Multiple Inputs usage¶
Example created by Wilson Rocha Lacerda Junior
Generating 2 input 1 output sample data¶
The data is generated by simulating the following model:
$y_k = 0.4y_{k-1}^2 + 0.1y_{k-1}x1_{k-1} + 0.6x2_{k-1} -0.3x1_{k-1}x2_{k-2} + e_{k}$
If colored_noise is set to True:
$e_{k} = 0.8\nu_{k-1} + \nu_{k}$
where $x$ is a uniformly distributed random variable and $\nu$ is a gaussian distributed variable with $\mu=0$ and $\sigma=0.001$
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pip install sysidentpy
pip install sysidentpy
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sysidentpy.model_structure_selection import FROLS
from sysidentpy.basis_function._basis_function import Polynomial
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.utils.display_results import results
from sysidentpy.utils.plotting import plot_residues_correlation, plot_results
from sysidentpy.residues.residues_correlation import (
compute_residues_autocorrelation,
compute_cross_correlation,
)
from sysidentpy.utils.generate_data import get_miso_data, get_siso_data
import numpy as np import pandas as pd import matplotlib.pyplot as plt from sysidentpy.model_structure_selection import FROLS from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.metrics import root_relative_squared_error from sysidentpy.utils.display_results import results from sysidentpy.utils.plotting import plot_residues_correlation, plot_results from sysidentpy.residues.residues_correlation import ( compute_residues_autocorrelation, compute_cross_correlation, ) from sysidentpy.utils.generate_data import get_miso_data, get_siso_data
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x_train, x_valid, y_train, y_valid = get_miso_data(
n=1000, colored_noise=False, sigma=0.001, train_percentage=90
)
x_train, x_valid, y_train, y_valid = get_miso_data( n=1000, colored_noise=False, sigma=0.001, train_percentage=90 )
There is a specific difference for multiple input data.
- You have to pass the lags for each input in a nested list (e.g., [[1, 2], [1, 2]])
The remainder settings remains the same.
Build the model¶
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basis_function = Polynomial(degree=2)
model = FROLS(
order_selection=True,
n_terms=4,
extended_least_squares=False,
ylag=2,
xlag=[[1, 2], [1, 2]],
info_criteria="aic",
estimator="least_squares",
basis_function=basis_function,
)
basis_function = Polynomial(degree=2) model = FROLS( order_selection=True, n_terms=4, extended_least_squares=False, ylag=2, xlag=[[1, 2], [1, 2]], info_criteria="aic", estimator="least_squares", basis_function=basis_function, )
c:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\utils\deprecation.py:37: FutureWarning: Passing a string to define the estimator will rise an error in v0.4.0. You'll have to use FROLS(estimator=LeastSquares()) instead. The only change is that you'll have to define the estimator first instead of passing a string like 'least_squares'. This change will make easier to implement new estimators and it'll improve code readability. warnings.warn(message, FutureWarning)
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model.fit(X=x_train, y=y_train)
model.fit(X=x_train, y=y_train)
Out[4]:
<sysidentpy.model_structure_selection.forward_regression_orthogonal_least_squares.FROLS at 0x21b0dea3ac0>
Model evaluation¶
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yhat = model.predict(X=x_valid, y=y_valid)
rrse = root_relative_squared_error(y_valid, yhat)
print(rrse)
r = pd.DataFrame(
results(
model.final_model,
model.theta,
model.err,
model.n_terms,
err_precision=8,
dtype="sci",
),
columns=["Regressors", "Parameters", "ERR"],
)
print(r)
plot_results(y=y_valid, yhat=yhat, n=1000)
ee = compute_residues_autocorrelation(y_valid, yhat)
plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$")
x1e = compute_cross_correlation(y_valid, yhat, x_valid[:, 0])
plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
yhat = model.predict(X=x_valid, y=y_valid) rrse = root_relative_squared_error(y_valid, yhat) print(rrse) r = pd.DataFrame( results( model.final_model, model.theta, model.err, model.n_terms, err_precision=8, dtype="sci", ), columns=["Regressors", "Parameters", "ERR"], ) print(r) plot_results(y=y_valid, yhat=yhat, n=1000) ee = compute_residues_autocorrelation(y_valid, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_valid, yhat, x_valid[:, 0]) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
0.0028414982487199258
Regressors Parameters ERR
0 x2(k-1) 5.9998E-01 9.04865107E-01
1 x2(k-2)x1(k-1) -3.0020E-01 5.13018913E-02
2 y(k-1)^2 4.0022E-01 4.35070199E-02
3 x1(k-1)y(k-1) 1.0013E-01 3.18875414E-04
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xaxis = np.arange(1, model.n_info_values + 1)
plt.plot(xaxis, model.info_values)
plt.xlabel("n_terms")
plt.ylabel("Information Criteria")
xaxis = np.arange(1, model.n_info_values + 1) plt.plot(xaxis, model.info_values) plt.xlabel("n_terms") plt.ylabel("Information Criteria")
Out[6]:
Text(0, 0.5, 'Information Criteria')
