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https://issues.apache.org/jira/browse/SPARK-18581?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15695481#comment-15695481
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Hao Ren commented on SPARK-18581:
---------------------------------
[~srowen]
I have updated the description. The problem is that my covariance matrix is non
invertible, since one of the features is zero for all data points.
> MultivariateGaussian does not check if covariance matrix is invertible
> ----------------------------------------------------------------------
>
> Key: SPARK-18581
> URL: https://issues.apache.org/jira/browse/SPARK-18581
> Project: Spark
> Issue Type: Bug
> Components: MLlib
> Affects Versions: 1.6.2, 2.0.2
> Reporter: Hao Ren
>
> When training GaussianMixtureModel, I found some probability much larger than
> 1. That leads me to that fact that, the value returned by
> MultivariateGaussian.pdf can be 10^5, etc.
> After reviewing the code, I found that problem lies in the computation of
> determinant of the covariance matrix.
> The computation is simplified by using pseudo-determinant of a positive
> defined matrix.
> In my case, I have a feature = 0 for all data point.
> As a result, covariance matrix is not invertible <=> det(covariance matrix) =
> 0 => pseudo-determinant will be very close to zero,
> Thus, log(pseudo-determinant) will be a large negative number which finally
> make logpdf very biger, pdf will be even bigger > 1.
> As said in comments of MultivariateGaussian.scala,
> """
> Singular values are considered to be non-zero only if they exceed a tolerance
> based on machine precision.
> """
> But if a singular value is considered to be zero, means the covariance matrix
> is non invertible which is a contradiction to the assumption that it should
> be invertible.
> So we should check if there a single value is smaller than the tolerance
> before computing the pseudo determinant
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