Presentation is loading. Please wait.

Presentation is loading. Please wait.

S TATISTICAL R ELATIONAL L EARNING Joint Work with Sriraam Natarajan, Kristian Kersting, Jude Shavlik.

Published byJack Hanson Modified over 9 years ago

Similar presentations

Presentation on theme: "S TATISTICAL R ELATIONAL L EARNING Joint Work with Sriraam Natarajan, Kristian Kersting, Jude Shavlik."— Presentation transcript:

1 S TATISTICAL R ELATIONAL L EARNING Joint Work with Sriraam Natarajan, Kristian Kersting, Jude Shavlik

2 B AYESIAN N ETWORKS BurglaryEarthquake Alarm JohnCalls eba 000.1 010.8 100.6 110.9 e 0.01 b MaryCalls

3 B AYESIAN N ETWORK FOR A C ITY BurglaryEarthquake Alarm Calls(H1)Calls(H3) BurglaryEarthquake Alarm Calls(H2) BurglaryEarthquake Alarm Calls(H2)Calls(H4) BurglaryEarthquake Alarm Calls(H3)Calls(H5) BurglaryEarthquake Alarm Calls(H4)Calls(H6) H1 H2 H3 H4 H5

4 S HARED V ARIABLES Earthquake(BL) Alarm(H1) Alarm(H2) Alarm(H3) Alarm(H4) Burglary(H4) Burglary(H2) Burglary(H3) Burglary(H1) Calls(H1) Calls(H4) Calls(H5) Calls(H2)Calls(H3)

5 F IRST O RDER L OGIC Burglary(house) Earthquake(city) Alarm(house) Calls(nhouse) HouseInCity(house, city) Alarm(house) :- HouseInCity(house, city), Earthquake(city), Burglary(house) eba 000.1 010.8 100.6 110.9 Neighbor(house, nhouse)

6 L OGIC + P ROBABILITY = S TATISTICAL R ELATIONAL L EARNING M ODELS Logic Probabilities Add Probabilities Statistical Relational Learning (SRL) Add Relations PRating CRating Diff

7 A LPHABETIC S OUP  Knowledge-based model construction [Wellman et al., 1992]  PRISM [Sato & Kameya 1997]  Stochastic logic programs [Muggleton, 1996]  Probabilistic relational models [Friedman et al., 1999]  Bayesian logic programs [Kersting & De Raedt, 2001]  Bayesian logic [Milch et al., 2005]  Markov logic [Richardson & Domingos, 2006]  Relational dependency networks [Neville & Jensen 2007]  ProbLog [De Raedt et al., 2007] And many others!

8 R ELATIONAL D ATABASE ProfLevel ProfCourseRating CourseDiff StudentCourseGrade StudentIQSatisfaction

9 F IRST O RDER L OGIC Prof(P) Level(P,L) Diff(C) Course(C) taughtBy(P,C) ratings(P,C,R) Student(S) IQ(S,I) satis(S,B) takes(S,C) grde(S,C,G) ProfLevel ProfCourseRating CourseDiff StudentCourseGrade StudentIQSatisfaction

10 G RAPHICAL M ODEL satisfaction(S, B) Diff(S, C, D)grades(S, C, G) avgGrade(S, G) avgDiff(S, D) P(satisfaction(S, B) | avgGrade(S, G), avgDiff(D))

11 R ELATIONAL D ECISION T REE speed(X,S), S>120 job(X, politician) knows(X,Y) job(Y, politician) N N N Y Y no yes no yes no yes NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary

12 R ELATIONAL D ECISION T REE NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary speed(Alice,150), 150>120 job(X, politician) knows(X,Y) job(Y, politician) N N N Y Y no yes no yes no yes

13 R ELATIONAL D ECISION T REE NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary speed(Alice,150), 150>120 job(Alice, politician) knows(X,Y) job(Y, politician) N N N Y Y no yes no yes no yes

14 R ELATIONAL D ECISION T REE NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary speed(Alice,150), 150>120 job(Alice, politician) knows(Alice,John) job(Y, politician) N N N Y Y no yes no yes no yes

15 R ELATIONAL D ECISION T REE NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary speed(Alice,150), 150>120 job(Alice, politician) knows(Alice,John) job(John, politician) N N N Y Y no yes no yes no yes

16 R ELATIONAL D ECISION T REE NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary speed(Alice,150), 150>120 job(Alice, politician) knows(Alice,John) job(John, politician) N N N Y Y no yes no yes no yes

17 R ELATIONAL D ECISION T REE NameSpeedJobFine Bob120TeacherN Alice150WriterN John180PoliticianN Mary160StudentY Mike140EngineerY Person1Person2 AliceJohn MaryMike MaryAlice BobMike BobMary speed(Alice,150), 150>120 job(Alice, politician) knows(Alice,John) job(John, politician) N N N Y Y no yes no yes no yes

18 R ELATIONAL P ROBABILITY T REES Use probabilities on the leaves Can be used to represent the conditional distributions Can use regression values on leaves to represent regression functions speed(X,S), S>120 job(X, politician) knows(X,Y) job(Y, politician) 0.1 0.2 0.4 0.8 no yes no yes no yes

19 S TRUCTURE L EARNING P ROBLEM Learn the structure of the conditional distributions Find the parents and the distribution for the target concept satisfaction(S, B) avgGrade(S, G)avgDiff(S, D) IQ(S, I) level(P, L)

20 R ELATIONAL T REE L EARNING 20 student(X ) paper(X,Y) 0.7-0.2 -0.9 student(X) = T paper(X,Y) = Tpaper(X,Y) = F student(X) = F XΔ x10.7 x2-0.2 x3-0.9 XY x1y1 x1y2 x3y1 X x1 x2 paper(X, Y) student(X) adviser(X) XΔ x10.7 x2-0.2 XΔ x3-0.9 XΔ x2-0.2 XΔ x10.7 0.25

21 Sequentially learn models where each subsequent model corrects the previous model F UNCTIONAL G RADIENT B OOSTING Data Predictions - Residues = Initial Model + + Induce Iterate Final Model = ++ + + … ψmψm Natarajan et al MLJ’12

22 B OOSTING A LGORITHM For each gradient step m=1 to M For each query predicate, P Generate trainset using previous model, F m-1 Learn a regression function, T m,p For each example, x Compute gradient for x Add to trainset Add T m,p to the model, F m

23 UW-CSE AUC-ROCAUC-PRLikelihood Training Time Boosting0.960.930.819 s RDN0.880.780.801 s Alchemy0.530.620.7393 hrs Predict advisedBy relation Given student, professor, courseTA, courseProf, etc relations 5-fold cross validation http://pages.cs.wisc.edu/~tushar/rdnboost/index.html

24 CARDIA Family history, medical history, physical activity, nutrient intake, obesity questions, pysochosocial, pulmonary function etc Goal is to identify risk factors in early adulthood that causes serious cardio-vascular issues in older adults Extremely rich dataset with 25 years of information S. Natarajan, J. Carr

25 R ESULTS

26 I MITATION L EARNING Expert agent performs actions (trajectories) Goal: Learn a policy from these trajectories to suggest actions based on current state Natarajan et al. IJCAI’11

27 Gridworld domainRobocup domain

28 A LZHEIMER ' S R ESEARCH AD – Progressive neurodegenerative condition resulting in loss of cognitive abilities and memory MRI – neuroimaging method Visualization of brain anatomy Humans are not very good at identifying people with AD, especially before cognitive decline MRI data – major source for distinguishing AD vs CN (Cognitively normal) or MCI vs CN Natarajan et al. Under review

29 P ROPOSITIONAL M ODELS ( WITH AAL)

30 C ONCLUSION Statistical Relational Learning combines first-order logic with probabilistic models Relational trees used to represent conditional distributions Boosting trees can be used to efficiently learn structure of SRL models

31

Download ppt "S TATISTICAL R ELATIONAL L EARNING Joint Work with Sriraam Natarajan, Kristian Kersting, Jude Shavlik."

Similar presentations

Bayesian networks Chapter 14 Section 1 – 2. Outline Syntax Semantics Exact computation.

Bayesian networks Chapter 14 Section 1 – 2. Outline Syntax Semantics Exact computation.
A Tutorial on Learning with Bayesian Networks

A Tutorial on Learning with Bayesian Networks
Probabilistic Reasoning Bayesian Belief Networks Constructing Bayesian Networks Representing Conditional Distributions Summary.

Probabilistic Reasoning Bayesian Belief Networks Constructing Bayesian Networks Representing Conditional Distributions Summary.
Efficient Inference Methods for Probabilistic Logical Models

Efficient Inference Methods for Probabilistic Logical Models
University of Texas at Austin Machine Learning Group Department of Computer Sciences University of Texas at Austin Discriminative Structure and Parameter.

University of Texas at Austin Machine Learning Group Department of Computer Sciences University of Texas at Austin Discriminative Structure and Parameter.
CPSC 322, Lecture 30Slide 1 Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 30 March, 25, 2015 Slide source: from Pedro Domingos UW.

CPSC 322, Lecture 30Slide 1 Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 30 March, 25, 2015 Slide source: from Pedro Domingos UW.
Sriraam Natarajan Introduction to Probabilistic Logical Models Slides based on tutorials by Kristian Kersting, James Cussens, Lise Getoor & Pedro Domingos.

Sriraam Natarajan Introduction to Probabilistic Logical Models Slides based on tutorials by Kristian Kersting, James Cussens, Lise Getoor & Pedro Domingos.
BAYESIAN NETWORKS. Bayesian Network Motivation  We want a representation and reasoning system that is based on conditional independence  Compact yet.

BAYESIAN NETWORKS. Bayesian Network Motivation  We want a representation and reasoning system that is based on conditional independence  Compact yet.
Belief networks Conditional independence Syntax and semantics Exact inference Approximate inference CS 460, Belief Networks1 Mundhenk and Itti 2008. Based.

Belief networks Conditional independence Syntax and semantics Exact inference Approximate inference CS 460, Belief Networks1 Mundhenk and Itti Based.
1 Knowledge Engineering for Bayesian Networks. 2 Probability theory for representing uncertainty l Assigns a numerical degree of belief between 0 and.

1 Knowledge Engineering for Bayesian Networks. 2 Probability theory for representing uncertainty l Assigns a numerical degree of belief between 0 and.
Bayesian Networks. Introduction A problem domain is modeled by a list of variables X 1, …, X n Knowledge about the problem domain is represented by a.

Bayesian Networks. Introduction A problem domain is modeled by a list of variables X 1, …, X n Knowledge about the problem domain is represented by a.
Bayesian Networks Chapter 14 Section 1, 2, 4. Bayesian networks A simple, graphical notation for conditional independence assertions and hence for compact.

Bayesian Networks Chapter 14 Section 1, 2, 4. Bayesian networks A simple, graphical notation for conditional independence assertions and hence for compact.
Speeding Up Inference in Markov Logic Networks by Preprocessing to Reduce the Size of the Resulting Grounded Network Jude Shavlik Sriraam Natarajan Computer.

Speeding Up Inference in Markov Logic Networks by Preprocessing to Reduce the Size of the Resulting Grounded Network Jude Shavlik Sriraam Natarajan Computer.
Markov Logic: A Unifying Framework for Statistical Relational Learning Pedro Domingos Matthew Richardson

Markov Logic: A Unifying Framework for Statistical Relational Learning Pedro Domingos Matthew Richardson
CPSC 322, Lecture 26Slide 1 Reasoning Under Uncertainty: Belief Networks Computer Science cpsc322, Lecture 27 (Textbook Chpt 6.3) March, 16, 2009.

CPSC 322, Lecture 26Slide 1 Reasoning Under Uncertainty: Belief Networks Computer Science cpsc322, Lecture 27 (Textbook Chpt 6.3) March, 16, 2009.
Review: Bayesian learning and inference

Review: Bayesian learning and inference
Bayesian Networks. Motivation The conditional independence assumption made by naïve Bayes classifiers may seem to rigid, especially for classification.

Bayesian Networks. Motivation The conditional independence assumption made by naïve Bayes classifiers may seem to rigid, especially for classification.
Probabilistic Reasoning Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 14 (14.1, 14.2, 14.3, 14.4) Capturing uncertain knowledge Probabilistic.

Probabilistic Reasoning Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 14 (14.1, 14.2, 14.3, 14.4) Capturing uncertain knowledge Probabilistic.
CSE 574 – Artificial Intelligence II Statistical Relational Learning Instructor: Pedro Domingos.

CSE 574 – Artificial Intelligence II Statistical Relational Learning Instructor: Pedro Domingos.
1 Data Mining with Bayesian Networks (I) Instructor: Qiang Yang Hong Kong University of Science and Technology Thanks: Dan Weld, Eibe.

1 Data Mining with Bayesian Networks (I) Instructor: Qiang Yang Hong Kong University of Science and Technology Thanks: Dan Weld, Eibe.

Similar presentations

Ads by Google