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[doc] Fix typo [skip ci] (#8907)

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@ -575,27 +575,26 @@ allocation or have different amount of available resources during different
sessions. There are heuristics and guidelines on how to achieve it but no proven method sessions. There are heuristics and guidelines on how to achieve it but no proven method
for guaranteeing such deterministic behavior. The Dask interface in XGBoost tries to for guaranteeing such deterministic behavior. The Dask interface in XGBoost tries to
provide reproducible result with best effort. This section highlights some known criteria provide reproducible result with best effort. This section highlights some known criteria
and try share some insight into the issue. and try to share some insights into the issue.
There are primarily two different tasks for XGBoost the carry out, training and There are primarily two different tasks for XGBoost the carry out, training and
inference. Inference is reproducible given the same software and hardware along with the inference. Inference is reproducible given the same software and hardware along with the
same run-time configurations like number of threads. The remaining of this section will same run-time configurations. The remaining of this section will focus on training.
focus on training.
Many of the challenges come from the fact that we are using approximation algorithms, The Many of the challenges come from the fact that we are using approximation algorithms, The
sketching algorithm used to find histogram bins is an approximation to the exact quantile sketching algorithm used to find histogram bins is an approximation to the exact quantile
algorithm, the `AUC` metric in a distributed environment is an approximation to the exact algorithm, the `AUC` metric in a distributed environment is an approximation to the exact
`AUC` score, and floating-point number if an approximation to real numbers. Floating point `AUC` score, and floating-point number is an approximation to real number. Floating-point
is an issue as its summation is not associative, meaning :math:`(a + b) + c` does not is an issue as its summation is not associative, meaning :math:`(a + b) + c` does not
necessarily equal to :math:`a + (b + c)`, even though this property holds true for real necessarily equal to :math:`a + (b + c)`, even though this property holds true for real
number. As a result, whenever we change the order of summation, the result can number. As a result, whenever we change the order of a summation, the result can
differ. This imposes the requirement that, in order to have reproducible output from differ. This imposes the requirement that, in order to have reproducible output from
XGBoost, the entire pipeline needs to be reproducible. XGBoost, the entire pipeline needs to be reproducible.
- The software stack is the same for each runs. This goes without saying. XGBoost might - The software stack is the same for each runs. This goes without saying. XGBoost might
generate different outputs between different versions. This is expected as we might generate different outputs between different versions. This is expected as we might
change the default value of hyper-parameter, or the parallel strategy that generates change the default value of hyper-parameter, or the parallel strategy that generates
different floating point result. We guarantee the correctness the algorithms, but there different floating-point result. We guarantee the correctness the algorithms, but there
are lots of wiggle room for the final output. The situation is similar for many are lots of wiggle room for the final output. The situation is similar for many
dependencies, for instance, the random number generator might differ from platform to dependencies, for instance, the random number generator might differ from platform to
platform. platform.
@ -622,10 +621,10 @@ XGBoost, the entire pipeline needs to be reproducible.
- The operations performed on dataframes need to be reproducible. There are some - The operations performed on dataframes need to be reproducible. There are some
operations like `DataFrame.merge` not being deterministic on parallel hardwares like GPU operations like `DataFrame.merge` not being deterministic on parallel hardwares like GPU
where the order of the index of merge result might differ from run to run. where the order of the index might differ from run to run.
It's expected to have different results when training the model on distributed environment It's expected to have different results when training the model in a distributed
than training the model using a single node due to aforementioned criteria. environment than training the model using a single node due to aforementioned criteria.
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