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# torchaudio.functional.frechet_distance¶

torchaudio.functional.frechet_distance(mu_x, sigma_x, mu_y, sigma_y)[source]

Computes the Fréchet distance between two multivariate normal distributions .

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

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