Exception-enriched Rule Learning from Knowledge Graphs€¦ · Exception-enriched Rule Learning...
Transcript of Exception-enriched Rule Learning from Knowledge Graphs€¦ · Exception-enriched Rule Learning...
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Exception-enriched Rule Learning from Knowledge
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
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Knowledge Graphs (KGs)
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• Huge collection of < 𝑠𝑢𝑏𝑗𝑒𝑐𝑡, 𝑝𝑟𝑒𝑑𝑖𝑐𝑎𝑡𝑒, 𝑜𝑏𝑗𝑒𝑐𝑡 > triples
• Positive facts under Open World Assumption (OWA)
• Possibly incomplete and/or inaccurate
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Mining Rules from KGs
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Amsterdam
isMarriedToJohn Kate
Chicago
isMarriedToBrad Anna
Berlin
hasBrother
isMarriedToDave ClaraisMarriedToBob Alice
Researcher
Berlin Football
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Mining Rules from KGs
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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]
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Mining Rules from KGs
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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
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Our Goal
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𝑟: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛 𝑋, 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
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Problem Statement
• Quality-based theory revision problem
• Given• Knowledge graph 𝐾𝐺
• Set of Horn rules 𝑅𝐻
• Find the nonmonotonic revision 𝑅𝑁𝑀 of 𝑅𝐻
• Maximize top-k avg. confidence
• Minimize conflicting prediction
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Problem Statement
• Quality-based theory revision problem
• Given• Knowledge graph 𝐾𝐺
• Set of Horn rules 𝑅𝐻
• Find the nonmonotonic revision 𝑅𝑁𝑀 of 𝑅𝐻
• Maximize top-k avg. confidence
• Minimize conflicting prediction
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Unknown
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Problem Statement: Conflicting Predictions
• Defining conflicts
• Measuring conflicts (auxiliary rules)
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𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋)
𝑟2𝑎𝑢𝑥: 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 =
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Problem Statement: Conflicting Predictions
• Defining conflicts
• Measuring conflicts (auxiliary rules)
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𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋)
𝑟2𝑎𝑢𝑥: 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 =
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Problem Statement: Conflicting Predictions
• Defining conflicts
• Measuring conflicts (auxiliary rules)
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𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋)
𝑟2𝑎𝑢𝑥: 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 =
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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
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bornInUSA livesInUSA stateless emigrant singer poet
p1 ✓ ✓
p2 ✓ ✓
p3 ✓ ✓
p4 ✓ ✓ ✓
p5 ✓ ✓ ✓
p6 ✓ ✓
p7 ✓ ✓
p8 ✓ ✓ ✓ ✓
p9 ✓ ✓ ✓
p10 ✓ ✓ ✓ ✓
p11 ✓ ✓ ✓
Step 1: Mining Horn Rules
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𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)
No
rmal
Ab
-no
rmal
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bornInUSA livesInUSA stateless emigrant singer poet
p1 ✓ ✓
p2 ✓ ✓
p3 ✓ ✓
p4 ✓ ✓ ✓
p5 ✓ ✓ ✓
p6 ✓ ✓
p7 ✓ ✓
p8 ✓ ✓ ✓ ✓
p9 ✓ ✓ ✓
p10 ✓ ✓ ✓ ✓
p11 ✓ ✓ ✓
𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)
No
rmal
Ab
-no
rmal
Step 2: Extracting Exception Witness Set (EWS)
14𝐸𝑊𝑆𝑖 = {𝑒𝑚𝑖𝑔𝑟𝑎𝑛𝑡 𝑋 , 𝑝𝑜𝑒𝑡 𝑋 }
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Step 3: Constructing Candidate Revisions
• Horn rules
• Rule revisions
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𝑟1: 𝑙𝑖𝑣𝑒𝑠𝐼𝑛𝑈𝑆𝐴 𝑋 ← 𝑏𝑜𝑟𝑛𝐼𝑛𝑈𝑆𝐴 𝑋 , 𝑛𝑜𝑡 𝑝𝑜𝑒𝑡 𝑋𝑟1: 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), … }
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Step 4: Selecting the 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.
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• Partial materialization
Ranking Rule’s Revisions
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bornInUSA livesInUSA stateless emigrant singer poet
p1 ✓ ✓
p2 ✓ ✓
p3 ✓ ✓
p4 ✓ ✓ ✓
p5 ✓ ✓ ✓
p6 ✓ ✓
p7 ✓ ✓
p8 ✓ ✓ ✓ ✓
p9 ✓ ✓ ✓
p10 ✓ ✓ ✓ ✓
p11 ✓ ✓ ✓
𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)
No
rmal
Ab
-no
rmal
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• Partial materialization
bornInUSA livesInUSA stateless emigrant singer poet
p1 ✓ ✓
p2 ✓ ✓
p3 ✓ ✓
p4 ✓ ✓ ✓ ✓
p5 ✓ ✓ ✓ ✓
p6 ✓ ✓ ✓
p7 ✓ ✓ ✓
p8 ✓ ✓ ✓ ✓
p9 ✓ ✓ ✓ ✓ ✓
p10 ✓ ✓ ✓ ✓
p11 ✓ ✓ ✓ ✓
𝒓𝒊: 𝒍𝒊𝒗𝒆𝒔𝑰𝒏𝑼𝑺𝑨 𝑿 ← 𝒃𝒐𝒓𝒏𝑰𝒏𝑼𝑺𝑨(𝑿)
No
rmal
Ab
-no
rmal
Ranking Rule’s Revisions
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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
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Experiments
• 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
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Experiments
• 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
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Experiments
• Examples
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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)
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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
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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.
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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.
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Problem Statement: Ruleset Quality
• 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
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𝑞𝑟𝑚 𝑅𝑁𝑀, 𝐺 =
𝑟 ∈𝑅𝑁𝑀
𝑟𝑚(𝑟, 𝐺)
𝑅𝑁𝑀
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Problem Statement: Conflicting Predictions
• Measuring conflicts (auxiliary rules)
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𝑟2: 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑛𝑜𝑡 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋)
𝑟2𝑎𝑢𝑥: 𝑛𝑜𝑡_𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑𝐼𝑛𝐽𝑃 𝑋 ← ℎ𝑎𝑠𝐽𝑃𝐶𝑜𝑚𝑝𝑜𝑠𝑒𝑟 𝑋 , 𝑝𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟𝑈𝑆𝐴(𝑋)
𝑞𝑐𝑜𝑛𝑓𝑙𝑖𝑐𝑡 𝑅𝑁𝑀, 𝐺 =|{(𝑝 𝑎 , 𝑛𝑜𝑡_𝑝 𝑎 ), … }|
{𝑛𝑜𝑡_𝑝 𝑎 , … }
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Propositionalization
• Unary predicates
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Binary Predicates
• hasType(enstein, scientist)
• isMarriedTo(elsa, einstein)
• bornIn(einstein, um)
Unary
• isAScientist(einstein)
• isMarriedToEinstein(elsa)
• bornInUlm(einstein)
Abstraction
• isAScientist(einstein)
• isMarriedToScientist(elsa)
• bornInGermany(einstein)
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Experiments
• Input
• Experiment statistics
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YAGO3 IMDB
Input Facts 10M 2M
Horn Rules 10K 25K
Revised Rules 6K 22K
General-purpose KG Domain-specific KG (Movies)
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Experiments
• Predictions assessment• Run DLV on YAGO and 𝑅𝐻 then 𝑅𝑁𝑀 seperately
• Sample facts such that fact 𝑓 ∈ 𝑌𝐴𝐺𝑂𝐻\𝑌𝐴𝐺𝑂𝑁𝑀
• 73% of the sampled facts were found to be erroneous
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checked predictions
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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 𝑟𝑎𝑢𝑥
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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.