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# In this tutorial, we compare the prediction intervals estimated by MAPIE on a
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# simple, one-dimensional, ground truth function
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# :math:`f(x) = x \times \sin(x)`.
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# Throughout this tutorial, we will answer the following questions:
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# - How well do the MAPIE strategies capture the aleatoric uncertainty
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# existing in the data?
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# - How do the prediction intervals estimated by the resampling strategies
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# evolve for new *out-of-distribution* data ?
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# - How do the prediction intervals vary between regressor models ?
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# Throughout this tutorial, we estimate the prediction intervals first using
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# a polynomial function, and then using a boosting model, and a simple neural
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# network.
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# **For practical problems, we advise using the faster CV+ or
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# Jackknife+-after-Bootstrap strategies.
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# For conservative prediction interval estimates, you can alternatively
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