Github user tgaloppo commented on a diff in the pull request:
https://github.com/apache/spark/pull/3871#discussion_r22545409
--- 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 --
(u, d) is the eigendecomposition of sigma, so sigma = u * diag(d) * u^-1
... but we have a special case since covariance matrices are always symmetric
and positive semi-definite, in which case u * u.t = I, making it equivalent to
the singular value decomposition... so sigma = u * diag(d) * u.t ... so in svd
terms, v.t = u.t, then the inverse is v * inv(diag(d)) * u.t = u * inv(diag(d))
* u.t ...
Have I lost my bearings?
---
If your project is set up for it, you can reply to this email and have your
reply appear on GitHub as well. If your project does not have this feature
enabled and wishes so, or if the feature is enabled but not working, please
contact infrastructure at infrastruct...@apache.org or file a JIRA ticket
with INFRA.
---
---------------------------------------------------------------------
To unsubscribe, e-mail: reviews-unsubscr...@spark.apache.org
For additional commands, e-mail: reviews-h...@spark.apache.org
