[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, 4 insertions, 4 deletions

diff --git a/mllib/src/main/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussian.scala b/mllib/src/main/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussian.scala
index 92a5af708d..0724af9308 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussian.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/stat/distribution/MultivariateGaussian.scala
@@ -56,7 +56,7 @@ class MultivariateGaussian @Since("1.3.0") (
 
   /**
    * Compute distribution dependent constants:
-   *    rootSigmaInv = D^(-1/2)^ * U, where sigma = U * D * U.t
+   *    rootSigmaInv = D^(-1/2)^ * U.t, where sigma = U * D * U.t
    *    u = log((2*pi)^(-k/2)^ * det(sigma)^(-1/2)^)
    */
   private val (rootSigmaInv: DBM[Double], u: Double) = calculateCovarianceConstants
@@ -104,11 +104,11 @@ class MultivariateGaussian @Since("1.3.0") (
    *
    *    sigma = U * D * U.t
    *    inv(Sigma) = U * inv(D) * U.t
-   *               = (D^{-1/2}^ * U).t * (D^{-1/2}^ * U)
+   *               = (D^{-1/2}^ * U.t).t * (D^{-1/2}^ * U.t)
    *
    * and thus
    *
-   *    -0.5 * (x-mu).t * inv(Sigma) * (x-mu) = -0.5 * norm(D^{-1/2}^ * U  * (x-mu))^2^
+   *    -0.5 * (x-mu).t * inv(Sigma) * (x-mu) = -0.5 * norm(D^{-1/2}^ * U.t  * (x-mu))^2^
    *
    * To guard against singular covariance matrices, this method computes both the
    * pseudo-determinant and the pseudo-inverse (Moore-Penrose).  Singular values are considered
@@ -130,7 +130,7 @@ class MultivariateGaussian @Since("1.3.0") (
       // by inverting the square root of all non-zero values
       val pinvS = diag(new DBV(d.map(v => if (v > tol) math.sqrt(1.0 / v) else 0.0).toArray))
 
-      (pinvS * u, -0.5 * (mu.size * math.log(2.0 * math.Pi) + logPseudoDetSigma))
+      (pinvS * u.t, -0.5 * (mu.size * math.log(2.0 * math.Pi) + logPseudoDetSigma))
     } catch {
       case uex: UnsupportedOperationException =>
         throw new IllegalArgumentException("Covariance matrix has no non-zero singular values")