def TrainSTLSQ(X: np.ndarray,
y: np.ndarray,
alpha: float,
delta_threshold: float,
max_iterations: int = 100,
test_size: float = 0.2,
random_state: int = 0) -> np.ndarray:
"""[summary]
Args:
X (np.ndarray): [description]
y (np.ndarray): [description]
alpha (float): [description]
delta_threshold (float): [description]
max_iterations (int, optional): [description]. Defaults to 100.
test_size (float, optional): [description]. Defaults to 0.2.
random_state (int, optional): [description]. Defaults to 0.
Returns:
np.ndarray: [description]
"""
# Split data
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=test_size, random_state=random_state)
# Set up the initial tolerance l0 penalty and estimates
l0 = 1e-3 * np.linalg.cond(X)
delta_t = delta_threshold # for interal use, can be updated
# Initial estimate
optimizer = STLSQ(threshold=0, alpha=0.0,
fit_intercept=False) # Now similar to LSTSQ
y_predict = optimizer.fit(X_train, y_train).predict(X_test)
min_loss = np.linalg.norm(y_predict - y_test,
2) + l0 * np.count_nonzero(optimizer.coef_)
# Setting alpha and tolerance
best_threshold = delta_t
threshold = delta_t
for iteration in np.arange(max_iterations):
optimizer.set_params(alpha=alpha, threshold=threshold)
y_predict = optimizer.fit(X_train, y_train).predict(X_test)
loss = np.linalg.norm(y_predict - y_test,
2) + l0 * np.count_nonzero(optimizer.coef_)
if (loss <= min_loss) and not (np.all(optimizer.coef_ == 0)):
min_loss = loss
best_threshold = threshold
threshold += delta_threshold
else: # if loss increases, we need to a) lower the current threshold and/or decrease step size
new_lower_threshold = np.max([0, threshold - 2 * delta_t])
delta_t = 2 * delta_t / (max_iterations - iteration)
threshold = new_lower_threshold + delta_t
optimizer.set_params(alpha=alpha, threshold=best_threshold)
optimizer.fit(X_train, y_train)
return optimizer.coef_
def test_alternate_parameters(data_derivative_1d, kwargs):
x, x_dot = data_derivative_1d
x = x.reshape(-1, 1)
model = STLSQ(**kwargs)
model.fit(x, x_dot)
model.fit(x, x_dot, sample_weight=x[:, 0])
check_is_fitted(model)
def TrainSTLSQ(
X: np.ndarray,
y: np.ndarray,
alpha: float,
delta_threshold: float,
max_iterations: int = 100,
test_size: float = 0.2,
random_state: int = 0,
) -> np.ndarray:
"""PDE-FIND sparsity selection algorithm. Based on method described by Rudy et al. (10.1126/sciadv.1602614).
Args:
X (np.ndarray): Training input data of shape (n_samples, n_features).
y (np.ndarray): Training target data of shape (n_samples, n_outputs).
alpha (float): Magnitude of the L2 regularization.
delta_threshold (float): Initial stepsize for the search of the threshold
max_iterations (int, optional): Maximum number of iterations. Defaults to 100.
test_size (float, optional): Fraction of the data that is assigned to the test-set. Defaults to 0.2.
random_state (int, optional): Defaults to 0.
Returns:
np.ndarray: Coefficient vector.
"""
# Split data
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=test_size, random_state=random_state)
# Set up the initial tolerance l0 penalty and estimates
l0 = 1e-3 * np.linalg.cond(X)
delta_t = delta_threshold # for interal use, can be updated
# Initial estimate
optimizer = STLSQ(threshold=0, alpha=0.0,
fit_intercept=False) # Now similar to LSTSQ
y_predict = optimizer.fit(X_train, y_train).predict(X_test)
min_loss = np.linalg.norm(y_predict - y_test,
2) + l0 * np.count_nonzero(optimizer.coef_)
# Setting alpha and tolerance
best_threshold = delta_t
threshold = delta_t
for iteration in np.arange(max_iterations):
optimizer.set_params(alpha=alpha, threshold=threshold)
y_predict = optimizer.fit(X_train, y_train).predict(X_test)
loss = np.linalg.norm(y_predict - y_test,
2) + l0 * np.count_nonzero(optimizer.coef_)
if (loss <= min_loss) and not (np.all(optimizer.coef_ == 0)):
min_loss = loss
best_threshold = threshold
threshold += delta_threshold
else: # if loss increases, we need to a) lower the current threshold and/or decrease step size
new_lower_threshold = np.max([0, threshold - 2 * delta_t])
delta_t = 2 * delta_t / (max_iterations - iteration)
threshold = new_lower_threshold + delta_t
optimizer.set_params(alpha=alpha, threshold=best_threshold)
optimizer.fit(X_train, y_train)
return optimizer.coef_