wsingular

wsingular.sinkhorn_singular_vectors(dataset: torch.Tensor, dtype: str, device: str, n_iter: int, tau: float = 0, eps: float = 0.05, p: int = 1, writer=None, small_value: float = 1e-06, normalization_steps: int = 1, C_ref: Optional[torch.Tensor] = None, D_ref: Optional[torch.Tensor] = None, log_loss: bool = False, progress_bar: bool = False) → Tuple[torch.Tensor, torch.Tensor]

Performs power iterations and returns Sinkhorn Singular Vectors. Early stopping is possible with Ctrl-C.

Parameters:

  • dataset (torch.Tensor) – The input dataset. Alternatively, you can give a tuple of tensors (A, B).

  • dtype (str) – The dtype

  • device (str) – The device

  • n_iter (int) – The number of power iterations.

  • tau (float, optional) – The regularization parameter for the norm R. Defaults to 0.

  • eps (float) – The entropic regularization parameter.

  • p (int, optional) – The order of the norm R. Defaults to 1.

  • writer (SummaryWriter, optional) – If set, the progress will be written to the Tensorboard writer. Defaults to None.

  • small_value (float, optional) – A small value for numerical stability. Defaults to 1e-6.

  • normalization_steps (int, optional) – How many Sinkhorn iterations for the initial normalization of the dataset. Must be > 0. Defaults to 1, which is just regular normalization, along columns for A and along rows for B. For large numbers of steps, A and B are bistochastic.

  • C_ref (torch.Tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • D_ref (torch.Tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • log_loss (bool, optional) – Whether to return the loss. Defaults to False.

  • progress_bar (bool, optional) – Whether to display a progress bar for individual matrix computations. Defaults to False.

Returns:

Sinkhorn Singular Vectors (C,D). If log_loss, it returns (C, D, loss_C, loss_D)

Return type:

Tuple[torch.Tensor, torch.Tensor]

wsingular.stochastic_sinkhorn_singular_vectors(dataset: torch.Tensor, dtype: torch.dtype, device: str, n_iter: int, tau: float = 0, eps: float = 0.05, sample_prop: float = 0.1, p: int = 1, step_fn: ~typing.Callable = <function <lambda>>, mult_update: bool = False, writer=None, small_value: float = 1e-06, normalization_steps: int = 1, C_ref: ~typing.Optional[torch.Tensor] = None, D_ref: ~typing.Optional[torch.Tensor] = None, progress_bar: bool = False) → Tuple[torch.Tensor, torch.Tensor]

Performs stochastic power iterations and returns Sinkhorn Singular Vectors. Early stopping is possible with Ctrl-C.

Parameters:

  • dataset (torch.Tensor) – The input dataset. Alternatively, you can give a tuple of tensors (A, B).

  • dtype (torch.dtype) – The dtype

  • device (str) – The device

  • n_iter (int) – The number of power iterations.

  • tau (float, optional) – The regularization parameter for the norm R. Defaults to 0.

  • eps (float, optional) – The entropic regularization parameter. Defaults to 5e-2.

  • sample_prop (float, optional) – The proportion of indices to update at each step. Defaults to 1e-1.

  • p (int, optional) – The order of the norm R. Defaults to 1.

  • step_fn (Callable, optional) – The function that defines step size from the iteration number (which starts at 1). Defaults to lambdak:1/np.sqrt(k).

  • mult_update (bool, optional) – If True, use multiplicative update instead of additive update. Defaults to False.

  • writer (SummaryWriter, optional) – If set, the progress will be written to the Tensorboard writer. Defaults to None.

  • small_value (float, optional) – A small value for numerical stability. Defaults to 1e-6.

  • normalization_steps (int, optional) – How many Sinkhorn iterations for the initial normalization of the dataset. Must be > 0. Defaults to 1, which is just regular normalization, along columns for A and along rows for B. For large numbers of steps, A and B are bistochastic.

  • C_ref (torch.tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • D_ref (torch.Tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • progress_bar (bool, optional) – Whether to display a progress bar for individual matrix computations. Defaults to False.

Returns:

Sinkhorn Singular Vectors (C,D)

Return type:

Tuple[torch.Tensor, torch.Tensor]

wsingular.stochastic_wasserstein_singular_vectors(dataset: torch.Tensor, dtype: torch.dtype, device: str, n_iter: int, tau: float = 0, sample_prop: float = 0.1, p: int = 1, step_fn: ~typing.Callable = <function <lambda>>, mult_update: bool = False, writer=None, small_value: float = 1e-06, normalization_steps: int = 1, C_ref: ~typing.Optional[torch.Tensor] = None, D_ref: ~typing.Optional[torch.Tensor] = None, progress_bar: bool = False) → Tuple[torch.Tensor, torch.Tensor]

Performs stochastic power iterations and returns Wasserstein Singular Vectors. Early stopping is possible with Ctrl-C.

Parameters:

  • dataset (torch.Tensor) – The input dataset. Alternatively, you can give a tuple of tensors (A, B).

  • dtype (torch.dtype) – The dtype

  • device (str) – The device

  • n_iter (int) – The number of power iterations.

  • tau (float, optional) – The regularization parameter for the norm R. Defaults to 0.

  • sample_prop (float, optional) – The proportion of indices to update at each step. Defaults to 1e-1.

  • p (int, optional) – The order of the norm R. Defaults to 1.

  • step_fn (Callable, optional) – The function that defines step size from the iteration number (which starts at 1). Defaults to lambdak:1/np.sqrt(k).

  • mult_update (bool, optional) – If True, use multiplicative update instead of additive update. Defaults to False.

  • writer (SummaryWriter, optional) – If set, the progress will be written to the Tensorboard writer. Defaults to None.

  • small_value (float, optional) – A small value for numerical stability. Defaults to 1e-6.

  • normalization_steps (int, optional) – How many Sinkhorn iterations for the initial normalization of the dataset. Must be > 0. Defaults to 1, which is just regular normalization, along columns for A and along rows for B. For large numbers of steps, A and B are bistochastic.

  • C_ref (torch.tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • D_ref (torch.Tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • progress_bar (bool, optional) – Whether to display a progress bar for individual matrix computations. Defaults to False.

Returns:

Wasserstein Singular Vectors (C,D)

Return type:

Tuple[torch.Tensor, torch.Tensor]

wsingular.wasserstein_singular_vectors(dataset: torch.Tensor, dtype: torch.dtype, device: str, n_iter: int, tau: float = 0, p: int = 1, writer=None, small_value: float = 1e-06, normalization_steps: int = 1, C_ref: Optional[torch.Tensor] = None, D_ref: Optional[torch.Tensor] = None, log_loss: bool = False, progress_bar: bool = False) → Tuple[torch.Tensor, torch.Tensor]

Performs power iterations and returns Wasserstein Singular Vectors. Early stopping is possible with Ctrl-C.

Parameters:

  • dataset (torch.Tensor) – The input dataset, rows as samples. Alternatively, you can give a tuple of tensors (A, B).

  • dtype (str) – The dtype

  • device (str) – The device

  • n_iter (int) – The number of power iterations.

  • tau (float, optional) – The regularization parameter for the norm R. Defaults to 0.

  • p (int, optional) – The order of the norm R. Defaults to 1.

  • writer (SummaryWriter, optional) – If set, the progress will be written to the Tensorboard writer. Defaults to None.

  • small_value (float, optional) – A small value for numerical stability. Defaults to 1e-6.

  • normalization_steps (int, optional) – How many Sinkhorn iterations for the initial normalization of the dataset. Must be > 0. Defaults to 1, which is just regular normalization, along columns for A and along rows for B. For large numbers of steps, A and B are bistochastic.

  • C_ref (torch.Tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • D_ref (torch.Tensor, optional) – If set, Hilbert distances to this reference will be computed. Defaults to None.

  • log_loss (bool, optional) – Whether to return the loss. Defaults to False.

  • progress_bar (bool, optional) – Whether to display a progress bar for individual matrix computations. Defaults to False.

Returns:

Wasserstein sigular vectors (C,D). If log_loss, it returns (C, D, loss_C, loss_D)

Return type:

Tuple[torch.Tensor, torch.Tensor]