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Labels are expensive to obtain, thus selecting which products to get labels for is key to optimally use any available labeling budget, both when training and evaluating a model. At the same time, if available labels are not correctly used, incorrect or suboptimal results can be produced.

In this talk I will discuss some of the challenges and potential pitfalls of acquiring and using labels for classification in a quickly evolving environment. I will present a system that store labels, provides a way to select labels to optimize budget while providing accurate and unbias evaluations of the classification models.

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- 1. Classiﬁcation Labels in a Fast Moving Environment Classiﬁcation Labels in a Fast Moving Environment Alessandro Magnani @WalmartLabs, Walmart Global eCommerce California, USA Friday 13th November, 2015
- 2. Classiﬁcation Labels in a Fast Moving Environment Classiﬁcation Model Performance Items Classiﬁer Editor N sampled items true label yi estimate ˜yi accuracyEvaluation ◮ correctly evaluating classiﬁcation models is critical and requires labels ◮ labeling products is expensive ◮ need to correctly and optimally use labels
- 3. Classiﬁcation Labels in a Fast Moving Environment Classiﬁcation Model Performance Items Classiﬁer Editor N sampled items true label yi estimate ˜yi accuracyEvaluation Measure accuracy common approach: ◮ sample uniformly at random N items ◮ compute accuracy 1 N N i=1 ½{˜yi =yi }
- 4. Classiﬁcation Labels in a Fast Moving Environment Practical challenges Items Classiﬁer Editor N sampled items true label yi estimate ˜yi accuracyEvaluation ◮ items change over time
- 5. Classiﬁcation Labels in a Fast Moving Environment Practical challenges Items Classiﬁer Editor N sampled items true label yi estimate ˜yi accuracyEvaluation ◮ items change over time ◮ evaluation required over multiple subsets
- 6. Classiﬁcation Labels in a Fast Moving Environment Practical challenges Items Classiﬁer Editor N sampled items true label yi estimate ˜yi accuracyEvaluation ◮ items change over time ◮ evaluation required over multiple subsets ◮ existing labels potentially hard to reuse
- 7. Classiﬁcation Labels in a Fast Moving Environment A motivating example compute accuracy over 1M items 1K labels budget ◮ sample 1K items and get labels yi ◮ measure accuracy 1 1K 1K i=1 ½{˜yi =yi } 1M p 1 1K
- 8. Classiﬁcation Labels in a Fast Moving Environment A motivating example 500K items added, compute accuracy on all 1.5M items ◮ use previous accuracy measure ◮ most likely inaccurate 1M 1.5M p 1 1K
- 9. Classiﬁcation Labels in a Fast Moving Environment A motivating example 500K items added, compute accuracy on all 1.5M items 500 labels extra budget ◮ sample 500 items from the 1.5M ◮ compute accuracy on new 500 labels ◮ previous 1K labels “wasted” 1M 1.5M p 1 3K
- 10. Classiﬁcation Labels in a Fast Moving Environment A motivating example 500K items added, compute accuracy on all 1.5M items 500 labels extra budget, better approach ◮ sample 500 items from new items ◮ compute accuracy on all 1.5K labels ◮ no label “wasted” 1M 1.5M p 1 1K
- 11. Classiﬁcation Labels in a Fast Moving Environment A motivating example 500K items added, compute accuracy on all 1.5M items only 250 labels extra budget? ◮ sample 250 items from new items ◮ need to account for diﬀerence in sampling ◮ accuracy: 1M 1.5M p 1 2K 1 1.5K 1K i=1 ½{˜yi =yi } + 2 250 i=1 ½{˜ynew i =ynew i }
- 12. Classiﬁcation Labels in a Fast Moving Environment A motivating example What are the challenges? ◮ sampling new test labels for every measure is generally expensive
- 13. Classiﬁcation Labels in a Fast Moving Environment A motivating example What are the challenges? ◮ sampling new test labels for every measure is generally expensive ◮ knowing how previous labels were sampled required to optimally sample new items for test
- 14. Classiﬁcation Labels in a Fast Moving Environment A motivating example What are the challenges? ◮ sampling new test labels for every measure is generally expensive ◮ knowing how previous labels were sampled required to optimally sample new items for test ◮ computing accuracy using all labels requires knowledge of sampling proﬁle
- 15. Classiﬁcation Labels in a Fast Moving Environment A motivating example What are the challenges? ◮ sampling new test labels for every measure is generally expensive ◮ knowing how previous labels were sampled required to optimally sample new items for test ◮ computing accuracy using all labels requires knowledge of sampling proﬁle ◮ overtime reusing labels can become very tricky
- 16. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework ◮ pi is probability of item i to be selected for test (Bernoulli) ◮ each item carries pi and is marked if selected (store the sampling proﬁle) ◮ accuracy: 1 i selected 1 pi i selected 1 pi ½{˜yi =yi }
- 17. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework ◮ pi is probability of item i to be selected for test (Bernoulli) ◮ each item carries pi and is marked if selected (store the sampling proﬁle) ◮ accuracy: 1 i selected 1 pi i selected 1 pi ½{˜yi =yi } ◮ for evaluation to be possible pj > 0 for all j labeled/unlabeled
- 18. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework ◮ pi is probability of item i to be selected for test (Bernoulli) ◮ each item carries pi and is marked if selected (store the sampling proﬁle) ◮ accuracy: 1 i selected 1 pi i selected 1 pi ½{˜yi =yi } ◮ for evaluation to be possible pj > 0 for all j labeled/unlabeled ◮ all labels are used
- 19. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework ◮ pi is probability of item i to be selected for test (Bernoulli) ◮ each item carries pi and is marked if selected (store the sampling proﬁle) ◮ accuracy: 1 i selected 1 pi i selected 1 pi ½{˜yi =yi } ◮ for evaluation to be possible pj > 0 for all j labeled/unlabeled ◮ all labels are used ◮ with uniform sampling this is simply “standard” accuracy
- 20. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework ◮ pi is probability of item i to be selected for test (Bernoulli) ◮ each item carries pi and is marked if selected (store the sampling proﬁle) ◮ accuracy: 1 i selected 1 pi i selected 1 pi ½{˜yi =yi } ◮ for evaluation to be possible pj > 0 for all j labeled/unlabeled ◮ all labels are used ◮ with uniform sampling this is simply “standard” accuracy ◮ very closely related to importance sampling
- 21. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework given existing sampling pi and extra budget how do we sample? ◮ minimize accuracy variance with budget constraint ◮ can be formulated as an optimization problem ◮ easy to solve
- 22. Classiﬁcation Labels in a Fast Moving Environment Evaluation framework it works as you’d expect as budget grows: p p ◮ new budget (blue) used more where pi is smaller ◮ given enough budget we obtain uniform sampling
- 23. Classiﬁcation Labels in a Fast Moving Environment Extensions ◮ framework works more generally for supervised learning ◮ framework can work with a wide range of diﬀerent metrics ◮ optimal sampling can use model posterior to reduce variance ◮ this framework can be used on the training side together with active learning

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