarriedTo(elsa, einstein) • bornIn(einstein, um) Unary • isAScientist(einstein) • isMarriedToEinstein(elsa) • bornInUlm(einstein) Abstraction • isAScientist(einstein) • isMarriedToScientist(elsa) • bornInGermany(einstein)
- 29. Experiments • Input • Experimentstatistics 29 YAGO3 IMDB Input Facts 10M 2M Horn Rules 10K 25K Revised Rules 6K 22K General-purpose KG Domain-specific KG (Movies)
- 30. Experiments • Predictions assessment •Run DLV on YAGO and 𝑅 𝐻 then 𝑅 𝑁𝑀 seperately • Sample facts such that fact 𝑓 ∈ 𝑌𝐴𝐺𝑂 𝐻𝑌𝐴𝐺𝑂 𝑁𝑀 • 73% of the sampled facts were found to be erroneous 30 checked predictions
- 31. Ranking Rule’s Revisions •Partial materialization ranker • Augment the original 𝐾𝐺 with predictions of other rules • Rank revisions on Avg. confidence of the 𝑟 and 𝑟 𝑎𝑢𝑥 31 𝑠𝑐𝑜𝑟𝑒 𝑟𝑒, 𝐾𝐺∗ = 𝑐𝑜𝑛𝑓 𝑟𝑒, 𝐾𝐺∗ + 𝑐𝑜𝑛𝑓(𝑟𝑒 𝑎𝑢𝑥, 𝐾𝐺∗) 2 where 𝑟𝑒 is the rule 𝑟 with exception 𝑒 & 𝐾𝐺∗ is the augmented 𝐾𝐺.