Transfer Learning by Mapping and Revising Relational Knowledge Raymond J. Mooney University of Texas at Austin with acknowledgements to Lily Mihalkova, Tuyen Huynh 1 Transfer Learning Most machine learning methods learn each new task from scratch, failing to utilize previously learned knowledge. Transfer learning concerns using knowledge acquired in a previous source task to facilitate learning in a related target task. Usually assume significant training data was available in the source domain but limited training data is available in the target domain. By exploiting knowledge from the source, learning in the target can be: More accurate: Learned knowledge makes better predictions.
Faster: Training time is reduced. 2 Transfer Learning Curves Predictive Accuracy Transfer learning increases accuracy in the target domain. Jump start TRANSFER FROM SOURCE NO TRANSFER Advantage from Limited target data
Amount of training data in target domain 3 Recent Work on Transfer Learning Recent DARPA program on Transfer Learning has led to significant recent research in the area. Some work focuses on feature-vector classification. Hierarchical Bayes (Yu et al., 2005; Lawrence & Platt, 2004) Informative Bayesian Priors (Raina et al., 2005) Boosting for transfer learning (Dai et al., 2007) Structural Correspondence Learning (Blitzer et al., 2007) Some work focuses on Reinforcement Learning Value-function transfer (Taylor & Stone, 2005; 2007)
Advice-based policy transfer (Torrey et al., 2005; 2007) 4 Similar Research Problems Multi-Task Learning (Caruana, 1997) Learn multiple tasks simultaneously; each one helped by the others. Life-Long Learning (Thrun, 1996) Transfer learning from a number of prior source problems, picking the correct source problems to use. 5 Logical Paradigm Represents knowledge and data in binary symbolic logic such as First Order Predicate Calculus.
+ Rich representation that handles arbitrary sets of objects, with properties, relations, quantifiers, etc. Unable to handle uncertain knowledge and probabilistic reasoning. 6 Probabilistic Paradigm Represents knowledge and data as a fixed set of random variables with a joint probability distribution. + Handles uncertain knowledge and probabilistic reasoning. Unable to handle arbitrary sets of objects, with properties, relations, quantifiers, etc. 7
Statistical Relational Learning (SRL) Most machine learning methods assume i.i.d. examples represented as fixed-length feature vectors. Many domains require learning and making inferences about unbounded sets of entities that are richly relationally connected. SRL methods attempt to integrate methods from predicate logic and probabilistic graphical models to handle such structured, multi-relational data. 8 Statistical Relational Learning Actor pacino brando Directo
coppola r Multi-Relational Data WorkedFo pacino r coppola Movie godFather pacino brando coppola
Learning Algorithm Probabilistic Graphical Model 9 Multi-Relational Data Challenges Examples cannot be effectively represented as feature vectors. Predictions for connected facts are not independent. (e.g. WorkedFor(brando, coppolo), Movie(godFather, brando)) Data is not i.i.d. Requires collective inference (classification) (Taskar et al., 2001) A single independent example (mega-example) often contains information about a large number of interconnected entities and can vary in length. Leave one university out testing (Craven et al., 1998)
10 TL and SRL and I.I.D. Standard Machine Learning assumes examples are: Independent and Identically Distributed SRL breaks the assumption that examples are independent TL breaks the assumption that test examples are drawn from the same distribution as the training instances 11 Multi-Relational Domains Domains about people Academic departments (UW-CSE) Movies (IMDB)
Biochemical domains Mutagenesis Alzheimer drug design Linked text domains WebKB Cora 12 Relational Learning Methods Inductive Logic Programming (ILP) Produces sets of first-order rules Not appropriate for probabilistic reasoning If a student wrote a paper with a professor, then the professor is the students advisor SRL models & learning algorithms
SLPs (Muggleton, 1996) PRMs (Koller, 1999) BLPs (Kersting & De Raedt, 2001) RMNs (Taskar et al., 2002) MLNs (Richardson & Domingos, 2006) Markov logic networks 13 MLN Transfer (Mihalkova, Huynh, & Mooney, 2007) Given two multi-relational domains, such as: Source: UW-CSE Professor(A) Student(A) Publication(T, A) AdvisedBy(A, B)
Target: IMDB Director(A) Actor(A) Movie(T, A) WorkedFor(A, B) Transfer a Markov logic network learned in the Source to the Target by: Mapping the Source predicates to the Target Revising the mapped knowledge 14 First-Order Logic Basics Literal: A predicate (or its negation) applied to constants and/or variables. Gliteral: Ground literal; WorkedFor(brando, coppola) Vliteral: Variablized literal; WorkedFor(A, B)
We assume predicates have typed arguments. For example: Movie(godFather, coppola) movieTitle person 15 First-Order Clauses Clause: A disjunction of literals Can be rewritten as a set of rules: 16 Representing the Data Actor(pacino) WorkedFor(pacino, coppola) Movie(godFather, pacino)
Actor(brando) WorkedFor(brando, coppola) Movie(godFather, brando) Director(coppola) Movie(godFather, coppola) Makes a closed world assumption: The gliterals listed are true; the rest are false 17 Markov Logic Networks (Richardson & Domingos, 2006) Set of first-order clauses, each assigned a weight. Larger weight indicates stronger belief that the
clause should hold. The clauses are called the structure of the MLN. 5.3 3.2 0. 5 18 Markov Networks (Pearl, 1988) A concise representation of the joint probability distribution of a set of random variables using an undirected graph. Joint distribution Reputation of Author Algorithm Experiments
Quality of Paper R A E Q e e e e
0.7 e e e p 0.1 e e p e
0.03 Same probability distribution can be represented as the product of a set of functions defined over the cliques of the graph 19 Markov Network Equations General form Log-linear models weights
features20 Ground Markov Network for an MLN MLNs are templates for constructing Markov networks for a given set of constants: Include a node for each type-consistent grounding (a gliteral) of each predicate in the MLN. Two nodes are connected by an edge if their corresponding gliterals appear together in any grounding of any clause in the MLN. Include a feature for each grounding of each clause in the MLN with weight equal to the weight of the clause. 21 constants: coppola, brando, godFather
22 MLN Equations all cla uses in t h e mo de l un o r g all f fi o s ding
Compare to log-linear Markov networks: 23 MLN Equation Intuition A possible world (a truth assignment to all gliterals) becomes exponentially less likely as the total weight of all the grounded clauses it violates increases. 24 MLN Inference Given truth assignments for given set of evidence gliterals, infer the probability that each member of set of unknown query gliterals is true. 25
0.9 F Actor(brando) Director(brando) 0.1 0.7 WorkedFor(brando, brando) WorkedFor(brando, coppola) T T
MLN Inference Algorithms Gibbs Sampling (Richardson & Domingos, 2006) MC-SAT (Poon & Domingos, 2006) 27 MLN Learning Weight-learning (Richardson & Domingos, 2006; Lowd & Domingos, 2007) Performed using optimization methods. Structure-learning (Kok & Domingos, 2005) Proceeds in iterations of beam search, adding the best-performing clause after each iteration to the MLN. Clauses are evaluated using WPLL score. 28 WPLL
(Kok & Domingos, 2005) Weighted pseudo log-likelihood Compute the likelihood of the data according to the model and take log For each gliteral, condition on its Markov blanket for tractability Weight it so that predicates with greater arity do not dominate 29 Alchemy Open-source package of MLN software provided by UW that includes:
Inference algorithms Weight learning algorithms Structure learning algorithm Sample data sets All our software uses and extends Alchemy. 30 TAMAR (Transfer via Automatic Mapping And Revision) Publication(T,A) AdvisedBy(A,B) Publication(T,B) (clause from UW-CSE) M-TAMAR Movie(T,A) WorkedFor(A,B) Movie(T,B) Predicate Mapping: Publication Movie
AdvisedBy WorkedFor Target (IMDB) Data R-TAMAR Movie(T,A) WorkedFor(A,B) Relative(A,B) Movie(T,B) 31 Predicate Mapping Each clause is mapped independently of the others. The algorithm considers all possible ways to map a clause such that: Each predicate in the source clause is mapped to some target predicate. Each argument type in the source is mapped to exactly one argument type in the target.
Each mapped clause is evaluated by measuring its WPLL for the target data, and the most accurate mapping is kept. 32 Predicate Mapping Example Publication(title, person) person) AdvisedBy(person, person) Movie(name, WorkedFor(person, person) Consistent Type Mapping: title name person person
33 Predicate Mapping Example 2 Publication(title, person) gend) AdvisedBy(person, person) gend) Gender(person, SameGender(gend, Consistent Type Mapping: title person person gend 34 TAMAR (Transfer via Automatic Mapping And Revision) Publication(T,A) AdvisedBy(A,B) Publication(T,B) (clause from UW-CSE)
M-TAMAR Movie(T,A) WorkedFor(A,B) Movie(T,B) Target (IMDB) Data R-TAMAR Movie(T,A) WorkedFor(A,B) Relative(A,B) Movie(T,B) 35 Transfer Learning as Revision Regard mapped source MLN as an approximate model for the target task that needs to be accurately and efficiently revised. Thus our general approach
is similar to that taken by theory revision systems TopBottom-up down Source MLN Source MLN Data-Driven Revision Proposer (Richards & Mooney, 1995). Revisions are proposed in a bottom-up fashion.
Target Training Data 36 R-TAMAR Clause Clause Clause Clause Clause 1 2 3 4 5 wt wt wt
wt wt Relational Data New Candidate New Clause 1 wt 0.1 Clauses New Clause 3 New Clause 5 wt 0.5 wt 1.3 Selfdiagnosis New clause discovery New Clause 6
New Clause 7 Too Long Clause 1 Clause Good 2 Too Clause Short 3 Clause Good 4 Clause Too Long 5 wt wt wt
wt wt Directed Beam Search wt -0.2 wt 1.7 Change in WPLL 37 R-TAMAR: Self-Diagnosis Use mapped source MLN to make inferences in the target and observe the behavior of each clause: Consider each predicate P in the domain in turn. Use Gibbs sampling to infer truth values for the gliterals of P, using the remaining gliterals as evidence.
Bin the clauses containing gliterals of P based on whether they behave as desired. Revisions are focused only on clauses in the Bad bins. 38 Self-Diagnosis: Clause Bins Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Current gliteral: Movie(rainMaker, coppola) WorkedFor(brando, coppola) Actor(brando) Relevant;Good
Movie(godFather, brando) Movie(godFather, coppola) Current gliteral: Movie(rainMaker, coppola) WorkedFor(brando, coppola) Actor(brando) Relevant;Good e h t n Relevant; Bad ng
Le Irrelevant;Good en Bad Irrelevant; t r o h S 42 Structure Revisions Using directed beam search:
Literal deletions attempted only from clauses marked for shortening. Literal additions attempted only for clauses marked for lengthening. Training is much faster since search space is constrained by: 1. Limiting the clauses considered for updates. 2. Restricting the type of updates allowed. 43 New Clause Discovery Uses Relational Pathfinding (Richards & Mooney, 1992) Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Movie(rainMaker, coppola) WorkedFor(brando, coppola) brando WorkedFor
ie i v o M e ie Mov ov M godFather coppola
rainMaker 44 Weight Revision Publication(T,A) AdvisedBy(A,B) Publication(T,B) M-TAMAR Movie(T,A) WorkedFor(A,B) Movie(T,B) Target (IMDB) Data R-TAMAR Movie(T,A) WorkedFor(A,B) Relative(A,B) Movie(T,B) MLN Weight Training 0.8 Movie(T,A) WorkedFor(A,B) Relative(A,B) Movie(T,B)
45 Experiments: Domains UW-CSE Data about members of the UW CSE department Predicates include Professor, Student, AdvisedBy, TaughtBy, Publication, etc. IMDB Data about 20 movies Predicates include Actor, Director, Movie, WorkedFor, Genre, etc. WebKB Entity relations from the original WebKB domain (Craven et al. 1998) Predicates include Faculty, Student, Project, CourseTA, etc. 46
Dataset Statistics Data is organized as mega-examples Each mega-example contains information about a group of related entities. Mega-examples are independent and disconnected from each other. Data Set # MegaExamples # Constants # Types # # True Predicates Gliterals
2,065 688,193 47 Manually Developed Source KB UW-KB is a hand-built knowledge base (set of clauses) for the UW-CSE domain. When used as a source domain, transfer learning is a form of theory refinement that also includes mapping to a new domain with a different representation. 48 Systems Compared TAMAR: Complete transfer system. ScrKD: Algorithm of Kok & Domingos (2005) learning from scratch.
TrKD: Algorithm of Kok & Domingos (2005) performing transfer, using M-TAMAR to produce a mapping. 49 Methodology: Training & Testing Generated learning curves using leave-one-out CV Each run keeps one mega-example for testing and trains on the remaining ones, provided one by one. Curves are averages over all runs. Evaluated learned MLN by performing inference for all gliterals of each predicate in turn, providing the rest as evidence, and averaging the results. 50 Methodology: Metrics Kok & Domingos (2005)
CLL: Conditional Log Likelihood The log of the probability predicted by the model that a gliteral has the correct truth value given in the data. Averaged over all test gliterals. AUC: Area under the precision recall (PR) curve Produce a PR curve by varying the probability threshold. Compute the area under this curve. 51 Metrics to Summarize Curves Transfer Ratio (Cohen et al. 2007) Gives overall idea of improvement achieved over learning from scratch 52
Transfer Scenarios Source/target pairs tested: WebKB IMDB UW-CSE IMDB UW-KB IMDB WebKB UW-CSE IMDB UW-CSE WebKB not used as a target since one mega-example is sufficient to learn an accurate theory for its limited predicate set. 53 Negative Transfer
TransferPositive Ratio Transfer AUC Transfer Ratio 2 1.8 1.6 1.4 1.2 TrKD TAMAR 1 0.8 0.6 0.4 0.2 0 WebKB to IMDB
UW-CSE to IMDB UW-KB to IMDB Experiment WebKB to UW-CSE IMDB to UW-CSE 54 NegativeTransfer Transfer Ratio Positive Transfer CLL Transfer Ratio 1.8 1.6 1.4
1.2 1 TrKD TAMAR 0.8 0.6 0.4 0.2 0 WebKB to IMDB UW-CSE to IMDB UW-KB to IMDB WebKB to UW-CSE Experiments
IMDB to UW-CSE 55 Sample Learning Curve ScrKD TrKD, Hand Mapping TAMAR, Hand Mapping TrKD TAMAR 56 Total Training Time in Minutes 1200.00 1000.00 Minutes
800.00 TrKD TAMAR Scr KD 600.00 Number of seconds to find best mapping: 400.00 0.89 9.10 9.99 6.75
42.3 200.00 0.00 WebKB to IMDB UW-CSE to IMDB UW-KB to IMDB Experiment WebKB to UW-CSE IMDB to UW-CSE 57
Future Research Issues More realistic application domains. Application to other SRL models (e.g. SLPs, BLPs). More flexible predicate mapping Allow argument ordering or arity to change. Map 1 predicate to conjunction of > 1 predicates AdvisedBy(X,Y) Movie(M,X) Director(M,Y) 58 Multiple Source Transfer Transfer from multiple source problems to a given target problem. Determine which clauses to map and revise from different source MLNs. 59 Source Selection
Select useful source domains from a large number of previously learned tasks. Ideally, picking source domain(s) is sublinear in the number of previously learned tasks. 60 Conclusions Presented TAMAR, a complete transfer system for SRL that: Maps relational knowledge in the source to the target domain. Revises the mapped knowledge to further improve accuracy. Showed experimentally that TAMAR improves speed and accuracy over existing methods. 61
Questions? Related papers at: http://www.cs.utexas.edu/users/ml/publication/transfer.html 62 Why MLNs? Inherit the expressivity of first-order logic Can apply insights from ILP Inherit the flexibility of probabilistic graphical models Can deal with noisy & uncertain environments Undirected models Do not need to learn causal directions Subsume all other SRL models that are special cases of first-order logic or probabilistic graphical models [Richardson 04] Publicly available software package: Alchemy
63 Predicate Mapping Comments A particular source predicate can be mapped to different target predicates in different clauses. This makes our approach context sensitive. More scalable. In the worst-case, the number of mappings is exponential in the number of predicates. The number of predicates in a clause is generally much smaller than the total number of predicates in a domain. 64 Relationship to Structure Mapping Engine (Falkenheiner et al., 1989) A system for mapping relations using analogy based on a psychological theory.
Mappings are evaluated based only on the structural relational similarity between the two domains. Does not consider the accuracy of mapped knowledge in the target when determining the preferred mapping. Determines a single global mapping for a given source & target. 65 Summary of Methodology 1. Learn MLNs for each point on learning curve 2. Perform inference over learned models 3. Summarize inference results using 2 metrics: CLL and AUC, thus producing two learning curves 4. Summarize each learning curve using transfer ratio and percentage improvement from one mega-example
66 CLL Percent Improvement Percent Improvement from 1 Example 80 70 60 50 TrKD TAMAR 40 30
20 10 0 WebKB to IMDB UW-CSE to IMDB UW-KB to IMDB WebKB to UW-CSE Experiment IMDB to UW-CSE 67 AUC Percent Improvement
Percent Improvement from 1 Example 60 50 40 30 TrKD TAMAR 20 10 0 WebKB to IMDB UW-CSE to IMDB
UW-KB to IMDB WebKB to UW-CSE IMDB to UW-CSE -10 Experiment 68
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