The equidensity contours of a non-singular multivariate normal distribution are ellipsoids ( i . e . linear transformations of hyperspheres ) centered at the mean.
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A different type of generalization is the normal-inverse-Wishart distribution, essentially the product of a multivariate normal distribution with an inverse Wishart distribution.
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In fact, the DoG as the difference of two Multivariate normal distribution has always a total null sum and convolving it with a uniform signal generates no response.
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Here, p _ \ mathcal { N } ( x | C ) denotes the likelihood of x from a multivariate normal distribution with zero mean and covariance matrix C.
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In statistics, the "'matrix normal distribution "'is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables.
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Both of these expectations are needed when deriving the variational Bayes update equations in a Bayes network involving a Wishart distribution ( which is the conjugate prior of the multivariate normal distribution ).
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In cases where the contribution of random noise is additive and has a multivariate normal distribution, the problem of maximum likelihood sequence estimation can be reduced to that of a least squares minimization.
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The "'logistic normal distribution "'is a generalization of the logit normal distribution to D-dimensional probability vectors by taking a logistic transformation of a multivariate normal distribution.
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The matrix " t "-distribution shares the same relationship with the multivariate " t "-distribution that the matrix normal distribution shares with the multivariate normal distribution.
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In order to produce a sample, typically the generator is seeded with a randomized input that is sampled from a predefined latent space ( e . g ., a multivariate normal distribution ).
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