SSM¶

Bases: abc.ABC, etna.core.mixins.BaseMixin

Base class for State Space Model.

The system dynamics is described with the following equations:

\[y_t = a^T_t l_{t-1} + b_t + \sigma_t\varepsilon_t\]

\[l_t = F_t l_{t-1} + g_t\epsilon_t\]

\[l_0 \sim N(\mu_0, diag(\sigma_0^2)), \varepsilon_t \sim N(0, 1), \epsilon_t \sim N(0, 1),\]

where

\(y\) - state of the system

\(l\) - state of the system in the latent space

\(a\) - emission coefficient

\(F\) - transition coefficient

\(g\) - innovation coefficient

\(\sigma\) - noise standard deviation

\(\mu_0\) - prior mean

\(\sigma_0\) - prior standard deviation

Inherited-members

Methods

`emission_coeff`(datetime_index)	Emission coefficient matrix.
`generate_datetime_index`(timestamps)	Generate datetime index to use in the State Space Model.
`innovation_coeff`(datetime_index)	Innovation coefficient matrix.
`latent_dim`()	Dimension of the latent space.
`set_params`(**params)	Return new object instance with modified parameters.
`to_dict`()	Collect all information about etna object in dict.
`transition_coeff`(datetime_index)	Transition coefficient matrix.

abstract emission_coeff(datetime_index: torch.Tensor) → torch.Tensor[source]¶

Emission coefficient matrix.

Parameters: datetime_index (torch.Tensor) – Tensor with the index values. Values should be from 0 to seasonal period.
Returns: Emission coefficient matrix.
Return type: torch.Tensor

abstract generate_datetime_index(timestamps: numpy.ndarray) → numpy.ndarray[source]¶

Generate datetime index to use in the State Space Model.

Parameters: timestamps (numpy.ndarray) – Array with timestamps.
Returns: Datetime index for State Space Model.
Return type: numpy.ndarray

abstract innovation_coeff(datetime_index: torch.Tensor) → torch.Tensor[source]¶

Innovation coefficient matrix.

Parameters: datetime_index (torch.Tensor) – Tensor with the index values. Values should be from 0 to seasonal period.
Returns: Innovation coefficient matrix.
Return type: torch.Tensor

abstract latent_dim() → int[source]¶

Dimension of the latent space.

Returns: Dimension of the latent space.
Return type: int

abstract transition_coeff(datetime_index: torch.Tensor) → torch.Tensor[source]¶

Transition coefficient matrix.

Parameters: datetime_index (torch.Tensor) – Tensor with the index values. Values should be from 0 to seasonal period.
Returns: Transition coefficient matrix.
Return type: torch.Tensor