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From Feature Construction, to Simple but Effective Modeling, to Domain Transfer Wei Fan IBM T.J.Watson www.cs.columbia.edu/~wfan www.weifan.info weifan@us.ibm.comweifan@us.ibm.com, wei.fan@gmail.com

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Feature Vector Most data mining and machine learning model assume the following structured data: (x 1, x 2,..., x k ) -> y where xis are independent variable y is dependent variable. y drawn from discrete set: classification y drawn from continuous variable: regression

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Frequent Pattern-Based Feature Construction Data not in the pre-defined feature vectors Transactions Biological sequence Graph database Frequent pattern is a good candidate for discriminative features So, how to mine them?

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FP: Sub-graph A discovered pattern NSC 4960 NSC 191370 NSC 40773 NSC 164863 NSC 699181 (example borrowed from George Karypis presentation)

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Computational Issues Measured by its frequency or support. E.g. frequent subgraphs with sup 10% Cannot enumerate sup = 10% without first enumerating all patterns > 10%. Random sampling not work since it is not exhaustive. NP hard problem

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1. Mine frequent patterns (>sup) Frequent Patterns 1---------------------- ---------2----------3 ----- 4 --- 5 -------- --- 6 ------- 7------ DataSet mine Mined Discriminative Patterns 1 2 4 select 2. Select most discriminative patterns; 3. Represent data in the feature space using such patterns; 4. Build classification models. F1 F2 F4 Data1 1 1 0 Data2 1 0 1 Data3 1 1 0 Data4 0 0 1 ……… represent | Petal.Width< 1.75 setosa versicolor virginica Petal.Length< 2.45 Any classifiers you can name NN DT SVM LR Conventional Procedure Feature Construction followed by Selection Two-Step Batch Method

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Two Problems Mine step combinatorial explosion Frequent Patterns 1---------------------- ---------2----------3 ----- 4 --- 5 -------- --- 6 ------- 7------ DataSe t mine 1. exponential explosion 2. patterns not considered if minsupport isnt small enough

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Two Problems Select step Issue of discriminative power Frequent Patterns 1---------------------- ---------2----------3 ----- 4 --- 5 -------- --- 6 ------- 7------ Mined Discriminative Patterns 1 2 4 select 3. InfoGain against the complete dataset, NOT on subset of examples 4. Correlation not directly evaluated on their joint predictability

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Direct Mining & Selection via Model- based Search Tree Basic Flow Mined Discriminative Patterns Compact set of highly discriminative patterns 1 2 3 4 5 6 7. Divide-and-Conquer Based Frequent Pattern Mining 2 Mine & Select P: 20% Y 3 Y 6 Y + Y Y 4 N Few Data N N + N 5 N Mine & Select P:20% 7 N … … Y dataset 1 Mine & Select P: 20% Most discriminative F based on IG Feature Miner Classifier Global Support: 10*20%/10000 =0.02%

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Analyses (I) 1. Scalability of pattern enumeration Upper bound (Theorem 1): Scale down ratio: 2. Bound on number of returned features

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Analyses (II) 3. Subspace pattern selection Original set: Subset: 4. Non-overfitting 5. Optimality under exhaustive search

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Experimental Studies: Itemset Mining (I) Scalability Comparison Datasets#Pat using MbT sup Ratio (MbT #Pat / #Pat using MbT sup) Adult2528090.41% Chess + ~0% Hypo4234390.0035% Sick48183910.00032% Sonar955070.00775% 2 Mine & Select P: 20% Y 3 Y + Y Y Few Data N + N dataset 1 Mine & Select P: 20% Most discriminative F based on IG Global Support: 10*20%/10000 =0.02% 6 Y 5 N Mine & Select P:20% 7 N 4 N 2 Y 3 Y + Y Y Few Data N + N dataset 1 Mine & Select P: 20% Most discriminative F based on IG Global Support: 10*20%/10000 =0.02% 6 Y 5 N Mine & Select P:20% 7 N 4 N

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Experimental Studies: Itemset Mining (II) Accuracy of Mined Itemsets 4 Wins 1 loss But, much smaller number of patterns

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Experimental Studies: Itemset Mining (III) Convergence

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Experimental Studies: Graph Mining (I) 9 NCI anti-cancer screen datasets The PubChem Project. URL: pubchem.ncbi.nlm.nih.gov. Active (Positive) class : around 1% - 8.3% 2 AIDS anti-viral screen datasets URL: http://dtp.nci.nih.gov. H1: CM+CA – 3.5% H2: CA – 1%

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Experimental Studies: Graph Mining (II) Scalability 2 Mine & Select P: 20% Y 3 Y + Y Y Few Data N + N dataset 1 Mine & Select P: 20% Most discriminative F based on IG Global Support: 10*20%/10000 =0.02% 6 Y 5 N Mine & Select P:20% 7 N 4 N 2 Y 3 Y + Y Y Few Data N + N dataset 1 Mine & Select P: 20% Most discriminative F based on IG Global Support: 10*20%/10000 =0.02% 6 Y 5 N Mine & Select P:20% 7 N 4 N

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Experimental Studies: Graph Mining (III) AUC and Accuracy AUC 11 Wins 10 Wins 1 Loss

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AUC of MbT, DT MbT VS Benchmarks Experimental Studies: Graph Mining (IV) 7 Wins, 4 losses

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Summary Model-based Search Tree Integrated feature mining and construction. Dynamic support Can mine extremely small support patterns Both a feature construction and a classifier Not limited to one type of frequent pattern: plug-play Experiment Results Itemset Mining Graph Mining New: Found a DNA sequence not previously reported but can be explained in biology. Code and dataset available for download

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Even the true distribution is unknown, still assume that the data is generated by some known function. Estimate parameters inside the function via training data CV on the training data Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Some unknown distribution How to train models? There probably will always be mistakes unless: 1.The chosen model indeed generates the distribution 2.Data is sufficient to estimate those parameters But how about, you dont know which to choose or use the wrong one? List of methods: Logistic Regression Probit models Naïve Bayes Kernel Methods Linear Regression RBF Mixture models After structure is prefixed, learning becomes optimization to minimize errors: quadratic loss exponential loss slack variables

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How to train models II Not quite sure the exact function, but use a family of free-form functions given some preference criteria. There probably will always be mistakes unless: the training data is sufficiently large. free form function/criteria is appropriate. List of methods: Decision Trees RIPPER rule learner CBA: association rule clustering-based methods … … Preference criteria Simplest hypothesis that fits the data is the best. Heuristics: info gain, gini index, Kearns-Mansour, etc pruning: MDL pruning, reduced error-pruning, cost-based pruning. Truth: none of purity check functions guarantee accuracy on unseen test data, it only tries to build a smaller model

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Can Data Speak for Themselves? Make no assumption about the true model, neither parametric form nor free form. Encode the data in some rather neutral representations: Think of it like encoding numbers in computers binary representation. Always cannot represent some numbers, but overall accurate enough. Main challenge: Avoid rote learning: do not remember all the details Generalization Evenly representing numbers – Evenly encoding the data.

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Potential Advantages If the accuracy is quite good, then Method is quite automatic and easy to use No Brainer – DM can be everybodys tool.

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Encoding Data for Major Problems Classification: Given a set of labeled data items, such as, (amt, merchant category, outstanding balance, date/time, ……,) and the label is whether it is a fraud or non-fraud. Label: set of discrete values classifier: predict if a transaction is a fraud or non-fraud. Probability Estimation: Similar to the above setting: estimate the probability that a transaction is a fraud. Difference: no truth is given, i.e., no true probability Regression: Given a set of valued data items, such as (zipcode, capital gain, education, …), interested value is annual gross income. Target value: continuous values. Several other on-going problems

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Encoding Data in Decision Trees Think of each tree as a way to encode the training data. Why tree? a decision tree records some common characteristic of the data, but not every piece of trivial detail Obviously, each tree encodes the data differently. Subjective criteria that prefers some encodings than others are always adhoc. Do not prefer anything then – just do it randomly Minimizes the difference by multiple encodings, and then average them.

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Random Decision Tree to Encode Data - classification, regression, probability estimation At each node, an un-used feature is chosen randomly A discrete feature is un-used if it has never been chosen previously on a given decision path starting from the root to the current node. A continuous feature can be chosen multiple times on the same decision path, but each time a different threshold value is chosen

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Continued We stop when one of the following happens: A node becomes too small (<= 3 examples). Or the total height of the tree exceeds some limits: Such as the total number of features.

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Illustration of RDT B1: {0,1} B2: {0,1} B3: continuous B2: {0,1} B3: continuous B2: {0,1} B3: continuous B3: continous Random threshold 0.3 Random threshold 0.6 B1 chosen randomly B2 chosen randomly B3 chosen randomly

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Classification | Petal.Width< 1.75 setosa 50/0/0 versicolor 0/49/5 virginica 0/1/45 Petal.Length< 2.45 P( setosa |x,θ) = 0 P( versicolor |x,θ) = 49/54 P( virginica |x,θ) = 5/54

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Regression | Petal.Width< 1.75 setosa Height=10in versicolor Height=15 in virginica Height=12in Petal.Length< 2.45 15 in average value of all examples In this leaf node

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Prediction Simply Averaging over multiple trees

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Potential Advantage Training can be very efficient. Particularly true for very large datasets. No cross-validation based estimation of parameters for some parametric methods. Natural multi-class probability. Natural multi-label classification and probability estimation. Imposes very little about the structures of the model.

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Reasons The true distribution P(y|X) is never known. Is it an elephant? Every random tree is not a random guess of this P(y|X). Their structure is, but not the node statistics Every random tree is consistent with the training data. Each tree is quite strong, not weak. In other words, if the distribution is the same, each random tree itself is a rather decent model.

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Expected Error Reduction Proven that for quadratic loss, such as: for probability estimation: ( P(y|X) – P(y|X, θ) ) 2 regression problems ( y – f(x) ) 2 General theorem: the expected quadratic loss of RDT (and any other model averaging) is less than any combined model chosen at random.

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Theorem Summary

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Number of trees Sampling theory: The random decision tree can be thought as sampling from a large (infinite when continuous features exist) population of trees. Unless the data is highly skewed, 30 to 50 gives pretty good estimate with reasonably small variance. In most cases, 10 are usually enough.

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Variance Reduction

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Optimal Decision Boundary from Tony Lius thesis (supervised by Kai Ming Ting)

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RDT looks like the optimal boundary

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Regression Decision Boundary (GUIDE) Properties Broken and Discontinuous Some points are far from truth Some wrong ups and downs

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RDT Computed Function Properties Smooth and Continuous Close to true function All ups and downs caught

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Hidden Variable

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Limitation of GUIDE Need to decide grouping variables and independent variables. A non-trivial task. If all variables are categorical, GUIDE becomes a single CART regression tree. Strong assumption and greedy-based search. Sometimes, can lead to very unexpected results.

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It grows like …

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ICDM08 Cup Crown Winner Nuclear ban monitoring RDT based approach is the highest award winner.

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Ozone Level Prediction (ICDM06 Best Application Paper) Daily summary maps of two datasets from Texas Commission on Environmental Quality (TCEQ)

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SVM: 1-hr criteria CV

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AdaBoost: 1-hr criteria CV

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SVM: 8-hr criteria CV

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AdaBoost: 8-hr criteria CV

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Other Applications Credit Card Fraud Detection Late and Default Payment Prediction Intrusion Detection Semi Conductor Process Control Trading anomaly detection

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Conclusion Imposing a particular form of model may not be a good idea to train highly-accurate models for general purpose of DM. It may not even be efficient for some forms of models. RDT has been show to solve all three major problems in data mining, classification, probability estimation and regressions, simply, efficiently and accurately. When physical truth is unknown, RDT is highly recommended Code and dataset is available for download.

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Standard Supervised Learning New York Times training (labeled) test (unlabeled) Classifier 85.5% New York Times

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In Reality…… New York Times training (labeled) test (unlabeled) Classifier 64.1% New York Times Labeled data not available! Reuters

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Domain Difference Performance Drop traintest NYT New York Times Classifier 85.5% Reuters NYT ReutersNew York Times Classifier 64.1% ideal setting realistic setting

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A Synthetic Example Training (have conflicting concepts) Test Partially overlapping

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Goal Source Domain Target Domain Source Domain Source Domain To unify knowledge that are consistent with the test domain from multiple source domains (models)

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Summary Transfer from one or multiple source domains Target domain has no labeled examples Do not need to re-train Rely on base models trained from each domain The base models are not necessarily developed for transfer learning applications

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Locally Weighted Ensemble M1M1 M2M2 MkMk …… Training set 1 Test example x Training set 2 Training set k …… x-feature value y-class label Training set

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Modified Bayesian Model Averaging M1M1 M2M2 MkMk …… Test set Bayesian Model Averaging M1M1 M2M2 MkMk …… Test set Modified for Transfer Learning

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Global versus Local Weights 2.40 5.23 -2.69 0.55 -3.97 -3.62 2.08 -3.73 5.08 2.15 1.43 4.48 …… xy 100001…100001… M1M1 0.6 0.4 0.2 0.1 0.6 1 … M2M2 0.9 0.6 0.4 0.1 0.3 0.2 … wgwg 0.3 … wlwl 0.2 0.6 0.7 0.5 0.3 1 … wgwg 0.7 … wlwl 0.8 0.4 0.3 0.5 0.7 0 … Locally weighting scheme Weight of each model is computed per example Weights are determined according to models performance on the test set, not training set Training

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Synthetic Example Revisited Training (have conflicting concepts) Test Partially overlapping M1M1 M2M2 M1M1 M2M2

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Optimal Local Weights C1C1 C2C2 Test example x 0.9 0.1 0.4 0.6 0.8 0.2 Higher Weight Optimal weights Solution to a regression problem 0.9 0.4 0.1 0.6 w1w1 w2w2 = 0.8 0.2 H wf

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Approximate Optimal Weights How to approximate the optimal weights M should be assigned a higher weight at x if P(y|M,x) is closer to the true P(y|x) Have some labeled examples in the target domain Use these examples to compute weights None of the examples in the target domain are labeled Need to make some assumptions about the relationship between feature values and class labels Optimal weights Impossible to get since f is unknown!

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Clustering-Manifold Assumption Test examples that are closer in feature space are more likely to share the same class label.

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Graph-based Heuristics Graph-based weights approximation Map the structures of models onto test domain Clustering Structure M1M1 M2M2 weight on x

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Graph-based Heuristics Local weights calculation Weight of a model is proportional to the similarity between its neighborhood graph and the clustering structure around x. Higher Weight

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Local Structure Based Adjustment Why adjustment is needed? It is possible that no models structures are similar to the clustering structure at x Simply means that the training information are conflicting with the true target distribution at x Clustering Structure M1M1 M2M2 Error

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Local Structure Based Adjustment How to adjust? Check if is below a threshold Ignore the training information and propagate the labels of neighbors in the test set to x Clustering Structure M1M1 M2M2

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Verify the Assumption Need to check the validity of this assumption Still, P(y|x) is unknown How to choose the appropriate clustering algorithm Findings from real data sets This property is usually determined by the nature of the task Positive cases: Document categorization Negative cases: Sentiment classification Could validate this assumption on the training set

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Algorithm Check Assumption Neighborhood Graph Construction Model Weight Computation Weight Adjustment

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Data Sets Different applications Synthetic data sets Spam filtering: public email collection personal inboxes (u01, u02, u03) (ECML/PKDD 2006) Text classification: same top-level classification problems with different sub-fields in the training and test sets (Newsgroup, Reuters) Intrusion detection data: different types of intrusions in training and test sets.

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Baseline Methods One source domain: single models Winnow (WNN), Logistic Regression (LR), Support Vector Machine (SVM) Transductive SVM (TSVM) Multiple source domains: SVM on each of the domains TSVM on each of the domains Merge all source domains into one: ALL SVM, TSVM Simple averaging ensemble: SMA Locally weighted ensemble without local structure based adjustment: pLWE Locally weighted ensemble: LWE Implementation Package: Classification: SNoW, BBR, LibSVM, SVMlight Clustering: CLUTO package

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Performance Measure Prediction Accuracy 0-1 loss: accuracy Squared loss: mean squared error Area Under ROC Curve (AUC) Tradeoff between true positive rate and false positive rate Should be 1 ideally

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A Synthetic Example Training (have conflicting concepts) Test Partially overlapping

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Experiments on Synthetic Data

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Spam Filtering Problems Training set: public emails Test set: personal emails from three users: U00, U01, U02 pLWE LR SVM SMA TSVM WNN LWE pLWE LR SVM SMA TSVM WNN LWE Accuracy MSE

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20 Newsgroup C vs S R vs T R vs S C vs T C vs R S vs T

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pLWE LR SVM SMA TSVM WNN LWE Acc pLWE LR SVM SMA TSVM WNN LWE MSE

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Reuters pLWE LR SVM SMA TSVM WNN LWE pLWE LR SVM SMA TSVM WNN LWE Accuracy MSE Problems Orgs vs People (O vs Pe) Orgs vs Places (O vs Pl) People vs Places (Pe vs Pl)

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Intrusion Detection Problems (Normal vs Intrusions) Normal vs R2L (1) Normal vs Probing (2) Normal vs DOS (3) Tasks 2 + 1 -> 3 (DOS) 3 + 1 -> 2 (Probing) 3 + 2 -> 1 (R2L)

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Conclusions Locally weighted ensemble framework transfer useful knowledge from multiple source domains Graph-based heuristics to compute weights Make the framework practical and effective Code and Dataset available for download

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More information www.weifan.info or www.weifan.info www.cs.columbia.edu/~wfan For code, dataset and papers

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