Model Selection

ROLCH employs online model selection based on information criteria (IC). We calculate the IC based on the Residual Sum of Squares (RSS), which can be tracked online.

API Reference

rolch.information_criterion

information_criterion(n_observations: Union[int, np.ndarray], n_parameters: Union[int, np.ndarray], rss: Union[float, np.ndarray], criterion: Literal['aic', 'bic', 'hqc'] = 'aic') -> Union[float, np.ndarray]

Calcuate the information criteria.

The information criteria are calculated from the Resdiual Sum of Squares \(RSS\). The function provides the calculation of Akaikes IC, the bayesian IC and the Harman-Quinn IC.

Parameters:

Name	Type	Description	Default
n_observations	Union[int, ndarray]	Number of observations	required
n_parameters	Union[int, ndarray]	Number of parameters	required
rss	Union[float, ndarray]	Residual sum of squares	required
criterion	Literal['aic', 'bic', 'hqc']	Information criteria to calculate. Defaults to "aic".	'aic'

Raises:

Type	Description
ValueError	Raises if the criterion is not one of aic, bic or hqc.

Returns:

Type	Description
Union[float, ndarray]	Union[float, np.ndarray]: The value of the IC for given inputs.

rolch.select_best_model_by_information_criterion

select_best_model_by_information_criterion(n_observations: float, n_parameters: np.ndarray, rss: np.ndarray, criterion: Literal['aic', 'bic', 'hqc', 'max']) -> int

Calculates the information criterion and returns the model with the best (lowest) IC.

Note

The information criterion max will always return the largest model.

Parameters:

Name	Type	Description	Default
n_observations	float	Number of observations	required
n_parameters	ndarray	Number of parameters per model	required
rss	ndarray	Residual sum of squares per model	required
criterion	Literal['aic', 'bic', 'hqc', 'max']	Information criterion.	required

Raises:

Type	Description
ValueError	Raises if the criterion is not one of aic, bic, hqc or max.

Returns:

Name	Type	Description
int	int	Index of the model with the best (lowest) IC.