Covariant matrix with zero eigenvalues

by Michael   Last Updated September 12, 2019 00:19 AM

For computing log-likelihood of points being in a certain multivariate distribution I am trying to invert the covariance matrix $\Sigma$. Unfortunately, $\Sigma$ turned out to be singular, with multiple zero eigenvalues. Using pseudo-inverse leads to very low log-likelihood, which is expected. How could I address this? Would it help to reduce the dimension of the problem?

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