torchaudio.functional.frechet_distance

torchaudio.functional.frechet_distance(mu_x, sigma_x, mu_y, sigma_y)

Computes the Fréchet distance between two multivariate normal distributions [Dowson and Landau, 1982].

Concretely, for multivariate Gaussians $X(\mu_X, \Sigma_X)$ and $Y(\mu_Y, \Sigma_Y)$, the function computes and returns $F$ as

$$F(X, Y) = || \mu_X - \mu_Y ||_2^2 + \text{Tr}\left( \Sigma_X + \Sigma_Y - 2 \sqrt{\Sigma_X \Sigma_Y} \right)$$

Parameters:

• mu_x (torch.Tensor) – mean $\mu_X$ of multivariate Gaussian $X$, with shape (N,).

• sigma_x (torch.Tensor) – covariance matrix $\Sigma_X$ of $X$, with shape (N, N).

• mu_y (torch.Tensor) – mean $\mu_Y$ of multivariate Gaussian $Y$, with shape (N,).

• sigma_y (torch.Tensor) – covariance matrix $\Sigma_Y$ of $Y$, with shape (N, N).

Returns:

the Fréchet distance between $X$ and $Y$.

Return type:

torch.Tensor