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https://issues.apache.org/jira/browse/SPARK-22451?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16241634#comment-16241634
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Weichen Xu commented on SPARK-22451:
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[~josephkb] I think it can be reconstructed from a summary with only
O(numCategories) values, let me give an simple example to explain how it works
(but if I am wrong correct me):
Suppose an unordered features containing values [a, b, c, d, e, f], we first
get separate statistics for stat[a], stat[b], stat[c], stat[d], stat[e], stat[f]
then, if we want to get stats for split [a, c, d], we can compute it by stat[a]
+ stat[c] + stat[d].
[~Siddharth Murching] can also help to confirm the correctness of this.
> Reduce decision tree aggregate size for unordered features from
> O(2^numCategories) to O(numCategories)
> ------------------------------------------------------------------------------------------------------
>
> Key: SPARK-22451
> URL: https://issues.apache.org/jira/browse/SPARK-22451
> Project: Spark
> Issue Type: Improvement
> Components: ML
> Affects Versions: 2.2.0
> Reporter: Weichen Xu
> Original Estimate: 24h
> Remaining Estimate: 24h
>
> Do not need generate all possible splits for unordered features before
> aggregate,
> in aggregete (executor side):
> 1. Change `mixedBinSeqOp`, for each unordered feature, we do the same stat
> with ordered features. so for unordered features, we only need
> O(numCategories) space for this feature stat.
> 2. After driver side get the aggregate result, generate all possible split
> combinations, and compute the best split.
> This will reduce decision tree aggregate size for each unordered feature from
> O(2^numCategories) to O(numCategories), `numCategories` is the arity of this
> unordered feature.
> This also reduce the cpu cost in executor side. Reduce time complexity for
> this unordered feature from O(numPoints * 2^numCategories) to O(numPoints).
> This won't increase time complexity for unordered features best split
> computing in driver side.
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