canari.component.autoregression_component

class canari.component.autoregression_component.Autoregression(std_error: float | None = None, phi: float | None = None, mu_states: list[float] | None = None, var_states: list[float] | None = None)

Bases: BaseComponent

Autoregression class, inheriting from Canari’s BaseComponent. It models residuals following a univariate AR(1) process with optional treatement and estimation of the autoregressive coefficient (phi) and process noise standard deviation (std_error) as hidden states.

Parameters:

• std_error (Optional[float]) – Standard deviation of the process noise. Defaults to None. If None, it will be learned using Approximate Gaussian Variance Inference (AGVI).

• phi (Optional[float]) – Autoregressive coefficient. Defaults to None. If None, it will be learned using Gaussian Multiplicative Approximation (GMA).

• mu_states (Optional[list[float]]) – Initial mean of the hidden state. Defaults: initialized to zeros.

• var_states (Optional[list[float]]) – Initial variance of the hidden state. Defaults: initialized to zeros.

Behavior:

• Adds 2 extra (dummy) states if phi is None.

• Adds 3 extra (dummy) states if std_error is None.

References

Deka, B., Nguyen, L.H. and Goulet, J.-A. (2024). Analytically Tractable Heteroscedastic Uncertainty Quantification in Bayesian Neural Networks for Regression Tasks. Neurocomputing. Volume 572, pp.127183.

Deka, B. and Goulet, J.-A. (2023). Approximate Gaussian Variance Inference for State-Space Models. International Journal of Adaptive Control and Signal Processing. Volume 37, Issue 11, pp. 2934-2962.

Examples

>>> from canari.component import Autoregression
>>> # With known parameters
>>> ar = Autoregression(phi=0.9, std_error=0.1)
>>> # With known mu_states and var_states
>>> ar = Autoregression(mu_states=[0.1], var_states=[0.1], phi=0.9, std_error=0.1)
>>> # With parameters to be estimated
>>> ar = Autoregression()
>>> ar.component_name
autoregression
>>> ar.states_name
['autoregression', 'phi', 'phi_autoregression', 'AR_error', 'W2', 'W2bar']
>>> ar.mu_states
>>> ar.var_states
>>> ar.transition_matrix
>>> ar.observation_matrix
>>> ar.process_noise_matrix

initialize_component_name()

Initialize the component’s name. str.

initialize_mu_states()

Initialize the mean of the hidden states. Output an 2D array.

initialize_num_states()

Initialize the number of hidden states. int.

initialize_observation_matrix()

Initialize the observation matrix. Output an 2D array.

initialize_process_noise_matrix()

Initialize the process noise covariance matrix. Output an 2D array.

initialize_states_name()

Initialize the names of all hidden states. list[str].

initialize_transition_matrix()

Initialize the transition matrix. Output an 2D array.

initialize_var_states()

Initialize the covariance matrix of the hidden states. Output an 2D array.