SSM

class SSM[source]

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