distr_multivariate_normal function

Gaussian distribution

Creates a multivariate normal (also called Gaussian) distribution parameterized by a mean vector and a covariance matrix.

distr_multivariate_normal(
  loc,
  covariance_matrix = NULL,
  precision_matrix = NULL,
  scale_tril = NULL,
  validate_args = NULL
)

Arguments

• loc: (Tensor): mean of the distribution
• covariance_matrix: (Tensor): positive-definite covariance matrix
• precision_matrix: (Tensor): positive-definite precision matrix
• scale_tril: (Tensor): lower-triangular factor of covariance, with positive-valued diagonal
• validate_args: Bool wether to validate the arguments or not.

Details

The multivariate normal distribution can be parameterized either in terms of a positive definite covariance matrix $\mathbf{\Sigma}$

or a positive definite precision matrix $\mathbf{\Sigma}^{-1}$

or a lower-triangular matrix $\mathbf{L}$ with positive-valued diagonal entries, such that $\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top$. This triangular matrix can be obtained via e.g. Cholesky decomposition of the covariance.

Note

Only one of covariance_matrix or precision_matrix or scale_tril can be specified. Using scale_tril will be more efficient: all computations internally are based on scale_tril. If covariance_matrix or precision_matrix is passed instead, it is only used to compute the corresponding lower triangular matrices using a Cholesky decomposition.

Examples

if (torch_is_installed()) {
m <- distr_multivariate_normal(torch_zeros(2), torch_eye(2))
m$sample() # normally distributed with mean=`[0,0]` and covariance_matrix=`I`
}

See Also

Distribution for details on the available methods.

Other distributions: distr_bernoulli(), distr_chi2(), distr_gamma(), distr_normal(), distr_poisson()