Github user tgaloppo commented on a diff in the pull request:
https://github.com/apache/spark/pull/3871#discussion_r22521704
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/stat/impl/MultivariateGaussian.scala
---
@@ -17,23 +17,84 @@
package org.apache.spark.mllib.stat.impl
-import breeze.linalg.{DenseVector => DBV, DenseMatrix => DBM, Transpose,
det, pinv}
+import breeze.linalg.{DenseVector => DBV, DenseMatrix => DBM, diag, max,
eigSym}
-/**
- * Utility class to implement the density function for multivariate
Gaussian distribution.
- * Breeze provides this functionality, but it requires the Apache
Commons Math library,
- * so this class is here so-as to not introduce a new dependency in
Spark.
- */
+import org.apache.spark.mllib.util.MLUtils
+
+/**
+ * This class provides basic functionality for a Multivariate Gaussian
(Normal) Distribution. In
+ * the event that the covariance matrix is singular, the density will be
computed in a
+ * reduced dimensional subspace under which the distribution is supported.
+ * (see
[[http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case]])
+ *
+ * @param mu The mean vector of the distribution
+ * @param sigma The covariance matrix of the distribution
+ */
private[mllib] class MultivariateGaussian(
val mu: DBV[Double],
val sigma: DBM[Double]) extends Serializable {
- private val sigmaInv2 = pinv(sigma) * -0.5
- private val U = math.pow(2.0 * math.Pi, -mu.length / 2.0) *
math.pow(det(sigma), -0.5)
-
+
+ /**
+ * Compute distribution dependent constants:
+ * rootSigmaInv = D^(-1/2) * U, where sigma = U * D * U.t
--- End diff --
I agree; I see no reason why U should always be symmetric (as you have
demonstrated). Before I roll back the change, I just want to make sure that I
did not misinterpret @mengxr , and/or that we are not missing something that he
sees.
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