On Appropriate Assumptions to Mine Data Streams: Analyses and Solutions Jing Gao† Wei Fan‡ Jiawei Han† †University of Illinois at Urbana-Champaign ‡IBM T. J. Watson Research Center

Introduction (1) Data Stream –Continuously arriving data flow –Applications: network traffic, credit card transaction flow, phone calling records, etc

Introduction (2) Stream Classification –Construct a classification model based on past records –Use the model to predict labels for new data –Help decision making Fraud? Fraud Classification model Labeling

Framework ……… ? Classification Model Predict

Existing Stream Mining Methods How to use old examples? –Throw away or fade out old examples –Select old examples or models which match the current concepts How to update the model? –Real Time Update –Batch Update Match the training distribution!

Existing Stream Mining Methods Shared distribution assumption –Training and test data are from the same distribution P(x,y) x-feature vector, y-class label –Validity of existing work relies on the shared distribution assumption Difference from traditional learning –Both distributions evolve ……… training ……… test ……… ……

Appropriateness of Shared Distribution An example of stream data –KDDCUP’99 Intrusion Detection Data –P(y) evolves Shift or delay inevitable –The future data could be different from current data –Matching the current distribution to fit the future one is a wrong way –The shared distribution assumption is inappropriate

Appropriateness of Shared Distribution Changes in P(y) –P(y) P(x,y)=P(y|x)P(x) –The change in P(y) is attributed to changes in P(y|x) and P(x) Time Stamp 1 Time Stamp 11 Time Stamp 21

Realistic and relaxed assumption The training and test distributions are similar to the degree that the model trained from the training set D has higher accuracy on the test set T than both random guessing and predicting the same class label. Training set Test set Model Random Guessing Fixed Guessing

Realistic and relaxed assumption Strengths of this assumption –Does not assume any exact relationship between training and test distribution –Simply assume that learning is useful Develop algorithms based on this assumption –Maximize the chance for models to succeed on future data instead of match current data

A Robust and Extensible Stream Mining Framework C1C1 C2C2 CkCk …… Training set Test set Simple Voting(SV)Averaging Probability(AP)

Why ensemble? Ensemble –Reduce variance caused by single models –Is more robust than single models when the distribution is evolving Expected error analysis –Single model: –Ensemble:

Why simple averaging? Combining outputs –Simple averaging: uniform weights w i =1/k –Weighted ensemble: non-uniform weights w i is inversely proportional to the training errors –w i should reflect P(M), the probability of model M after observing the data Uniform weights are the best –P(M) is changing and we could never estimate the true P(M) and when and how it changes –Uniform weights could minimize the expected distance between P(M) and weight vector

An illustration Single models (M1, M2, M3) have huge variance. Simple averaging ensemble (AP) is more stable and accurate. Weighted ensemble (WE) is not as good as AP since training errors and test errors may have different distributions. Average Probability Weighted Ensemble Single Models

Experiments Set up –Data streams with chunks T 1, T 2, …, T N –Use T i as the training set to classify T i+1 Measures –Mean Squared Error, Accuracy –Number of Wins, Number of Loses –Normalized Accuracy, MSE

Experiments Methods –Single models: Decision tree (DT), SVM, Logistic Regression (LR) –Weighted ensemble: weights reflect the accuracy on training set (WE) –Simple ensemble: voting (SV) or probability averaging (AP)

Experimental Results (1) Comparison on Synthetic Data Time 40 Time 100

Experimental Results (2) Comparison on Intrusion Data Set

Experimental Results (3) Classification Accuracy Comparison

Experimental Results (4) Mean Squared Error Comparison

Conclusions Realistic assumption –Take into account the difference between training and test distributions –Overly matching the training distribution is thus unsatisfactory Model averaging –Robust and accurate –Theoretically proved the effectiveness –Could give the best predictions on average

Thanks! Any questions?