A Framework for Scalable Cost-A Framework for Scalable Cost-sensitive Learning Based on sensitive Learning Based on Combining Probabilities and Combining Probabilities and BenefitsBenefits

Wei Fan, Haixun Wang, and Philip S. YuWei Fan, Haixun Wang, and Philip S. YuIBM T.J.WatsonIBM T.J.Watson

Salvatore J. StolfoSalvatore J. StolfoColumbia UniversityColumbia University

Scalable Issues of Data MiningScalable Issues of Data Mining

ƒ Two folds: the data and the algorithm.ƒ Dataset:

too big to fit into memory.inherently distributed across the network.incremental data available periodically.

Scalable Issues of Data Mining Scalable Issues of Data Mining

ƒ Learning algorithm:non-linear complexity in the size of dataset n. memory based due to random access pattern of record in dataset.significantly slower if dataset is not held entirely in memory.

ƒ State-of-the-artmany scalable solutions are algorithm specific.

decision trees: SPRINT, RainForest and BOATgeneral algorithms are not very scalable and only work for cost-insensitive problemsmeta-learning

ƒ Question: general and work for both cost-sensitive and cost-insentive problems.

Cost-sensitive ProblemsCost-sensitive Problems

ƒ Charity Donation:Solicit to people who will donate large amount of charity.Costs $0.68 to send a letter.E(x): expected donation amount.Only solicit if E(x) > 0.68, otherwise lose money.

ƒ Credit card fraud detection:Detect frauds with high transaction amount

$90 to challenge a potential fraudE(x): expected fraudulant transaction amount.Only challenge if E(x) > $90, otherwise lose money.

ƒ Question: how to estimate E(x) efficiently?

Basic FrameworkBasic Framework

D

D1 D2D2

large dataset

partition into

k subsets

ML1ML2 MLt

C1 C2Ck

generate

k models

Basic FrameworkBasic Framework

DTest Set

C1 C2 Ck

Sent to k models

P1 P2 PkCompute k predictions

Combine

P

Combine to one prediction

Cost-sensitive Decision MakingCost-sensitive Decision Making

ƒ Assume that records the benefit received by predicting an example of class to be an instance of class .

ƒ The expected benefit received to predict an example to be an instance of class (regardless of its true label) is

ƒ The optimal decision-making policy chooses the label that maximizes the expected benefit, i.e.,

ƒ When and is a

traditional accuracy-based problem.ƒ Total benefits

Charity Donation ExampleCharity Donation Example

ƒ It costs $.68 to send a solicitation.ƒ Assume that is the best

estimate of the donation amount,

ƒ The cost-sensitive decision making will solicit an individual if and only if

Credit Card Fraud Detection Credit Card Fraud Detection ExampleExample

ƒ It costs $90 to challenge a potential fraud

ƒ Assume that y(x) is the transaction amount

ƒ The cost-sensitive decision making policy will predict a transaction to be fraudulent if and only if

Adult DatasetAdult Dataset

ƒ Downloaded from UCI database.ƒ Associate a benefit factor 2 to positives

and a benefit factor 1 to negatives

ƒ The decision to predict positive is

Calculating probabilitiesCalculating probabilities

For decision trees, is the number of examples in a node and is the number of examples with class label , then the probability is more sophisticated methods

smoothing:early stopping, and early stopping plus smoothing

For rules, probability is calucated in the same way as decision trees

For naive Bayes, is the score for

class label , then

binning

Combining Technique-Combining Technique-AveragingAveraging

ƒ Each model computes an expected benefit for example over every class label

ƒ Combining individual expected benefit together

ƒ We choose the label with the highest combined expected benefit

1. Decision threshold line2. Examples on the left are more profitable than those on the right3. "Evening effect": biases towards big fish.

Why accuracy is higher?Why accuracy is higher?

More sophisticated combining More sophisticated combining approachesapproaches

ƒ Regression:Treat base classifiers' outputs as indepedent variables of regression and the true label as dependent variables.

ƒ Modify Meta-learning:Learning a classifier that maps the base classifiers' class label predictions to that the true class label.For cost-sensitive learning, the top level classifier output probability instead of just a label.

ExperimentsExperiments

ƒ Learner: C4.5 version 8ƒ Dataset:

Donation (KDD98)Credit CardAdult

ƒ Number of partitions: 8,16,32,64,128,and 256

Accuracy comparisionAccuracy comparision

Accuracy comparisonAccuracy comparison

Accuracy comparisonAccuracy comparison

Detailed SpreadDetailed Spread

Credit Card Fraud DatasetCredit Card Fraud Dataset

Adult DatasetAdult Dataset

Why accuracy is higher?Why accuracy is higher?

Scalability Analysis of Scalability Analysis of Averaging MethodAveraging Method

ƒ Baseline: a single model that is computed from the entire dataset as a whole.

ƒ Our approach: ensemble of multiple models, each of which is computed from disjoint datasets.

Scalability AnalysisScalability Analysis

ƒ Serial Improvment

ƒ Parallel Improvment

ƒ Speedup

ƒ Scaled Speedup

Scalability Results - Serial Scalability Results - Serial ImprovementImprovement

Scalability Results - Parallel Scalability Results - Parallel ImprovementImprovement

Scalability Results - SpeedupScalability Results - Speedup

D1 D2D2k sites

ML1ML2 MLt

C1 C2Ck

generate

k models

Fully distributed learning Fully distributed learning frameworkframework

Communication overheadCommunication overhead

Overhead analysisOverhead analysis

Summary and Future WorkSummary and Future Work

ƒ Evaluated a wide range of combining techniques include variations of averaging, regression and meta-learning for scalable cost-sensitive (and cost-insensitive learning).

ƒ Averaging, although simple, has the highest accuracy.

ƒ Previously proposed approaches have significantly more overhead and only work well for tradtional accuracy-based problems.

ƒ Future work: ensemble pruning and performance estimation

ƒ Suppose that is the probability that is an instance of class label .

ƒ An inductive model will always predict the label with the highest probability, i.e.,

ƒ The accuracy of a method on dataset is

Accuracy-based Problems (0-1 Accuracy-based Problems (0-1 loss)loss)