[SPARK-11302][MLLIB] 2) Multivariate Gaussian Model with Covariance matrix returns incorrect answer in some cases

Fix computation of root-sigma-inverse in multivariate Gaussian; add a test and fix related Python mixture model test.

Supersedes https://github.com/apache/spark/pull/9293

Author: Sean Owen <sowen@cloudera.com>

Closes #9309 from srowen/SPARK-11302.2.

1 files changed, 15 insertions, 0 deletions

diff --git a/mllib/src/test/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussianSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussianSuite.scala
index aa60deb665..6e7a003475 100644
--- a/mllib/src/test/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussianSuite.scala
+++ b/mllib/src/test/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussianSuite.scala
@@ -65,4 +65,19 @@ class MultivariateGaussianSuite extends SparkFunSuite with MLlibTestSparkContext
     assert(dist.pdf(x1) ~== 0.11254 absTol 1E-5)
     assert(dist.pdf(x2) ~== 0.068259 absTol 1E-5)
   }
+
+  test("SPARK-11302") {
+    val x = Vectors.dense(629, 640, 1.7188, 618.19)
+    val mu = Vectors.dense(
+      1055.3910505836575, 1070.489299610895, 1.39020554474708, 1040.5907503867697)
+    val sigma = Matrices.dense(4, 4, Array(
+      166769.00466698944, 169336.6705268059, 12.820670788921873, 164243.93314092053,
+      169336.6705268059, 172041.5670061245, 21.62590020524533, 166678.01075856484,
+      12.820670788921873, 21.62590020524533, 0.872524191943962, 4.283255814732373,
+      164243.93314092053, 166678.01075856484, 4.283255814732373, 161848.9196719207))
+    val dist = new MultivariateGaussian(mu, sigma)
+    // Agrees with R's dmvnorm: 7.154782e-05
+    assert(dist.pdf(x) ~== 7.154782224045512E-5 absTol 1E-9)
+  }
+
 }