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Hao Ren edited comment on SPARK-18581 at 11/25/16 2:07 PM: ----------------------------------------------------------- After reading the code comments, I find it takes into consideration the degenerate case of multivariate normal distribution: https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case I agree that the covariance matrix need not be invertible. However, the pdf of gaussian should always be smaller than 1, shouldn't it ? Let's focus on the MultivariateGaussian.calculateCovarianceConstants() function: The problem I faced is that my covariance matrix gives an eigenvalue vector 'd' as the following: DenseVector(2.7681862718766402E-17, 9.204832153027098E-5, 8.995053289618483E-4, 0.0030052504431952055, 0.006867041289040775, 0.030351586260721354, 0.03499956314691966, 0.04128248388411499, 0.055530636656481766, 0.09840067120993062, 0.13259027660865316, 0.16729084354080376, 0.18807175387781094, 0.19009666915093745, 0.19065188805766764, 0.19116928711151343, 0.19218984168511, 0.22044130291811304, 0.23164643534046853, 0.32957890755845165, 0.4557354551695869, 0.639320905646873, 0.8327082373125074, 1.7966679300383896, 2.5790389754725234) Meanwhile, the non-zero tolerance = 1.8514678433708895E-13 thus, {code} val logPseudoDetSigma = d.activeValuesIterator.filter(_ > tol).map(math.log).sum {code} logPseudoDetSigma = -58.40781006437829 -0.5 * (mu.size * math.log(2.0 * math.Pi) + logPseudoDetSigma) = 6.230441702072326 = u (same variable name in the code) Knowing that {code} private[mllib] def logpdf(x: BV[Double]): Double = { val delta = x - breezeMu val v = rootSigmaInv * delta u + v.t * v * -0.5 // u is used here } {code} If {code}v.t * v * -0.5{code} is a small negative number, then the logpdf will be about 6 => pdf = exp(6) = 403.4287934927351 In the gaussian mixture model case, some of the gaussian distributions could have a 'u' value much bigger, which results in a pdf = 2E10 was (Author: invkrh): After reading the code comments, I find it takes into consideration the degenerate case of multivariate normal distribution: https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case I agree that the covariance matrix need not be invertible. However, the pdf of gaussian should always be smaller than 1, shouldn't it ? Let's focus on the MultivariateGaussian.calculateCovarianceConstants() function: The problem I faced is that my covariance matrix gives an eigenvalue vector 'd' as the following: DenseVector(2.7681862718766402E-17, 9.204832153027098E-5, 8.995053289618483E-4, 0.0030052504431952055, 0.006867041289040775, 0.030351586260721354, 0.03499956314691966, 0.04128248388411499, 0.055530636656481766, 0.09840067120993062, 0.13259027660865316, 0.16729084354080376, 0.18807175387781094, 0.19009666915093745, 0.19065188805766764, 0.19116928711151343, 0.19218984168511, 0.22044130291811304, 0.23164643534046853, 0.32957890755845165, 0.4557354551695869, 0.639320905646873, 0.8327082373125074, 1.7966679300383896, 2.5790389754725234) Meanwhile, the non-zero tolerance = 1.8514678433708895E-13 thus, {code} val logPseudoDetSigma = d.activeValuesIterator.filter(_ > tol).map(math.log).sum {code} logPseudoDetSigma = -58.40781006437829 -0.5 * (mu.size * math.log(2.0 * math.Pi) + logPseudoDetSigma) = 6.230441702072326 = u (this variable name in the code) Knowing that {code} private[mllib] def logpdf(x: BV[Double]): Double = { val delta = x - breezeMu val v = rootSigmaInv * delta u + v.t * v * -0.5 // u is used here } {code} If {code}v.t * v * -0.5{code} is a small negative number, then the logpdf will be about 6 => pdf = exp(6) = 403.4287934927351 In the gaussian mixture model case, some of the gaussian distributions could have a 'u' value much bigger, which results in a pdf = 2E10 > 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 -- This message was sent by Atlassian JIRA (v6.3.4#6332) --------------------------------------------------------------------- To unsubscribe, e-mail: issues-unsubscr...@spark.apache.org For additional commands, e-mail: issues-h...@spark.apache.org