Preliminary results of an ongoing work titled "Efficient Rule Mining on RDF Data". University of Leipzig, AKSW Colloquium, April 3rd, 2017.

1. HORN CONCERTO
Efficient Rule Mining on RDF Data
Tommaso Soru
AKSW Colloquium, 03.04.2017

2. RDF Rule Mining
• RDFS/OWL rules are given as schema.
• Schema-free datasets might have an implicit schema.
• Why “mining”? Because rules are not visible in data.
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3. Motivation/1
Link Prediction Problem.
Given a union of graphs G = G1 ∪ … ∪ GN,
find new edges among vertices s and t in G.
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4. Motivation/2
Markov Logic Networks.
Given a collection of first-order
statements (evidence) and a set
of weighted first-order rules,
build an undirected weighted
graph where nodes are
statements and edges indicate
dependency.
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5. Motivation/3
RDFS/OWL
Interpretation
Rule Mining
Weight
Learning
Grounding Inference
Input
Dataset(s)
Predicted
TriplesMANDOLIN’s pipeline
Markov Logic Networks
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6. Rule Mining & Weight Learning
Given a directed labelled graph, find rules
and weights associated with them.
w rule
w1 p(x, y) ← q(x, y)
w2 p(x, y) ← q(y, x)
w3 p(x, y) ← q(x, z) ^ r(y, z)
w4 p(x, y) ← q(x, z) ^ r(z, y)
w5 p(x, y) ← q(z, x) ^ r(y, z)
w6 p(x, y) ← q(z, x) ^ r(z, y)
Horn Clauses
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7. Horn Clauses
A Horn clause is a clause (a disjunction of literals patterns)
with at most one positive, i.e. unnegated, literal pattern.
p ∨ ¬q1 ∨ ¬q2 ∨ ... ∨ ¬qn
p ← q1 ∧ q2 ∧ ... ∧ qn
head body
p(x,y)
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8. Confidence score (weight)
The confidence score of a rule is defined as the rate of
the occurrences of head and body together
over
the occurrences of the body.
p ← q1 ∧ q2 ∧ ... ∧ qn
head body
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9. The HORN CONCERTO approach
P(A | B) =
P(A∩ B)
P(B)
Bayes’ Theorem
p ← q1 ∧ q2 ∧ ... ∧ qn
Horn Clause
Event-based confidence score
P(p |
!
q) =
P(p ∩
!
q)
P(
!
q)
≈
p ∧
!
q{ }
!
q{ }
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10. Rules with
p ∧
!
q{ }
!
q{ }
SELECT ?p (COUNT(*) AS ?c) WHERE {
?x ?p ?y .
?x <target_q> ?y .
FILTER(?p != <target_q> )
} GROUP BY ?p
SELECT ?q (COUNT(*) AS ?c) WHERE {
[] ?q []
} GROUP BY ?q
!
q = 1
p(x, y) ← q(x, y)
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11. Rules with
p ∧
!
q{ }
!
q{ }
SELECT ?q ?r (COUNT(*) AS ?c) WHERE {
?x ?q ?z .
?z ?r ?y .
?x <target_p> ?y
} GROUP BY ?q ?r
SELECT (COUNT(*) AS ?c) WHERE {
?x <target_q> ?z .
?z <target_r> ?y
}
!
q = 2
p(x, y) ← q(x, z) ∧ r(z, y)
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12. Optimizations
• Select only top N properties.
• Order by descending score and prune when it’s lower
than a threshold T.
• Cache scores in-memory, as there might exist p1, p2
such that: pi(x,y) ← q(?,?), r(?,?).
• Parallelize algorithm by rule type.
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13. Evaluation Setup
• 8 CPUs, 32 GB RAM, Ubuntu 16.04
• Scalability study
DBpedia Person (7 million triples)
DBpedia 2016-04 (397 million triples)
FUTURE
• Rule effectiveness for link prediction
FB15k (592 thousand triples)
WN18 (151 thousand triples)
• Rule quality (human judgment?)
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14. Preliminary results – DBpedia Person
Runtime (s) # Rules Used RAM (GB)
AMIE+ > 10 days 6,337 4
Ontological PF > 3 hours > 1,000 4
HORN CONCERTO
single-thread
1.7 hours 3,125
client: 0.2
server: 1.0
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15. Preliminary results – DBpedia 2016-04
Runtime (s) # Rules Used RAM (GB)
HORN CONCERTO
single-thread
11 hours 887
client: 0.2
server: N/A
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16. Discussion
• AMIE+
Cons: indexes the graph in-memory.
• Ontological PF
Pros: Very fast
Cons: Relies on schema data (types domain, range)
• Horn Concerto
Pros: Works with SPARQL endpoint, fast also single-threaded,
may be able to overperform Ontological PF in RDF datasets with
available schema.
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17. Thank you.