Documentation for OFRBase
¶
Base methods for Orthogonal Forward Regression algorithm.
OFRBase
¶
Bases: BaseMSS
Base class for Model Structure Selection.
Source code in sysidentpy/model_structure_selection/ofr_base.py
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error_reduction_ratio(psi, y, process_term_number)
¶
Perform the Error Reduction Ration algorithm.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
y | array-like of shape = n_samples | The target data used in the identification process. | required |
psi | ndarray of floats | The information matrix of the model. | required |
process_term_number | int | Number of Process Terms defined by the user. | required |
Returns:
Name | Type | Description |
---|---|---|
err | array-like of shape = number_of_model_elements | The respective ERR calculated for each regressor. |
piv | array-like of shape = number_of_model_elements | Contains the index to put the regressors in the correct order based on err values. |
psi_orthogonal | ndarray of floats | The updated and orthogonal information matrix. |
References
- Manuscript: Orthogonal least squares methods and their application to non-linear system identification https://eprints.soton.ac.uk/251147/1/778742007_content.pdf
- Manuscript (portuguese): Identificação de Sistemas não Lineares Utilizando Modelos NARMAX Polinomiais - Uma Revisão e Novos Resultados
Source code in sysidentpy/model_structure_selection/ofr_base.py
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fit(*, X=None, y)
¶
Fit polynomial NARMAX model.
This is an 'alpha' version of the 'fit' function which allows a friendly usage by the user. Given two arguments, x and y, fit training data.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
X | ndarray of floats | The input data to be used in the training process. | None |
y | ndarray of floats | The output data to be used in the training process. | required |
Returns:
Name | Type | Description |
---|---|---|
model | ndarray of int | The model code representation. |
piv | array-like of shape = number_of_model_elements | Contains the index to put the regressors in the correct order based on err values. |
theta | array-like of shape = number_of_model_elements | The estimated parameters of the model. |
err | array-like of shape = number_of_model_elements | The respective ERR calculated for each regressor. |
info_values | array-like of shape = n_regressor | Vector with values of akaike's information criterion for models with N terms (where N is the vector position + 1). |
Source code in sysidentpy/model_structure_selection/ofr_base.py
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information_criterion(x, y)
¶
Determine the model order.
This function uses a information criterion to determine the model size. 'Akaike'- Akaike's Information Criterion with critical value 2 (AIC) (default). 'Bayes' - Bayes Information Criterion (BIC). 'FPE' - Final Prediction Error (FPE). 'LILC' - Khundrin's law ofiterated logarithm criterion (LILC).
Parameters:
Name | Type | Description | Default |
---|---|---|---|
y | array-like of shape = n_samples | Target values of the system. | required |
x | array-like of shape = n_samples | Input system values measured by the user. | required |
Returns:
Name | Type | Description |
---|---|---|
output_vector | array-like of shape = n_regressor | Vector with values of akaike's information criterion for models with N terms (where N is the vector position + 1). |
Source code in sysidentpy/model_structure_selection/ofr_base.py
predict(*, X=None, y, steps_ahead=None, forecast_horizon=None)
¶
Return the predicted values given an input.
The predict function allows a friendly usage by the user. Given a previously trained model, predict values given a new set of data.
This method accept y values mainly for prediction n-steps ahead (to be implemented in the future)
Parameters:
Name | Type | Description | Default |
---|---|---|---|
X | ndarray of floats | The input data to be used in the prediction process. | None |
y | ndarray of floats | The output data to be used in the prediction process. | required |
steps_ahead | int(default=None) | The user can use free run simulation, one-step ahead prediction and n-step ahead prediction. | None |
forecast_horizon | int | The number of predictions over the time. | None |
Returns:
Name | Type | Description |
---|---|---|
yhat | ndarray of floats | The predicted values of the model. |
Source code in sysidentpy/model_structure_selection/ofr_base.py
aic(n_theta, n_samples, e_var)
¶
Compute the Akaike information criteria value.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n_theta | int | Number of parameters of the model. | required |
n_samples | int | Number of samples given the maximum lag. | required |
e_var | float | Variance of the residues | required |
Returns:
Name | Type | Description |
---|---|---|
info_criteria_value | float | The computed value given the information criteria selected by the user. |
Source code in sysidentpy/model_structure_selection/ofr_base.py
aicc(n_theta, n_samples, e_var)
¶
Compute the Akaike information Criteria corrected value.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n_theta | int | Number of parameters of the model. | required |
n_samples | int | Number of samples given the maximum lag. | required |
e_var | float | Variance of the residues | required |
Returns:
Name | Type | Description |
---|---|---|
aicc | float | The computed aicc value. |
Source code in sysidentpy/model_structure_selection/ofr_base.py
bic(n_theta, n_samples, e_var)
¶
Compute the Bayesian information criteria value.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n_theta | int | Number of parameters of the model. | required |
n_samples | int | Number of samples given the maximum lag. | required |
e_var | float | Variance of the residues | required |
Returns:
Name | Type | Description |
---|---|---|
info_criteria_value | float | The computed value given the information criteria selected by the user. |
Source code in sysidentpy/model_structure_selection/ofr_base.py
fpe(n_theta, n_samples, e_var)
¶
Compute the Final Error Prediction value.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n_theta | int | Number of parameters of the model. | required |
n_samples | int | Number of samples given the maximum lag. | required |
e_var | float | Variance of the residues | required |
Returns:
Name | Type | Description |
---|---|---|
info_criteria_value | float | The computed value given the information criteria selected by the user. |
Source code in sysidentpy/model_structure_selection/ofr_base.py
get_info_criteria(info_criteria)
¶
Get info criteria.
Source code in sysidentpy/model_structure_selection/ofr_base.py
get_min_info_value(info_values)
¶
Find the index of the first increasing value in an array.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
info_values | array - like | A sequence of numeric values to be analyzed. | required |
Returns:
Type | Description |
---|---|
int | The index of the first element where the values start to increase monotonically. If no such element exists, the length of |
Notes
- The function assumes that
info_values
is a 1-dimensional array-like structure. - The function uses
np.diff
to compute the difference between consecutive elements in the sequence. - The function checks if any differences are positive, indicating an increase in value.
Examples:
>>> class MyClass:
... def __init__(self, values):
... self.info_values = values
... def get_min_info_value(self):
... is_monotonique = np.diff(self.info_values) > 0
... if any(is_monotonique):
... return np.where(is_monotonique)[0][0] + 1
... return len(self.info_values)
>>> instance = MyClass([3, 2, 1, 4, 5])
>>> instance.get_min_info_value()
3
Source code in sysidentpy/model_structure_selection/ofr_base.py
lilc(n_theta, n_samples, e_var)
¶
Compute the Lilc information criteria value.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n_theta | int | Number of parameters of the model. | required |
n_samples | int | Number of samples given the maximum lag. | required |
e_var | float | Variance of the residues | required |
Returns:
Name | Type | Description |
---|---|---|
info_criteria_value | float | The computed value given the information criteria selected by the user. |