Iterative Solver

kerch.method.iterative(obj, x0: Tensor, num_iter: int = 50, lr=0.001, verbose: bool = False)[source]

Minimizes to following problem for each point in order to find the preimage:

\[\tilde{\mathbf{x}} = \mathrm{argmin}_{\mathbf{x}} \mathtt{obj}(\mathbf{x}).\]

The method optimizes with an SGD algorithm.

Parameters:

  • verbose (bool, optional) – Shows the training loop. Defaults to False.

  • obj – Objective to minimize.

  • x0 (torch.Tensor [num_points, dim_input]) – Starting value for the optimization.

  • num_iter (int, optional) – Number of iterations for the optimization process. Defaults to 50.

  • lr (float, optional) – Learning rate of the optimizer. Defaults to 0.001.

Returns:

Solution \(\tilde{\mathbf{x}}\)

Return type:

torch.Tensor [num_points, dim_input]

kerch.method.iterative_preimage_k(k_image: Tensor, kernel: _BaseKernel, num_iter: int = 50, lr=0.001, light_cache=True, verbose: bool = False) → Tensor[source]

Minimizes to following problem for each point in order to find the preimage:

\[\tilde{\mathbf{x}} = \mathrm{argmin}_{\mathbf{x}} \big\lVert \mathtt{k\_image} - \mathtt{kernel.k(x)} \big\rVert_2^2\]

The method optimizes with an SGD algorithm.

Parameters:

  • verbose (bool, optional) – Shows the training loop. Defaults to False.

  • k_image (torch.Tensor [num_points, num_idx]) – coefficients in the RKHS to be inverted.

  • kernel (kerch.kernel.Kernel instance.) – kernel on which this RKHS is based.

  • num_iter (int, optional) – Number of iterations for the optimization process. Defaults to 50.

  • lr (float, optional) – Learning rate of the optimizer. Defaults to 0.001.

  • light_cache (bool, optional) – Specifies whether the cache has to made lighter during the pre-image to avoid keeping the statistics of each iteration. This results in a speedup. Defaults to True.

Returns:

Pre-image

Return type:

torch.Tensor [num_points, dim_input]

kerch.method.iterative_preimage_phi(phi_image: Tensor, kernel: _BaseKernel, num_iter: int = 50, lr=0.001, light_cache=True, verbose: bool = False) → Tensor[source]

Minimizes to following problem for each point in order to find the preimage:

\[\tilde{\mathbf{x}} = \mathrm{argmin}_{\mathbf{x}} \big\lVert \mathtt{phi\_image} - \mathtt{kernel.phi(x)} \big\rVert_2^2\]

The method optimizes with an SGD algorithm.

Parameters:

  • verbose (bool, optional) – Shows the training loop. Defaults to False.

  • phi_image (torch.Tensor [num_points, dim_feature]) – feature map image to be inverted.

  • kernel (kerch.kernel.Kernel instance.) – kernel on which this RKHS is based.

  • num_iter (int, optional) – Number of iterations for the optimization process. Defaults to 50.

  • lr (float, optional) – Learning rate of the optimizer. Defaults to 0.001.

  • light_cache (bool, optional) – Specifies whether the cache has to made lighter during the pre-image to avoid keeping the statistics of each iteration. This results in a speedup. Defaults to True.

Returns:

Pre-image

Return type:

torch.Tensor [num_points, dim_feature]