Meta-Model Structure Selection (MetaMSS) algorithm for building Polynomial NARX models¶
Example created by Wilson Rocha Lacerda Junior
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import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sysidentpy.model_structure_selection import MetaMSS, FROLS
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.basis_function._basis_function import Polynomial
from sysidentpy.parameter_estimation import RecursiveLeastSquares
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,
)
import pandas as pd import numpy as np import matplotlib.pyplot as plt from sysidentpy.model_structure_selection import MetaMSS, FROLS from sysidentpy.metrics import root_relative_squared_error from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.parameter_estimation import RecursiveLeastSquares 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, )
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df1 = pd.read_csv("./datasets/x_cc.csv")
df2 = pd.read_csv("./datasets/y_cc.csv")
df2[5000:80000].plot(figsize=(10, 4))
df1 = pd.read_csv("./datasets/x_cc.csv") df2 = pd.read_csv("./datasets/y_cc.csv") df2[5000:80000].plot(figsize=(10, 4))
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<Axes: >
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df1.iloc[::500].values.shape
df1.iloc[::500].values.shape
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(1000, 1)
We will decimate the data using d=500 in this example. Besides, we separate the MetaMSS data to use the same amount of samples in the prediction validation. Because MetaMSS need a train and test data to optimize the parameters of the model, in this case, we'll use 400 samples to train instead of 500 samples used for the other models.
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# we will decimate the data using d=500 in this example
x_train, x_test = np.split(df1.iloc[::500].values, 2)
y_train, y_test = np.split(df2.iloc[::500].values, 2)
# we will decimate the data using d=500 in this example x_train, x_test = np.split(df1.iloc[::500].values, 2) y_train, y_test = np.split(df2.iloc[::500].values, 2)
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basis_function = Polynomial(degree=2)
estimator = RecursiveLeastSquares()
model = MetaMSS(
xlag=5,
ylag=5,
estimator=estimator,
maxiter=5,
n_agents=15,
basis_function=basis_function,
random_state=42,
)
model.fit(X=x_train, y=y_train)
basis_function = Polynomial(degree=2) estimator = RecursiveLeastSquares() model = MetaMSS( xlag=5, ylag=5, estimator=estimator, maxiter=5, n_agents=15, basis_function=basis_function, random_state=42, ) model.fit(X=x_train, y=y_train)
c:\Users\wilso\miniconda3\envs\sysidentpy334\Lib\site-packages\numpy\core\fromnumeric.py:88: RuntimeWarning: overflow encountered in reduce return ufunc.reduce(obj, axis, dtype, out, **passkwargs) c:\Users\wilso\miniconda3\envs\sysidentpy334\Lib\site-packages\numpy\core\fromnumeric.py:88: RuntimeWarning: invalid value encountered in reduce return ufunc.reduce(obj, axis, dtype, out, **passkwargs) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\model_structure_selection\meta_model_structure_selection.py:455: RuntimeWarning: overflow encountered in square sum_of_squared_residues = np.sum(residues**2) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\model_structure_selection\meta_model_structure_selection.py:465: RuntimeWarning: invalid value encountered in sqrt se_theta = np.sqrt(var_e) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\metrics\_regression.py:216: RuntimeWarning: overflow encountered in square numerator = np.sum(np.square((yhat - y))) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\narmax_base.py:724: RuntimeWarning: overflow encountered in power regressor_value[j] = np.prod(np.power(raw_regressor, model_exponent)) c:\Users\wilso\miniconda3\envs\sysidentpy334\Lib\site-packages\numpy\linalg\linalg.py:2590: RuntimeWarning: divide by zero encountered in power absx **= ord
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<sysidentpy.model_structure_selection.meta_model_structure_selection.MetaMSS at 0x229e13e3150>
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yhat = model.predict(X=x_test, y=y_test, steps_ahead=None)
rrse = root_relative_squared_error(y_test[model.max_lag :, :], yhat[model.max_lag :, :])
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_test, yhat=yhat, n=1000)
ee = compute_residues_autocorrelation(y_test, yhat)
plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$")
x1e = compute_cross_correlation(y_test, yhat, x_test)
plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
yhat = model.predict(X=x_test, y=y_test, steps_ahead=None) rrse = root_relative_squared_error(y_test[model.max_lag :, :], yhat[model.max_lag :, :]) 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_test, yhat=yhat, n=1000) ee = compute_residues_autocorrelation(y_test, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_test, yhat, x_test) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")
0.035919583498004094
Regressors Parameters ERR
0 1 -6.1606E+02 0.00000000E+00
1 y(k-1) 1.3117E+00 0.00000000E+00
2 y(k-2) -3.0579E-01 0.00000000E+00
3 x1(k-1) 5.7920E+02 0.00000000E+00
4 x1(k-3) -1.8750E-01 0.00000000E+00
5 x1(k-1)y(k-1) -1.7305E-01 0.00000000E+00
6 x1(k-2)y(k-1) -1.1660E-01 0.00000000E+00
7 x1(k-1)y(k-2) 1.2182E-01 0.00000000E+00
8 x1(k-2)y(k-2) 3.4112E-02 0.00000000E+00
9 x1(k-1)y(k-3) -4.8970E-02 0.00000000E+00
10 x1(k-1)y(k-4) 1.3846E-02 0.00000000E+00
11 x1(k-2)^2 1.0290E+02 0.00000000E+00
12 x1(k-3)x1(k-2) 8.6745E-01 0.00000000E+00
13 x1(k-4)x1(k-2) 3.4336E-01 0.00000000E+00
14 x1(k-5)x1(k-2) 2.7815E-01 0.00000000E+00
15 x1(k-3)^2 -9.3749E-01 0.00000000E+00
16 x1(k-4)x1(k-3) 6.1039E-01 0.00000000E+00
17 x1(k-5)x1(k-3) 3.9361E-02 0.00000000E+00
18 x1(k-4)^2 -4.6335E-01 0.00000000E+00
19 x1(k-5)x1(k-4) -9.5668E-02 0.00000000E+00
20 x1(k-5)^2 3.6922E-01 0.00000000E+00
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# Plotting the evolution of the agents
plt.plot(model.best_by_iter)
model.best_by_iter[-1]
# Plotting the evolution of the agents plt.plot(model.best_by_iter) model.best_by_iter[-1]
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0.0017530517788608157
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# You have access to all tested models
# model.tested_models
# You have access to all tested models # model.tested_models
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from sklearn.neighbors import KNeighborsRegressor
from sklearn.svm import SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
from catboost import CatBoostRegressor
from sklearn.linear_model import ARDRegression
from sysidentpy.general_estimators import NARX
xlag = ylag = 5
estimators = [
(
"NARX_KNeighborsRegressor",
NARX(
base_estimator=KNeighborsRegressor(),
xlag=xlag,
ylag=ylag,
basis_function=basis_function,
),
),
(
"NARX_DecisionTreeRegressor",
NARX(
base_estimator=DecisionTreeRegressor(),
xlag=xlag,
ylag=ylag,
basis_function=basis_function,
),
),
(
"NARX_RandomForestRegressor",
NARX(
base_estimator=RandomForestRegressor(n_estimators=200),
xlag=xlag,
ylag=ylag,
basis_function=basis_function,
),
),
(
"NARX_Catboost",
NARX(
base_estimator=CatBoostRegressor(
iterations=800, learning_rate=0.1, depth=8
),
xlag=xlag,
ylag=ylag,
basis_function=basis_function,
fit_params={"verbose": False},
),
),
(
"NARX_ARD",
NARX(
base_estimator=ARDRegression(),
xlag=xlag,
ylag=ylag,
basis_function=basis_function,
),
),
(
"FROLS-Polynomial_NARX",
FROLS(
order_selection=True,
n_info_values=50,
ylag=ylag,
xlag=xlag,
basis_function=basis_function,
info_criteria="bic",
err_tol=None,
),
),
(
"MetaMSS",
MetaMSS(
norm=-2,
xlag=xlag,
ylag=ylag,
estimator=estimator,
maxiter=5,
n_agents=15,
loss_func="metamss_loss",
basis_function=basis_function,
random_state=42,
),
),
]
resultados = {}
for nome_do_modelo, modelo in estimators:
resultados["%s" % (nome_do_modelo)] = []
modelo.fit(X=x_train, y=y_train)
yhat = modelo.predict(X=x_test, y=y_test)
if nome_do_modelo in ["FROLS-Polynomial_NARX", "MetaMSS"]:
result = root_relative_squared_error(
y_test[modelo.max_lag :], yhat[modelo.max_lag :]
)
else:
result = root_relative_squared_error(y_test, yhat)
resultados["%s" % (nome_do_modelo)].append(result)
print(nome_do_modelo, "%.3f" % np.mean(result))
from sklearn.neighbors import KNeighborsRegressor from sklearn.svm import SVC from sklearn.tree import DecisionTreeRegressor from sklearn.ensemble import RandomForestRegressor from catboost import CatBoostRegressor from sklearn.linear_model import ARDRegression from sysidentpy.general_estimators import NARX xlag = ylag = 5 estimators = [ ( "NARX_KNeighborsRegressor", NARX( base_estimator=KNeighborsRegressor(), xlag=xlag, ylag=ylag, basis_function=basis_function, ), ), ( "NARX_DecisionTreeRegressor", NARX( base_estimator=DecisionTreeRegressor(), xlag=xlag, ylag=ylag, basis_function=basis_function, ), ), ( "NARX_RandomForestRegressor", NARX( base_estimator=RandomForestRegressor(n_estimators=200), xlag=xlag, ylag=ylag, basis_function=basis_function, ), ), ( "NARX_Catboost", NARX( base_estimator=CatBoostRegressor( iterations=800, learning_rate=0.1, depth=8 ), xlag=xlag, ylag=ylag, basis_function=basis_function, fit_params={"verbose": False}, ), ), ( "NARX_ARD", NARX( base_estimator=ARDRegression(), xlag=xlag, ylag=ylag, basis_function=basis_function, ), ), ( "FROLS-Polynomial_NARX", FROLS( order_selection=True, n_info_values=50, ylag=ylag, xlag=xlag, basis_function=basis_function, info_criteria="bic", err_tol=None, ), ), ( "MetaMSS", MetaMSS( norm=-2, xlag=xlag, ylag=ylag, estimator=estimator, maxiter=5, n_agents=15, loss_func="metamss_loss", basis_function=basis_function, random_state=42, ), ), ] resultados = {} for nome_do_modelo, modelo in estimators: resultados["%s" % (nome_do_modelo)] = [] modelo.fit(X=x_train, y=y_train) yhat = modelo.predict(X=x_test, y=y_test) if nome_do_modelo in ["FROLS-Polynomial_NARX", "MetaMSS"]: result = root_relative_squared_error( y_test[modelo.max_lag :], yhat[modelo.max_lag :] ) else: result = root_relative_squared_error(y_test, yhat) resultados["%s" % (nome_do_modelo)].append(result) print(nome_do_modelo, "%.3f" % np.mean(result))
NARX_KNeighborsRegressor 1.158 NARX_DecisionTreeRegressor 0.203 NARX_RandomForestRegressor 0.146 NARX_Catboost 0.120 NARX_ARD 0.083 FROLS-Polynomial_NARX 0.057
c:\Users\wilso\miniconda3\envs\sysidentpy334\Lib\site-packages\numpy\core\fromnumeric.py:88: RuntimeWarning: overflow encountered in reduce return ufunc.reduce(obj, axis, dtype, out, **passkwargs) c:\Users\wilso\miniconda3\envs\sysidentpy334\Lib\site-packages\numpy\core\fromnumeric.py:88: RuntimeWarning: invalid value encountered in reduce return ufunc.reduce(obj, axis, dtype, out, **passkwargs) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\model_structure_selection\meta_model_structure_selection.py:455: RuntimeWarning: overflow encountered in square sum_of_squared_residues = np.sum(residues**2) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\model_structure_selection\meta_model_structure_selection.py:465: RuntimeWarning: invalid value encountered in sqrt se_theta = np.sqrt(var_e) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\metrics\_regression.py:216: RuntimeWarning: overflow encountered in square numerator = np.sum(np.square((yhat - y))) C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\narmax_base.py:724: RuntimeWarning: overflow encountered in power regressor_value[j] = np.prod(np.power(raw_regressor, model_exponent)) c:\Users\wilso\miniconda3\envs\sysidentpy334\Lib\site-packages\numpy\linalg\linalg.py:2590: RuntimeWarning: divide by zero encountered in power absx **= ord
MetaMSS 0.036
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for model_name, metric in sorted(
resultados.items(), key=lambda x: np.mean(x[1]), reverse=False
):
print(model_name, np.mean(metric))
for model_name, metric in sorted( resultados.items(), key=lambda x: np.mean(x[1]), reverse=False ): print(model_name, np.mean(metric))
MetaMSS 0.035919583498004094 FROLS-Polynomial_NARX 0.05729765719062527 NARX_ARD 0.08265856190495872 NARX_Catboost 0.12034851661643597 NARX_RandomForestRegressor 0.14557973585496042 NARX_DecisionTreeRegressor 0.203057724881072 NARX_KNeighborsRegressor 1.157787546845798
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