VampLoss

class kooplearn.torch.nn.VampLoss(schatten_norm: int = 2, center_covariances: bool = True)[source]

Bases: Module

Variational Approach for learning Markov Processes (VAMP) score by Wu and Noé [1].

\[\mathcal{L}(x, y) = -\sum_{i} \sigma_{i}(A)^{p} \qquad \text{where}~A = \big(x^{\top}x\big)^{\dagger/2}x^{\top}y\big(y^{\top}y\big)^{\dagger/2}.\]
Parameters:

  • schatten_norm (int, optional) – Computes the VAMP-p score with p = schatten_norm.

  • 2. (Defaults to)

  • center_covariances (bool, optional) – Use centered covariances to compute the VAMP score.

  • True. (Defaults to)

Hint

Check out the Ordered MNIST example for a practical use of this loss function.

Methods

forward(x: Tensor, y: Tensor) → Tensor[source]

Forward pass of VAMP loss.

Parameters:

  • x (Tensor) – Features for x.

  • y (Tensor) – Features for y.

Raises:

NotImplementedError – If schatten_norm is not 1 or 2.

Shape:

x: \((N, D)\), where \(N\) is the batch size and \(D\) is the number of features.

y: \((N, D)\), where \(N\) is the batch size and \(D\) is the number of features.

[1]

Hao Wu and Frank Noé. Variational approach for learning markov processes from time series data. Journal of Nonlinear Science, 30(1):23–66, August 2019. URL: https://doi.org/10.1007/s00332-019-09567-y, doi:10.1007/s00332-019-09567-y.