LDS

class LDS(emission_coeff: torch.Tensor, transition_coeff: torch.Tensor, innovation_coeff: torch.Tensor, noise_std: torch.Tensor, prior_mean: torch.Tensor, prior_cov: torch.Tensor, offset: torch.Tensor, seq_length: int, latent_dim: int)

Bases: etna.core.mixins.BaseMixin

Class which implements Linear Dynamical System (LDS) as a distribution.

Create instance of LDS.

Parameters

• emission_coeff (torch.Tensor) – Emission coefficient matrix with shape (batch_size, seq_length, latent_dim).

• transition_coeff (torch.Tensor) – Transition coefficient matrix with shape (latent_dim, latent_dim).

• innovation_coeff (torch.Tensor) – Innovation coefficient matrix with shape (batch_size, seq_length, latent_dim).

• noise_std (torch.Tensor) – Noise standard deviation for targets with shape (batch_size, seq_length, 1).

• prior_mean (torch.Tensor) – Prior mean for latent state with shape (batch_size, latent_dim)

• prior_cov (torch.Tensor) – Prior covariance matrix for latent state with shape (batch_size, latent_dim, latent_dim)

• offset (torch.Tensor) – Offset for the target with shape (batch_size, seq_length, 1)

• seq_length (int) – Length of the sequence.

• latent_dim (int) – Dimension of the latent space.

Inherited-members

Methods

kalman_filter(targets)	Perform Kalman filtering of given observations.
kalman_filter_step(target, noise_std, ...)	One step of the Kalman filter.
log_likelihood(targets)	Compute the log-likelihood of the target.
sample(n_samples)	Sample the trajectories of targets from the current LDS.
set_params(**params)	Return new object instance with modified parameters.
to_dict()	Collect all information about etna object in dict.

kalman_filter(targets: torch.Tensor) → Tuple[torch.Tensor, torch.Tensor, torch.Tensor]

Perform Kalman filtering of given observations.

Parameters

targets (torch.Tensor) – Tensor with observations with shape (batch_size, seq_length, 1)

Returns

• Log probabilities with shape shape (batch_size, seq_length)

• Mean of p(l_T | l_{T-1}), where T is seq_length, with shape (batch_size, latent_dim)

• Covariance of p(l_T | l_{T-1}), where T is seq_length, with shape (batch_size, latent_dim, latent_dim)

Return type

Tuple[torch.Tensor, torch.Tensor, torch.Tensor]

kalman_filter_step(target: torch.Tensor, noise_std: torch.Tensor, prior_mean: torch.Tensor, prior_cov: torch.Tensor, emission_coeff: torch.Tensor, offset: torch.Tensor)

One step of the Kalman filter.

This function computes the filtered state (mean and covariance) given the LDS coefficients in the prior state (mean and variance) and observations.

Parameters

• target (torch.Tensor) – Observations of the system with shape (batch_size, 1)

• noise_std (torch.Tensor) – Standard deviation of the observations noise with shape (batch_size, 1)

• prior_mean (torch.Tensor) – Prior mean of the latent state with shape (batch_size, latent_dim)

• prior_cov (torch.Tensor) – Prior covariance of the latent state with shape (batch_size, latent_dim, latent_dim)

• emission_coeff (torch.Tensor) – Emission coefficient with shape (batch_size, latent_dim)

• offset (torch.Tensor) – Offset for the observations with shape (batch_size, 1)

Returns

• Log probability with shape (batch_size, 1)

• Filtered_mean with shape (batch_size, latent_dim, 1)

• Filtered_covariance with shape (batch_size, latent_dim, latent_dim)

log_likelihood(targets: torch.Tensor) → torch.Tensor

Compute the log-likelihood of the target.

Parameters

targets (torch.Tensor) – Tensor with targets of shape (batch_size, seq_length, 1)

Returns

Tensor with log-likelihoods of target of shape (batch_size, seq_length)

Return type

torch.Tensor

sample(n_samples: int) → torch.Tensor

Sample the trajectories of targets from the current LDS.

Parameters

n_samples (int) – Number of trajectories to sample.

Returns

Tensor with trajectories with shape (n_samples, batch_size, seq_length, 1).

Return type

torch.Tensor