[jira] [Commented] (SPARK-21057) Do not use a PascalDistribution in countApprox

["Sean Owen (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/SPARK-21057?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16046051#comment-16046051 ] 

Sean Owen commented on SPARK-21057:
-----------------------------------

That's not the intended interpretation of the negative binomial. The hypothetical is that you pick elements from the total data set at random, and a fraction p of the time you 'succeed ' in picking from among the elements already counted. The rest of the time you 'fail'. But if this goes on long enough to reach the observed count as the number of successes, then the number of failures models the size of the rest of the data.

Certainly, they both have the same expected value (good). I recall this had something to do with problems for very small counts, but this doesn't appear to be a problem in this code, now. If anything the condition should be a function of r and p. I also can't go back and see a clear theoretical justification. I agree, the Poisson analysis seems fine even for small p and r.

Try the change and see how it affects the tests.

> Do not use a PascalDistribution in countApprox
> ----------------------------------------------
>
>                 Key: SPARK-21057
>                 URL: https://issues.apache.org/jira/browse/SPARK-21057
>             Project: Spark
>          Issue Type: Bug
>          Components: Spark Core
>    Affects Versions: 2.1.1
>            Reporter: Lovasoa
>
> I was reading the source of Spark, and found this:
> https://github.com/apache/spark/blob/v2.1.1/core/src/main/scala/org/apache/spark/partial/CountEvaluator.scala#L50-L72
> This is the function that estimates the probability distribution of the total count of elements in an RDD given the count of only some partitions.
> This function does a strange thing: when the number of elements counted so far is less than 10 000, it models the total count with a negative binomial (Pascal) law, else, it models it with a Poisson law.
> Modeling our number of uncounted elements with a negative binomial law is like saying that we ran over elements, counting only some, and stopping after having counted a given number of elements.
> But this does not model what really happened.  Our counting was limited in time, not in number of counted elements, and we can't count only some of the elements in a partition.
> I propose to use the Poisson distribution in every case, as it can be justified under the hypothesis that the number of elements in each partition is independent and follows a Poisson law.



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