Abstract:
One of the challenges in big data analytics lies in being able to reason collectively about extremely large, heterogeneous, incomplete, noisy interlinked data. We need data science techniques which an represent and reason effectively with this form of rich and multi-relational graph data. In this presentation, I will describe some common collective inference patterns needed for graph data including: collective classification (predicting missing labels for nodes in a network), link prediction (predicting potential edges), and entity resolution (determining when two nodes refer to the same underlying entity). I will describe three key capabilities required: relational feature construction, collective inference, and scaling. Finally, I briefly describe some of the cutting edge analytic tools being developed within the machine learning, AI, and database communities to address these challenges.
21. Graph
Iden2fica2on
• Goal:
– Given
an
input
graph
infer
an
output
graph
• Three
major
components:
– En&ty
Resolu&on
(ER):
Infer
the
set
of
nodes
– Link
Predic&on
(LP):
Infer
the
set
of
edges
– Collec&ve
Classifica&on
(CC):
Infer
the
node
labels
• Challenge:
The
components
are
intra
and
inter-‐dependent
Namata,
Kok,
Getoor,
KDD
2011
25. Key Idea: Feature Construction
¢ Feature informativeness is key to the success of a
relational classifier
¢ Relational feature construction
l Node-specific measures
• Aggregates: summarize attributes of relational neighbors
• Structural properties: capture characteristics of the relational
structure
l Node-pair measures: summarize properties of
(potential) edges
• Attribute-based measures
• Edge-based measures
• Neighborhood similarity measures
26. Relational Classifiers
¢ Pros:
l Efficient: Can handle large amounts of data
• Features can often be pre-computed ahead of time
l Flexible: Can take advantage of well-understood classification/
regression algorithms
l One of the most commonly-used ways of incorporating
relational information
¢ Cons:
l Features are based on observed values/evidence, cannot be
based on attributes or relations that are being predicted
l Makes incorrect independence assumptions
l Hard to impose global constraints on joint assignments
• For example, when inferring a hierarchy of individuals, we may want
to enforce constraint that it is a tree
33. Link Prediction
§ People, emails, words,
communication, relations
§ Use model to express
dependencies
- “If email content suggests type X, it
is of type X”
- “If A sends deadline emails to B,
then A is the supervisor of B”
- “If A is the supervisor of B, and A is
the supervisor of C, then B and C are
colleagues”
#
34. Link Prediction
HasWord(E, “due”) => Type(E, deadline) : 0.6
§ People, emails, words,
communication, relations
§ Use model to express
dependencies
- “If email content suggests type X, it
is of type X”
- “If A sends deadline emails to B,
then A is the supervisor of B”
- “If A is the supervisor of B, and A is
the supervisor of C, then B and C are
colleagues”
#
complete by
due
35. Link Prediction
§ People, emails, words,
communication, relations
§ Use model to express
dependencies
- “If email content suggests type X, it
is of type X”
- “If A sends deadline emails to B,
then A is the supervisor of B”
- “If A is the supervisor of B, and A is
the supervisor of C, then B and C are
colleagues”
#
Sends(A,B,E) ^ Type(E,deadline) => Supervisor(A,B) : 0.8
36. Link Prediction
§ People, emails, words,
communication, relations
§ Use model to express
dependencies
- “If email content suggests type X, it
is of type X”
- “If A sends deadline emails to B,
then A is the supervisor of B”
- “If A is the supervisor of B, and A is
the supervisor of C, then B and C are
colleagues”
#
Supervisor(A,B) ^ Supervisor(A,C) => Colleague(B,C) : ∞
37. Entity Resolution
§ Entities
- People References
§ Attributes
- Name
§ Relationships
- Friendship
§ Goal: Identify
references that denote
the same person
John Smith J. Smith
name name
A B
C
E
friend friend
D F G
H
=
=
38. Entity Resolution
§ References, names,
friendships
§ Use model to express
dependencies
- ‘’If two people have similar names,
they are probably the same’’
- ‘’If two people have similar friends,
they are probably the same’’
- ‘’If A=B and B=C, then A and C must
also denote the same person’’
John Smith J. Smith
name name
A B
C
E
friend friend
D F G
H
=
=
39. Entity Resolution
§ References, names,
friendships
§ Use model to express
dependencies
- ‘’If two people have similar names,
A.name ≈{str_sim} B.name => A≈B : 0.8
they are probably the same’’
- ‘’If two people have similar friends,
they are probably the same’’
- ‘’If A=B and B=C, then A and C must
also denote the same person’’
John Smith J. Smith
name name
A B
C
E
friend friend
D F G
H
=
=
40. Entity Resolution
§ References, names,
friendships
§ Use model to express
dependencies
- ‘’If two people have similar names,
they are probably the same’’
- ‘’If two people have similar friends,
they are probably the same’’
- ‘’If A=B and B=C, then A and C must
also denote the same person’’
John Smith J. Smith
name name
A B
C
E
friend friend
D F G
H
=
=
{A.friends} ≈{} {B.friends} => A≈B : 0.6
41. Entity Resolution
§ References, names,
friendships
§ Use model to express
dependencies
- ‘’If two people have similar names,
they are probably the same’’
- ‘’If two people have similar friends,
they are probably the same’’
- ‘’If A=B and B=C, then A and C must
also denote the same person’’
John Smith J. Smith
name name
A B
C
E
friend friend
D F G
H
=
=
A≈B ^ B≈C => A≈C : ∞
42. Challenges
¢ Collective Classification: labeling nodes in graph
l irregular structure, not a chain, not a grid
l Challenge: One large partially labeled graph
¢ Link prediction: predicting edges in graph
l Dependencies among edges
l Don’t want to reason about all possible edges
l Challenge: scaling & extremely skewed probabilities
¢ Entity resolution: determine nodes that refer to
same entities in a graph
l Dependencies between clusters
l Challenge: enforcing constraints, e.g. transitive closure
44. Blocking: Motivation
¢ Naïve pairwise: |N|2 pairwise comparisons
l 1000 business listings each from 1,000 different cities
across the world
l 1 trillion comparisons
l 11.6 days (if each comparison is 1 μs)
¢ Mentions from different cities are unlikely to be
matches
l Blocking Criterion: City
l 1 billion comparisons
l 16 minutes (if each comparison is 1 μs)
45. Blocking: Motivation
¢ Mentions from different cities are unlikely to be
matches
l May miss potential matches
47
47. Blocking Algorithms 1
¢ Hash based blocking
l Each block Ci is associated with a hash key hi.
l Mention x is hashed to Ci if hash(x) = hi.
l Within a block, all pairs are compared.
l Each hash function results in disjoint blocks.
¢ What hash function?
l Deterministic function of attribute values
l Boolean Functions over attribute values
[Bilenko et al ICDM’06, Michelson et al AAAI’06,
Das Sarma et al CIKM ‘12]
l minHash (min-wise independent permutations)
[Broder et al STOC’98]; locality sensitive hashing
48. Blocking Algorithms 2
¢ Pairwise Similarity/Neighborhood based blocking
l Nearby nodes according to a similarity metric are
clustered together
l Results in non-disjoint canopies.
¢ Techniques
l Sorted Neighborhood Approach [Hernandez et al
SIGMOD’95]
l Canopy Clustering [McCallum et al KDD’00]
51. http://psl.umiacs.umd.edu
Matthias Stephen Bach Broecheler Alex Memory Lily Mihalkova Stanley Kok
Bert Huang
Angelika Kimmig
Ben London Arti Ramesh Jay Pujara Shobeir Fakhraei Hui Miao
52. http://psl.umiacs.umd.edu
Probabilistic Soft Logic (PSL)
Declarative language based on logics to express
collective probabilistic inference problems
- Predicate = relationship or property
- Atom = (continuous) random variable
- Rule = capture dependency or constraint
- Set = define aggregates
PSL Program = Rules + Input DB
54. PSL Foundations
§ PSL makes large-scale reasoning scalable by
mapping logical rules to convex functions
§ Three principles justify this mapping:
- LP programs for MAX SAT with approximation
guarantees [Goemans and Williamson, ’94]
- Pseudomarginal LP relaxations of Boolean Markov
random fields [Wainwright, et al., ’02]
- Łukasiewicz logic, a logic for reasoning about
continuous values [Klir and Yuan, ‘95]
55. Hinge-loss Markov Random Fields
P(Y|X) =
1
Z
exp
2
4
Xm
j=1
wj max{`j(Y,X), 0}pj
3
5
§ Continuous variables in [0,1]
§ Potentials are hinge-loss functions
§ Subject to arbitrary linear constraints
§ Log-concave!
56. PSL in a Slide
§ MAP Inference in PSL translates into convex optimization
problem - inference is really fast!
§ Inference further enhanced with state-of-the-art
optimization and distributed processing paradigms such as
ADMM GraphLab - inference even faster!
§ Outperforms discrete MRFs in terms of speed, and (very)
often accuracy
§ PSL is flexible: Applied to image segmentation, activity
recognition, stance-detection, sentiment analysis,
document classification, drug target prediction, latent
social groups and trust, engagement modeling, ontology
alignment, and looking for more!
60. Closing
Comments
• Need
new
sta2s2cal
and
ML
theory
for
very
large
graphs
– Be#er
understand
bias,
iden2fiability,
and
mechanism
design
in
graph
domains
• Important
topics
not
touched
on
– Genera2ve
mechanisms,
causal
reasoning,
dynamic
modeling
– Privacy,
Users,
Visualiza2on
• Many
exci2ng
opportuni2es
to
develop
new
theory
and
algorithms
and
apply
them
to
compelling
business,
intelligence,
social,
and
societal
problems!