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Commit 125246c

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add ridge_regression as parameter estimation method
1 parent bd763cf commit 125246c

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3 files changed

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3 files changed

+61
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‎sysidentpy/model_structure_selection/forward_regression_orthogonal_least_squares.py

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@@ -94,6 +94,8 @@ class FROLS(Estimators, BaseMSS):
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Weight factor to control the proportions of the error norms
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and offers an extra degree of freedom within the adaptation
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of the LMS mixed norm method.
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ridge_param : float, default=0.01
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Constant parameter used in ridge regression (K = ridge_param*I).
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model_type: str, default="NARMAX"
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The user can choose "NARMAX", "NAR" and "NFIR" models
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@@ -166,6 +168,7 @@ def __init__(
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eps: np.float64 = np.finfo(np.float64).eps,
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gama: float = 0.2,
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weight: float = 0.02,
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ridge_param: float = 0.01,
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basis_function: Union[Polynomial, Fourier] = Polynomial(),
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model_type: str = "NARMAX",
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):
@@ -193,6 +196,7 @@ def __init__(
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eps=eps,
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gama=gama,
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weight=weight,
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ridge_param=ridge_param,
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basis_function=basis_function,
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)
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self.ensemble = None

‎sysidentpy/parameter_estimation/estimators.py

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@@ -25,6 +25,7 @@ def __init__(
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eps=np.finfo(np.float64).eps,
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gama=0.2,
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weight=0.02,
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ridge_param: float=0.01,
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basis_function=None,
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):
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self.eps = eps
@@ -35,6 +36,7 @@ def __init__(
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self.delta = delta
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self.gama = gama
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self.weight = weight # <0 e <1
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self.ridge_param = ridge_param
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self.xi = None
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self.theta_evolution = None
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self.basis_function = basis_function
@@ -51,6 +53,7 @@ def _validate_params(self):
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"eps": self.eps,
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"gama": self.gama,
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"weight": self.weight,
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"ridge_param": self.ridge_param,
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}
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for attribute, value in attributes.items():
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if not isinstance(value, (np.integer, int, float)):
@@ -890,3 +893,41 @@ def least_mean_squares_mixed_norm(self, psi, y):
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theta[:, i] = tmp_list.flatten()
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return theta[:, -1].reshape(-1, 1)
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def ridge_regression(self, psi, y):
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"""Estimate the model parameters using SVD and Ridge Regression method.
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Parameters
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----------
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psi : ndarray of floats
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The information matrix of the model.
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y : array-like of shape = y_training
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The data used to training the model.
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Returns
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-------
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theta : array-like of shape = number_of_model_elements
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The estimated parameters of the model.
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References
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----------
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- Manuscript: Hoerl, A. E.; Kennard, R. W. Ridge regression:
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applications to nonorthogonal problems. Technometrics,
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Taylor & Francis, v. 12, n. 1, p. 69-82, 1970.
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- StackExchange: whuber. The proof of shrinking coefficients using ridge
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regression through "spectral decomposition".
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Cross Validated, accessed 21 September 2023,
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https://stats.stackexchange.com/q/220324
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"""
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self._check_linear_dependence_rows(psi)
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y = y[self.max_lag :, 0].reshape(-1, 1)
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U, d, Vt = np.linalg.svd(psi, full_matrices=False)
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D = np.diag(d)
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I = np.identity(len(D))
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theta = Vt.T @ np.linalg.inv(D**2 + self.ridge_param*I) @ D @ U.T @ y
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return theta

‎sysidentpy/parameter_estimation/tests/test_estimators.py

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@@ -227,5 +227,21 @@ def test_least_mean_squares_mixed_norm():
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assert_almost_equal(model.theta, theta, decimal=2)
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def test_ridge_regression():
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x, y, theta = create_test_data()
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basis_function = Polynomial(degree=2)
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model = FROLS(
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n_terms=5,
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extended_least_squares=False,
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ylag=[1, 2],
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xlag=2,
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estimator="ridge_regression",
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ridge_param=0.01,
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basis_function=basis_function,
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)
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model.fit(X=x, y=y)
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assert_almost_equal(model.theta, theta, decimal=2)
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def test_model_order_selection():
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assert_raises(ValueError, Estimators, max_lag=-1)

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