Statistical Relational Learning

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Statistical Relational Learning. Pedro Domingos Dept. Computer Science &amp; 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

Overview
• Motivation
• Some approaches
• Markov logic
• Application: Information extraction
• Challenges and open problems
Motivation
• 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
Some Approaches
• 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.
Markov Logic
• 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
Example: Friends & Smokers

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)

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

Key Ingredients
• 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
Alchemy
• 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.

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.

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.

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.

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
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)

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

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

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

Formulas

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”)

Formulas

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”)

Formulas

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”)

Formulas

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”)

Formulas

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”)

Formulas

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”)

Formulas

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”)

Formulas

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”)

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