Statistical Relational Learning

1
Statistical Relational Learning

• Pedro Domingos
• Dept. Computer Science Eng.
• University of Washington

2
Overview

• Motivation
• Some approaches
• Markov logic
• Application Information extraction
• Challenges and open problems

3
Motivation

• Most learners only apply to i.i.d. vectors
• But we need to do learning and (uncertain)
  inference over arbitrary structurestrees,
  graphs, class hierarchies,relational databases,
  etc.
• All these can be expressed in first-order logic
• Lets add learning and uncertain inference to
  first-order logic

4
Some Approaches

• Probabilistic logic Nilsson, 1986
• Statistics and beliefs Halpern, 1990
• Knowledge-based model constructionWellman et
  al., 1992
• Stochastic logic programs Muggleton, 1996
• Probabilistic relational models Friedman et al.,
  1999
• Relational Markov networks Taskar et al., 2002
• Markov logic Richardson Domingos, 2004
• Bayesian logic Milch et al., 2005
• Etc.

5
Markov Logic

• Logical formulas are hard constraintson the
  possible states of the world
• Lets make them soft constraintsWhen a state
  violates a formula,It becomes less probable, not
  impossible
• Give each formula a weight(Higher weight ?
  Stronger constraint)
• More preciselyConsider each grounding of a
  formula

6
Example Friends Smokers
Two constants Anna (A) and Bob (B)
Friends(A,B)
Smokes(A)
Friends(A,A)
Smokes(B)
Friends(B,B)
Cancer(A)
Cancer(B)
Friends(B,A)
7
Markov Logic (Contd.)

• Probability of a state x
• Most discrete statistical models are special
  cases (e.g., Bayes nets, HMMs, etc.)
• First-order logic is infinite-weight limit

Weight of formula i
No. of true groundings of formula i in x
8
Key Ingredients

• Logical inferenceSatisfiability testing
• Probabilistic inferenceMarkov chain Monte Carlo
• Inductive logic programmingSearch with clause
  refinement operators
• Statistical learningWeight optimization by
  conjugate gradient

9
Alchemy

• Open-source software available at
• A new kind of programming language
• Write formulas, learn weights, do inference
• Havent we seen this before?
• Yes, but without learning and uncertain inference

alchemy.cs.washington.edu
10
ExampleInformation Extraction
Parag Singla and Pedro Domingos,
Memory-Efficient Inference in Relational
Domains (AAAI-06). Singla, P., Domingos, P.
(2006). Memory-efficent inference in relatonal
domains. In Proceedings of the Twenty-First
National Conference on Artificial
Intelligence (pp. 500-505). Boston, MA AAAI
Press. H. Poon P. Domingos, Sound and
Efficient Inference with Probabilistic and
Deterministic Dependencies, in Proc. AAAI-06,
Boston, MA, 2006. P. Hoifung (2006). Efficent
inference. In Proceedings of the Twenty-First
National Conference on Artificial Intelligence.
11
Segmentation
Author
Title
Venue
Parag Singla and Pedro Domingos,
Memory-Efficient Inference in Relational
Domains (AAAI-06). Singla, P., Domingos, P.
(2006). Memory-efficent inference in relatonal
domains. In Proceedings of the Twenty-First
National Conference on Artificial
Intelligence (pp. 500-505). Boston, MA AAAI
Press. H. Poon P. Domingos, Sound and
Efficient Inference with Probabilistic and
Deterministic Dependencies, in Proc. AAAI-06,
Boston, MA, 2006. P. Hoifung (2006). Efficent
inference. In Proceedings of the Twenty-First
National Conference on Artificial Intelligence.
12
Entity Resolution
Parag Singla and Pedro Domingos,
Memory-Efficient Inference in Relational
Domains (AAAI-06). Singla, P., Domingos, P.
(2006). Memory-efficent inference in relatonal
domains. In Proceedings of the Twenty-First
National Conference on Artificial
Intelligence (pp. 500-505). Boston, MA AAAI
Press. H. Poon P. Domingos, Sound and
Efficient Inference with Probabilistic and
Deterministic Dependencies, in Proc. AAAI-06,
Boston, MA, 2006. P. Hoifung (2006). Efficent
inference. In Proceedings of the Twenty-First
National Conference on Artificial Intelligence.
13
Entity Resolution
Parag Singla and Pedro Domingos,
Memory-Efficient Inference in Relational
Domains (AAAI-06). Singla, P., Domingos, P.
(2006). Memory-efficent inference in relatonal
domains. In Proceedings of the Twenty-First
National Conference on Artificial
Intelligence (pp. 500-505). Boston, MA AAAI
Press. H. Poon P. Domingos, Sound and
Efficient Inference with Probabilistic and
Deterministic Dependencies, in Proc. AAAI-06,
Boston, MA, 2006. P. Hoifung (2006). Efficent
inference. In Proceedings of the Twenty-First
National Conference on Artificial Intelligence.
14
State of the Art

• Segmentation
• HMM (or CRF) to assign each token to a field
• Entity resolution
• Logistic regression to predict same
  field/citation
• Transitive closure
• Alchemy implementation Seven formulas

15
Types and Predicates
token Parag, Singla, and, Pedro, ... field
Author, Title, Venue citation C1, C2,
... position 0, 1, 2, ... Token(token,
position, citation) InField(position, field,
citation) SameField(field, citation,
citation) SameCit(citation, citation)
16
Types and Predicates
token Parag, Singla, and, Pedro, ... field
Author, Title, Venue, ... citation C1, C2,
... position 0, 1, 2, ... Token(token,
position, citation) InField(position, field,
citation) SameField(field, citation,
citation) SameCit(citation, citation)
Optional
17
Types and Predicates
token Parag, Singla, and, Pedro, ... field
Author, Title, Venue citation C1, C2,
... position 0, 1, 2, ... Token(token,
position, citation) InField(position, field,
citation) SameField(field, citation,
citation) SameCit(citation, citation)
Input
18
Types and Predicates
token Parag, Singla, and, Pedro, ... field
Author, Title, Venue citation C1, C2,
... position 0, 1, 2, ... Token(token,
position, citation) InField(position, field,
citation) SameField(field, citation,
citation) SameCit(citation, citation)
Output
19
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
20
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
21
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
22
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
23
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
24
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
25
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
ltgt InField(i1,f,c) f ! f gt
(!InField(i,f,c) v !InField(i,f,c)) Token(t,i
,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
26
Formulas
Token(t,i,c) gt InField(i,f,c) InField(i,f,c)
!Token(.,i,c) ltgt InField(i1,f,c) f ! f
gt (!InField(i,f,c) v !InField(i,f,c)) Token(
t,i,c) InField(i,f,c) Token(t,i,c)
InField(i,f,c) gt SameField(f,c,c) SameField(
f,c,c) ltgt SameCit(c,c) SameField(f,c,c)
SameField(f,c,c) gt SameField(f,c,c) SameCit
(c,c) SameCit(c,c) gt SameCit(c,c)
27
Results Segmentation on Cora
28
ResultsMatching Venues on Cora
29
Challenges and Open Problems

• Scaling up learning and inference
• Model design (aka knowledge engineering)
• Generalizing across domain sizes
• Continuous distributions
• Relational data streams
• Relational decision theory
• Statistical predicate invention
• Experiment design