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# Statistical Relational Learning - PowerPoint PPT Presentation

Statistical Relational Learning. Pedro Domingos Dept. Computer Science & Eng. University of Washington. Overview. Motivation Some approaches Markov logic Application: Information extraction Challenges and open problems. Motivation. Most learners only apply to i.i.d. vectors

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### Statistical Relational Learning

Pedro Domingos

Dept. Computer Science & Eng.

University of Washington

• Motivation

• Some approaches

• Markov logic

• Application: Information extraction

• Challenges and open problems

• Most learners only apply to i.i.d. vectors

• But we need to do learning and (uncertain) inference over arbitrary structures:trees, graphs, class hierarchies,relational databases, etc.

• All these can be expressed in first-order logic

• Let’s add learning and uncertain inference to first-order logic

• Probabilistic logic [Nilsson, 1986]

• Statistics and beliefs [Halpern, 1990]

• Knowledge-based model construction[Wellman 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.

• Logical formulas are hard constraintson the possible states of the world

• Let’s make them soft constraints:When a state violates a formula,It becomes less probable, not impossible

• Give each formula a weight(Higher weight  Stronger constraint)

• More precisely:Consider each grounding of a formula

Two constants: Anna (A) and Bob (B)

Friends(A,B)

Friends(A,A)

Smokes(A)

Smokes(B)

Friends(B,B)

Cancer(A)

Cancer(B)

Friends(B,A)

• 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

• Logical inference:Satisfiability testing

• Probabilistic inference:Markov chain Monte Carlo

• Inductive logic programming:Search with clause refinement operators

• Statistical learning:Weight optimization by conjugate gradient

• Open-source software available at:

• A new kind of programming language

• Write formulas, learn weights, do inference

• Haven’t we seen this before?

• Yes, but without learning and uncertain inference

alchemy.cs.washington.edu

Example:Information 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.

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.

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.

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.

• 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

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)

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

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

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

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Token(+t,i,c) => InField(i,+f,c)

InField(i,+f,c) ^ !Token(“.”,i,c) <=> InField(i+1,+f,c)

f != f’ => (!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’) => SameField(+f,c,c’)

SameField(+f,c,c’) <=> SameCit(c,c’)

SameField(f,c,c’) ^ SameField(f,c’,c”)

=> SameField(f,c,c”)

SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”)

Results:Matching Venues on Cora

• 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