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ReverseTesting: An Efficient Framework to Select Amongst Classifiers under Sample Selection Bias Wei Fan IBM T.J.Watson Ian Davidson SUNY Albany

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Where Sample Selection Bias Comes From? Universe of Examples: Joint probability distribution P(x,y) = P(y|x) P(x) DM models this universe Sampling process Training Data Question: Is the training data a good sample of the universe? Algorithm Model x y

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Universe of Examples Two classes: red and green red: f2>f1 green: f2<=f1

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Unbiased & Biased Samples Rather Unbiased Sample: evenly distributed Biased Sample: less likely to sample points close to decision boundary

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Single Decision Tree Error = 2.9% Error = 7.9% Trained from Unbiased SampleTrained from Biased Sample

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Random Decision Tree Error = 3.1%Error = 4.1% Trained from Unbiased SampleTrained from Biased Sample

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What can we observe? Sample Selection Bias does affect modeling. Some techniques are more sensitive to bias than others. Models accuracy do get affected. One important question: How to choose amongst the best classification algorithm, given potentially biased dataset?

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Ubiquitous Problem Fundamental assumption: training data is an unbiased sample from the universe of examples. Catalogue: Purchase history is normally only based on each merchant s own data However, may not be representative of a population that may potentially purchase from the merchant.. Drug Testing: Fraud Detection: Other examples (see Zadrozny 04 and Smith and Elkan 04)

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Effect of Bias on Model Construction Inductive model: P(y|x,M): non-trivial dependency on the constructed model M. Recall that P(y|x) is the true conditional probability independent from any modeling techniques. In general, P(y|x,M) != P(y|x). If the model M is the correct model, sample selection bias doesn t affect learning. (Fan,Davidson,Zadrozny, and Yu 05) Otherwise, it does. Key Issues: for real-world problems, we normally do not know the relationship between P(y|x,M) and P(y|x). No exact idea about where the bias comes from.

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Re-Capping Our focus How to choose amongst the best classification algorithm, given potentially biased dataset? No information on the exactly how the data is biased No information on if the learners are affected by the bias. No information on true model, P(y|x)

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Failure of Traditional Methods Given sample section bias, cross- validation based methods are a bad indicator of which methods are the most accurate. Results come next.

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ReverseTesting Basic idea: how to use testing data s feature vector x s to help ordering different models even when their true labels y are not known.

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Basic Procedure Train A B MA MB Test A B MAA MAB MBA MBB Train Estimate the performance of MA and MB based on the order of MAA, MAB, MBA and MBB DA DB Labeled test data

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Rule If A s labeled test data can construct more accurate models for both algorithm A and B evaluated on labeled training data, then A is expected to be more accurate. If MAA > MAB and MBA > MBB then choose A Similarly, If MAA < MAB and MBA < MBB then choose B Otherwise, undecided.

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Heuristics of ReverseTesting Assume that: A is more accurate than B Use both A and B labeled data to train two models. Using A s data is likely to train a more accurate model than B s data.

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Result Summary

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Why CV won t work? Sparse Region

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CV under-estimate in sparse regions 1. Examples in sparse regions are under represented in CV s averaged results. Comparing those examples near the decision boundary A model performs badly in these under sample regions are not accurately estimated in cross-validation. 2. CV could also create biased folds in these sparse regions. Their estimate on biased region itself could also be unreliable. 3. No information on how a model behaves on feature vectors not represented in the training data.

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Decision Boundary of one fold in 10-fold CV 1-foldFull Training Data

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Desiderata in ReverseTesting Not reduce the size of sparse regions as 10-fold CV does Not use training model or something close to training model. Utilize feature vectors not present in the training dataset.

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C45 Decision Boundary Training Data C45 labeled data RDT Data C45 labeled data RDT labeled data C45 can never learn such a model from training data

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RDT Decision Boundary C45 labeled dataRDT labeled data

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Model Comparison Feature vectors in testing data change the decision boundary. The model constructed by algorithm A from A s own labeled data != original training model. A s inductive bias is represented in B s space. Use the changed boundary to include more emphasis on these sparse regions for both A and B re-trained on the two labeled test datasets.

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Summary Sample Selection bias is a ubiquitous problem for DM and ML in practice. For most applications and modeling, techniques, sample selection bias does affect accuracy. Given sample selection bias, CV based method is bad at estimating order. ReverseTesting can do a much better job. Future work: not only orders but also estimates accuracy.

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