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Inductive Learning in Less Than One Sequential Data Scan Wei Fan, Haixun Wang, and Philip S. Yu IBM T.J.Watson Shaw-hwa Lo Columbia University

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Problems Many inductive algorithms are main memory-based. When the dataset is bigger than the memory, it will "thrash". Very low in efficiency when thrashing happens. For algorithms that are not memory-based, Do we need to see every piece of data? Probably not. Overfitting curve? Not practical.

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Basic Idea:One Scan Algorithm Batch 4 Batch 3 Batch 2 Batch 1 Algorithm Model

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Loss and Benefit Loss function: Evaluate performance. Benefit matrix – inverse of loss func Traditional 0-1 loss b[x,x] = 1, b[x,y] = 0 Cost-sensitive loss Overhead of $90 to investigate a fraud. b[fraud, fraud] = $tranamt - $90. b[fraud, nonfraud] = $0. b[nonfraud, fraud] = -$90. b[nonfraud, nonfraud] = $0.

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Probabilistic Modeling is the probability that x is an instance of class is the expected benefit Optimal decision

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Example p(fraud|x) = 0.5 and tranamt = $200 e(fraud|x) = b[fraud,fraud]p(fraud|x) + b[nonfraud, fraud] p(nonfraud|x) =(200 – 90) x (-90) x 0.5 = $10 E(nonfraud|x) = b[fraud,nonfraud]p(fraud|x) + b[nonfraud,nonfraud]p(nonfraud|x) = 0 x x 0.5 = always 0 Predict fraud since we get $10 back.

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Combining Multiple Models Individual benefits Averaged benefits Optimal decision

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How about accuracy

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Do we need all K models? We stop learning if k (< K) models have the same accuracy as K models with confidence p. Ends up scanning the dataset less than 1. Use statistical sampling.

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Less than one scan Batch 4 Batch 3 Batch 2 Batch 1 Algorithm Accurate Enough? Model No Yes

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Hoeffding s inequality Random variable within R=a-b After n observations, its mean value is y. What is its error with confidence p regardless of the distribution?

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When can we stop? Use k models highest expected benefit Hoeffding s error: second highedt expected benefit Hoeffding s error: The majority label is still with confidence p iff

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Less Than One Scan Algorithm Iterate the process on every instance from a validation set. Until every instance has the same prediction as the full ensemble with confidence p.

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Validation Set If we fail on one example x, we do not need to examine on another one. So we can keep only one example in memory at a time. If k base models s prediction on x is the same as K models. It is very likely that k+1 models will also be the same as K models with the same confidence.

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Validation Set At anytime, we only need to keep one data item x from the validation set. It is sequentially read from the validation set. The validation set is read only once. What can be a validation set? The training set itself A separate holdout set.

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Amount of Data Scan Training Set : at most one Validation Set: once. Using training as validation set: Once we decide to train model from a batch, we do not use it for validation again. How much is used to train model? Less than one.

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Experiments Donation Dataset: Total benefits: donated charity minus overhead to send solicitations.

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Experiment Setup Inductive learners: C4.5 RIPPER NB Number of base models: {8,16,32,64,128,256} Reports their average

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Baseline Results (with C4.5) Single model: $ Complete One Scan: $ The average of {8,16,32,64,128,256} We are actually $1410 higher than the single model.

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Less-than-one scan (with C4.5) Full one scan: $14702 Less-than-one scan: $14828 Actually a little higher, $126. How much data scanned with 99.7% confidence? 71%

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Other datasets Credit card fraud detection Total benefits: Recovered fraud amount minus overhead of investigation

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Results Baseline single: $ (with curtailed probability) One scan ensemble: $ Less than one scan: $ Data scan amount: 64%

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Smoothing effect.

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Related Work Ensenbles: Meta-learning (Chan and Stolfo): 2 scans Bagging (Breiman) and AdaBoost (Freund and Schapire): multiple Use of Hoeffding s inequality: Aggregate query (Hellerstein et al) Streaming decision tree (Hulten and Domingos) Single decision tree, less than one scan Scalable decision tree: SPRINT (Shafer et al): multiple scans BOAT (Gehrke et al): 2 scans

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Conclusion Both one scan and less than one scan have accuracy either similar or higher than the single model. Less than one scan uses approximately 60% – 90% of data for training with loss of accuracy.

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