projnormal.classes.ellipse

Class for the general projected normal distribution.

Classes

ProjNormalEllipse([n_dim, mean_x, ...])

Projected normal distribution variant, describing the variable \(y=x/\sqrt{x^T B x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) follows a multivariate normal distribution and \(B\) is a symmetric positive definite matrix.

class ProjNormalEllipse(n_dim=None, mean_x=None, covariance_x=None, B=None)

Bases: ProjNormal

Projected normal distribution variant, describing the variable \(y=x/\sqrt{x^T B x}\), where \(x \sim \mathcal{N}(\mu_x, \Sigma_x)\) follows a multivariate normal distribution and \(B\) is a symmetric positive definite matrix.

Parameters:

• n_dim (int) – Dimension of \(x\) (the embedding space). Optional: If mean_x and covariance_x are provided, it is not required.

• mean_x (torch.Tensor, optional) – Mean of \(x\). Shape (n_dim). Default is random.

• covariance_x (torch.Tensor, optional) – Covariance of \(x\). Shape (n_dim, n_dim). Default is the identity.

• B (torch.Tensor, optional) – SPD matrix defining the ellipse. Shape (n_dim, n_dim). Default is the identity matrix.

Variables:

• mean_x (torch.Tensor) – Mean of \(x\). Learnable parameter constrained to have unit norm. Shape (n_dim).

• covariance_x (torch.Tensor) – Covariance of \(x\). Learnable parameter constrained to be SPD. Shape (n_dim, n_dim).

• B (torch.Tensor) – Quadratic form matrix of the denominator. Shape (n_dim, n_dim). Learnable parameter constrained to be SPD.

log_pdf(y)

Compute the log pdf of points y.

Parameters:

y (torch.Tensor) – Points to evaluate the log pdf. Shape (n_points, n_dim).

Returns:

Log-PDF of y. Shape (n_points).

Return type:

torch.Tensor

moments()

Compute moments of the distribution via Taylor approximation.

Returns:

Dictionary with keys mean, covariance and second_moment, containing the corresponding moments of the distribution.

Return type:

dict

moments_empirical(n_samples=500000)

Compute moments of the distribution via sampling.

Parameters:

n_samples (int) – Number of samples to draw for empirical moments. Default is 200000.

Returns:

Dictionary with keys mean, covariance and second_moment, containing the corresponding moments of the distribution.

Return type:

dict

pdf(y)

Compute the pdf of points y.

Parameters:

y (torch.Tensor) – Points to evaluate the pdf. Shape (n_points, n_dim).

Returns:

PDF of the points y. Shape (n_points).

Return type:

torch.Tensor

sample(n_samples)

Sample from the distribution.

Parameters:

n_samples (int) – Number of samples to draw.

Returns:

Samples from the distribution. Shape (n_samples, n_dim).

Return type:

torch.Tensor