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From "Gilles (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-1441) SimpleRegression#getSlopeConfidenceInterval recalculates t distribution on every call
Date Fri, 26 Jan 2018 23:48:00 GMT

    [ https://issues.apache.org/jira/browse/MATH-1441?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16341802#comment-16341802
] 

Gilles commented on MATH-1441:
------------------------------

I reverted the change in commit 60bcdd450d6950da981d70b8b08379bdd744c82d because I couldn't
notice any performance improvement.
Please post the result of your benchmark on the current code ("master" branch). Thanks.

> SimpleRegression#getSlopeConfidenceInterval recalculates t distribution on every call
> -------------------------------------------------------------------------------------
>
>                 Key: MATH-1441
>                 URL: https://issues.apache.org/jira/browse/MATH-1441
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 3.6.1
>         Environment: Java 8, Linux x64.
>            Reporter: Max Aller
>            Priority: Minor
>              Labels: performance
>
> SimpleRegression#getSlopeConfidenceInterval, when called a lot (on the other of 100k
or 1M times), is surprisingly slow - 3M calls, on my 3rd gen i7 machine, takes *75 seconds*.
This is primarily because recalculating the inverse cumulative probability, and reconstructing
the TDistribution object itself, is somewhat expensive, entailing a lot of `log` and `sqrt`
and iteration and all that stuff.
> The confidence interval is based on two values - *n* and *alpha*. I'd posit that alpha
will _usually_ be one of a very small set of values, and n, well, at least in my case, I'm
always calling this method with the same number of data points - a moving window of time-series
data. But I recognize n might be all over the place for some users.
> In any event, I strongly believe some level of caching would greatly benefit the users
of Commons Math. I've forked my own version of getSlopeConfidenceInterval that uses caching.
Here's a test case demonstrating that:
> {code:java}
> class SlowRegressionsTest {
>     @Test
>     void slow() {
>         SimpleRegression simpleRegression = new SimpleRegression();
>         simpleRegression.addData(0.0, 0.0);
>         simpleRegression.addData(1.0, 1.0);
>         simpleRegression.addData(2.0, 2.0);
>         long start = System.currentTimeMillis();
>         for (int i = 0; i < 3_000_000; i++) {
>             simpleRegression.getSlopeConfidenceInterval();
>         }
>         long duration = System.currentTimeMillis() - start;
>         System.out.printf("`slow` took %dms%n", duration);
>     }
>     @Test
>     void fast() {
>         SimpleRegression simpleRegression = new SimpleRegression();
>         simpleRegression.addData(0.0, 0.0);
>         simpleRegression.addData(1.0, 1.0);
>         simpleRegression.addData(2.0, 2.0);
>         long start = System.currentTimeMillis();
>         for (int i = 0; i < 3_000_000; i++) {
>             SimpleRegressionUtilsKt.fastGetSlopeConfidenceInterval(simpleRegression);
>         }
>         long duration = System.currentTimeMillis() - start;
>         System.out.printf("`fast` took %dms%n", duration);
>     }
> }{code}
> which prints out
> {noformat}
> `fast` took 159ms
> `slow` took 75304ms{noformat}
> Nearly 500x faster - 53ns/call. My particular solution is written in Kotlin for Java
8, so not of direct relevance to you, but here it is:
> {code:java}
> package math
> import org.apache.commons.math3.distribution.TDistribution
> import org.apache.commons.math3.exception.OutOfRangeException
> import org.apache.commons.math3.exception.util.LocalizedFormats
> import org.apache.commons.math3.stat.regression.SimpleRegression
> import java.util.concurrent.ConcurrentHashMap
> @JvmOverloads
> fun SimpleRegression.fastGetSlopeConfidenceInterval(alpha: Double = 0.05): Double {
>     if (n < 3) {
>         return Double.NaN
>     }
>     if (alpha >= 1 || alpha <= 0) {
>         throw OutOfRangeException(
>             LocalizedFormats.SIGNIFICANCE_LEVEL,
>             alpha, 0, 1
>         )
>     }
>     // No advertised NotStrictlyPositiveException here - will return NaN above
>     // PATCH: use cached inverse cumulative probability
>     return slopeStdErr * getInverseCumulativeProbability(n, alpha)
> }
> private val cache = ConcurrentHashMap<Key, Double>()
> private data class Key(val n: Long, val alpha: Double)
> private fun getInverseCumulativeProbability(n: Long, alpha: Double): Double =
>     cache.getOrPut(Key(n, alpha)) {
>         TDistribution((n - 2).toDouble()).inverseCumulativeProbability(1.0 - alpha /
2.0)
>     }
> {code}
> Limitations: 1. Kotlin, 2. ConcurrentHashMap is unbounded here.
> I don't know how/if Commons Math does caching elsewhere, but it'd sure be handy here,
I believe. What are your thoughts?



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