[jira] [Updated] (SPARK-17455) IsotonicRegression takes non-polynomial time for some inputs

["Nic Eggert (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/SPARK-17455?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Nic Eggert updated SPARK-17455:
-------------------------------
    Issue Type: Bug  (was: Improvement)

> IsotonicRegression takes non-polynomial time for some inputs
> ------------------------------------------------------------
>
>                 Key: SPARK-17455
>                 URL: https://issues.apache.org/jira/browse/SPARK-17455
>             Project: Spark
>          Issue Type: Bug
>          Components: MLlib
>    Affects Versions: 1.3.1, 1.4.1, 1.5.2, 1.6.2, 2.0.0
>            Reporter: Nic Eggert
>
> The Pool Adjacent Violators Algorithm (PAVA) implementation that's currently in MLlib can take O(N!) time for certain inputs, when it should have worst-case complexity of O(N^2).
> To reproduce this, I pulled the private method poolAdjacentViolators out of mllib.regression.IsotonicRegression and into a benchmarking harness.
> Given this input
> {code}
> val x = (1 to length).toArray.map(_.toDouble)
> val y = x.reverse.zipWithIndex.map{ case (yi, i) => if (i % 2 == 1) yi - 1.5 else yi}
> val w = Array.fill(length)(1d)
> val input: Array[(Double, Double, Double)] = (y zip x zip w) map{ case ((y, x), w) => (y, x, w)}
> {code}
> I vary the length of the input to get these timings:
> || Input Length || Time (us) ||
> | 100 | 1.35 |
> | 200 | 3.14 | 
> | 400 | 116.10 |
> | 800 | 2134225.90 |
> (tests were performed using https://github.com/sirthias/scala-benchmarking-template)
> I can also confirm that I run into this issue on a real dataset I'm working on when trying to calibrate random forest probability output. Some partitions take > 12 hours to run. This isn't a skew issue, since the largest partitions finish in minutes. I can only assume that some partitions cause something approaching this worst-case complexity.
> I'm working on a patch that borrows the implementation that is used in scikit-learn and the R "iso" package, both of which handle this particular input in linear time and are quadratic in the worst case.



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