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DOC add ficticious example about network connections
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doc/modules/model_evaluation.rst

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@@ -97,6 +97,24 @@ R² gives the same ranking as squared loss.
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Furthermore, the Brier score is just a different name for the squared error
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in case of classification.
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**Ficticious Example:**
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Let's make the above arguments more tangible. Consider a setting of reliability
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engineering of network connections, e.g. internet or wifi. As provider of the network,
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you have access to the dataset of log entries of network connection containing network
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load over time and many interesting features. Your goal is to improve the raliability
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of the connections. In fact, you promise your customors that at least on 99% of all
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days there are no connection discontinuities larger 1 minute.
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Therefore, you are interested in a prediction of the 99% quantile (of connections per
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day free of interruptions larger than 1 minute) in order to know in advance when to add
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more bandwidth and thereby satisfy your customers. So the *target functional* is the
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99% quantile. From the table above, you choose the pinball loss as scoring function
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(fair enough, not much choice given), for model training (e.g.
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`HistGradientBoostingRegressor(loss="quantile", quantile=0.99)` as well as model
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evaluation (`mean_pinball_loss(..., alpha=0.9)` - we apoligize for the different
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argument names, `quantile` and `alpha`) be it in grid search for finding
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hyperparameters or in comparing to other models like
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`QuantileRegressor(quantile=0.99)`.
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.. topic:: References:
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.. [Gneiting2007] T. Gneiting and A. E. Raftery. :doi:`Strictly Proper

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