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

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

Nic Eggert created SPARK-17455:
----------------------------------

             Summary: IsotonicRegression takes non-polynomial time for some inputs
                 Key: SPARK-17455
                 URL: https://issues.apache.org/jira/browse/SPARK-17455
             Project: Spark
          Issue Type: Improvement
          Components: MLlib
    Affects Versions: 2.0.0, 1.6.2, 1.5.2, 1.4.1, 1.3.1
            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.



--
This message was sent by Atlassian JIRA
(v6.3.4#6332)

---------------------------------------------------------------------
To unsubscribe, e-mail: issues-unsubscribe@spark.apache.org
For additional commands, e-mail: issues-help@spark.apache.org