From ee07541e99f0d262bf662b669b6542cf302ff39c Mon Sep 17 00:00:00 2001
From: Sean Owen <srowen@gmail.com>
Date: Wed, 30 Jul 2014 08:55:15 -0700
Subject: [PATCH] SPARK-2748 [MLLIB] [GRAPHX] Loss of precision for small
arguments to Math.exp, Math.log
In a few places in MLlib, an expression of the form `log(1.0 + p)` is evaluated. When p is so small that `1.0 + p == 1.0`, the result is 0.0. However the correct answer is very near `p`. This is why `Math.log1p` exists.
Similarly for one instance of `exp(m) - 1` in GraphX; there's a special `Math.expm1` method.
While the errors occur only for very small arguments, given their use in machine learning algorithms, this is entirely possible.
Also note the related PR for Python: https://github.com/apache/spark/pull/1652
Author: Sean Owen <srowen@gmail.com>
Closes #1659 from srowen/SPARK-2748 and squashes the following commits:
c5926d4 [Sean Owen] Use log1p, expm1 for better precision for tiny arguments
---
.../org/apache/spark/graphx/util/GraphGenerators.scala | 6 ++++--
.../org/apache/spark/mllib/optimization/Gradient.scala | 8 ++++----
2 files changed, 8 insertions(+), 6 deletions(-)
diff --git a/graphx/src/main/scala/org/apache/spark/graphx/util/GraphGenerators.scala b/graphx/src/main/scala/org/apache/spark/graphx/util/GraphGenerators.scala
index 635514f09e..60149548ab 100644
--- a/graphx/src/main/scala/org/apache/spark/graphx/util/GraphGenerators.scala
+++ b/graphx/src/main/scala/org/apache/spark/graphx/util/GraphGenerators.scala
@@ -100,8 +100,10 @@ object GraphGenerators {
*/
private def sampleLogNormal(mu: Double, sigma: Double, maxVal: Int): Int = {
val rand = new Random()
- val m = math.exp(mu + (sigma * sigma) / 2.0)
- val s = math.sqrt((math.exp(sigma*sigma) - 1) * math.exp(2*mu + sigma*sigma))
+ val sigmaSq = sigma * sigma
+ val m = math.exp(mu + sigmaSq / 2.0)
+ // expm1 is exp(m)-1 with better accuracy for tiny m
+ val s = math.sqrt(math.expm1(sigmaSq) * math.exp(2*mu + sigmaSq))
// Z ~ N(0, 1)
var X: Double = maxVal
diff --git a/mllib/src/main/scala/org/apache/spark/mllib/optimization/Gradient.scala b/mllib/src/main/scala/org/apache/spark/mllib/optimization/Gradient.scala
index 679842f831..9d82f011e6 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/optimization/Gradient.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/optimization/Gradient.scala
@@ -68,9 +68,9 @@ class LogisticGradient extends Gradient {
val gradient = brzData * gradientMultiplier
val loss =
if (label > 0) {
- math.log(1 + math.exp(margin))
+ math.log1p(math.exp(margin)) // log1p is log(1+p) but more accurate for small p
} else {
- math.log(1 + math.exp(margin)) - margin
+ math.log1p(math.exp(margin)) - margin
}
(Vectors.fromBreeze(gradient), loss)
@@ -89,9 +89,9 @@ class LogisticGradient extends Gradient {
brzAxpy(gradientMultiplier, brzData, cumGradient.toBreeze)
if (label > 0) {
- math.log(1 + math.exp(margin))
+ math.log1p(math.exp(margin))
} else {
- math.log(1 + math.exp(margin)) - margin
+ math.log1p(math.exp(margin)) - margin
}
}
}
--
GitLab