Struct easy_ml::distributions::MultivariateGaussian

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pub struct MultivariateGaussian<T: Numeric + Real> {
    pub mean: Matrix<T>,
    pub covariance: Matrix<T>,
}

Expand description

A multivariate Gaussian distribution with mean vector μ, and covariance matrix Σ.

See: https://en.wikipedia.org/wiki/Multivariate_normal_distribution

Invariants

The mean Matrix must always be a column vector, and must be the same length as the covariance matrix.

Fields

mean: Matrix<T>

The mean is a column vector of expected values in each dimension

covariance: Matrix<T>

The covariance matrix is a NxN matrix where N is the number of dimensions for this Gaussian. A covariance matrix must always be symmetric, that is C[i,j] = C[j,i].

The covariance matrix is a measure of how much values from each dimension vary from their expected value with respect to each other.

For a 2 dimensional multivariate Gaussian the covariance matrix could be the 2x2 identity matrix:

[
  1.0, 0.0
  0.0, 1.0
]

In which case the two dimensions are completely uncorrelated as C[0,1] = C[1,0] = 0.

Implementations

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impl<T: Numeric + Real> MultivariateGaussian<T>

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pub fn new(mean: Matrix<T>, covariance: Matrix<T>) -> MultivariateGaussian<T>

Constructs a new multivariate Gaussian distribution from a Nx1 column vector of means and a NxN covariance matrix

This function does not check that the provided covariance matrix is actually a covariance matrix. If a square matrix that is not symmetric is supplied the gaussian is not defined.

Panics if the covariance matrix is not square, or the column vector is not the same length as the covariance matrix size. Does not currently panic if the covariance matrix is symmetric, but this could be checked in the future.

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impl<T: Numeric + Real> MultivariateGaussian<T> where
for<'a> &'a T: NumericRef<T> + RealRef<T>,

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pub fn draw(&self, source: &mut I, max_samples: usize) -> Option<Matrix<T>> where
I: Iterator<Item = T>,

Draws samples from this multivariate distribution.

For max_samples of M, sufficient random numbers from the source iterator, and this Gaussian’s dimensionality of N, returns an MxN matrix of drawn values.

The source iterator must have at least MxN random values if N is even, and Mx(N+1) random values if N is odd, or None will be returned. If the cholesky decomposition cannot be taken on this Gaussian’s covariance matrix then None is also returned.

Example of generating and feeding random numbers