def test_ElasticNet_friedman(self):
"""
Tests elastic-net regularisation on quadratic (2nd order) synthetic data with irrelevent features.
"""
# Generate friedman dataset with
X, y = datasets.gen_friedman(n_observations=200,
n_dim=10,
noise=0.2,
normalise=False,
random_seed=42)
X_train, X_test, y_train, y_test = datasets.train_test_split(
X, y, train=0.8, random_seed=42)
# Define param and basis
s = Parameter(distribution='uniform',
lower=-1,
upper=1,
order=4,
endpoints='both')
param = [s for _ in range(X.shape[1])]
basis = Basis('total-order')
# Fit OLS poly
poly_OLS = Poly(parameters=param,
basis=basis,
method='least-squares',
sampling_args={
'mesh': 'user-defined',
'sample-points': X_train,
'sample-outputs': y_train.reshape(-1, 1)
})
poly_OLS.set_model()
_, r2_OLS = poly_OLS.get_polyscore(X_test=X_test, y_test=y_test)
# Fit Poly with LASSO (alpha/param2 = 1.0) and check r2 improved
poly_LASSO = Poly(parameters=param,
basis=basis,
method='elastic-net',
sampling_args={
'mesh': 'user-defined',
'sample-points': X_train,
'sample-outputs': y_train.reshape(-1, 1)
},
solver_args={
'param1': 0.1,
'param2': 1.0
})
poly_LASSO.set_model()
_, r2_LASSO = poly_LASSO.get_polyscore(X_test=X_test, y_test=y_test)
self.assertTrue(r2_LASSO > r2_OLS)
# Finally, check LASSO has shrunk irrelevent Poly coefficients
coeffs = poly_LASSO.get_coefficients().squeeze()
ideal_coeffs = 126 #As tensor-grid, order=4, relevent_dims=5
idx = np.abs(coeffs).argsort()[::-1]
irrelevent_coeffs = np.sum(np.abs(
coeffs[idx[ideal_coeffs:]])) / np.sum(np.abs(coeffs))
self.assertTrue(irrelevent_coeffs < 1e-5,
msg='irrelevent_coeffs = %.2e' % irrelevent_coeffs)
def test_friedman(self):
"""
Test the gen_friedman() sythetic dataset generator and the train_test_split utility.
"""
N = 200
d = 6
X,y = datasets.gen_friedman(n_observations=N, n_dim=d, noise=0.0, normalise=False)
# Split the data
X_train,X_test,y_train,y_test = datasets.train_test_split(X,y,train=0.75,shuffle=True,random_seed=42)
# Check dims
N_train = int(N*0.75)
N_test = int(N*0.25)
np.testing.assert_equal(X_train.shape,np.array([N_train,d]))
np.testing.assert_equal(y_test.shape,np.array([N_test,]))
y_true = 10 * np.sin(np.pi * X_test[:, 0] * X_test[:, 1]) + 20 * (X_test[:, 2] - 0.5) ** 2 + 10 * X_test[:, 3] + 5 * X_test[:, 4]
np.testing.assert_array_equal(y_true,y_test)
def test_polyuq_prescribed(self):
"""
Tests the get poly uq routine when variance data is given in sampling_args.
"""
# Generate data
dim = 1
n = 5
N = 100
data_noise = 0.0
state = np.random.RandomState(42)
our_function = lambda x: 0.3 * x**4 - 1.6 * x**3 + 0.6 * x**2 + 2.4 * x - 0.5
X = state.uniform(-1, 1, N)
y = our_function(X)
X_train, X_test, y_train, y_test = datasets.train_test_split(
X, y, train=0.7, random_seed=42)
N_train = X_train.shape[0]
N_test = X_test.shape[0]
# Array of prescribed variances at each training data point
y_var = state.uniform(0.05, 0.2, N_train)**2
# Fit poly with prescribed variances
param = Parameter(distribution='Uniform', lower=-1, upper=1, order=n)
myParameters = [param for i in range(dim)
] # one-line for loop for parameters
myBasis = Basis('univariate')
poly = Poly(myParameters,
myBasis,
method='least-squares',
sampling_args={
'sample-points': X_train.reshape(-1, 1),
'sample-outputs': y_train.reshape(-1, 1),
'sample-output-variances': y_var
})
poly.set_model()
y_pred, y_std = poly.get_polyfit(X_test, uq=True)
np.testing.assert_array_almost_equal(y_std.mean(),
0.682095574,
decimal=5,
err_msg='Problem!')
def test_polyuq_empirical(self):
"""
Tests the get poly eq routine when no variance data is given, i.e. when estimating the
empirical variance from training data.
"""
# Generate data
dim = 3
n = 1
N = 200
data_noise = 0.05
X, y = datasets.gen_linear(n_observations=N,
n_dim=dim,
bias=0.5,
n_relevent=1,
noise=data_noise,
random_seed=1)
X_train, X_test, y_train, y_test = datasets.train_test_split(
X, y, train=0.7, random_seed=42)
N_train = X_train.shape[0]
N_test = X_test.shape[0]
# Fit poly and approx its variance
param = Parameter(distribution='Uniform', lower=-1, upper=1, order=n)
myParameters = [param for i in range(dim)
] # one-line for loop for parameters
myBasis = Basis('tensor-grid')
poly = Poly(myParameters,
myBasis,
method='least-squares',
sampling_args={
'sample-points': X_train,
'sample-outputs': y_train.reshape(-1, 1)
})
poly.set_model()
y_pred, y_std = poly.get_polyfit(X_test, uq=True)
np.testing.assert_array_almost_equal(y_std.mean(),
0.327769998,
decimal=5,
err_msg='Problem!')
def test_ElasticNet_linear(self):
"""
Tests elastic-net regularisation on linear (1st order) synthetic data with irrelevent features.
"""
# Generate 10D linear test data with 2 relevent features
X, y = datasets.gen_linear(n_observations=500,
n_dim=10,
bias=0.5,
n_relevent=2,
noise=0.2,
random_seed=1)
X_train, X_test, y_train, y_test = datasets.train_test_split(
X, y, train=0.8, random_seed=42)
# Define param and basis
s = Parameter(distribution='uniform',
lower=-1,
upper=1,
order=1,
endpoints='both')
param = [s for _ in range(X.shape[1])]
basis = Basis('total-order')
# Fit Poly with OLS and Elastic Net (but with lambda=0 so effectively OLS) and check r2 scores match
poly_OLS = Poly(parameters=param,
basis=basis,
method='least-squares',
sampling_args={
'mesh': 'user-defined',
'sample-points': X_train,
'sample-outputs': y_train.reshape(-1, 1)
})
poly_OLS.set_model()
_, r2_OLS = poly_OLS.get_polyscore(X_test=X_test, y_test=y_test)
poly_EN = poly = Poly(parameters=param,
basis=basis,
method='elastic-net',
sampling_args={
'mesh': 'user-defined',
'sample-points': X_train,
'sample-outputs': y_train.reshape(-1, 1)
},
solver_args={
'param1': 0.0,
'param2': 0.5
})
poly_EN.set_model()
_, r2_EN = poly_EN.get_polyscore(X_test=X_test, y_test=y_test)
np.testing.assert_array_almost_equal(r2_OLS,
r2_EN,
decimal=4,
err_msg='Problem!')
# Now fit Poly with LASSO (alpha/param2 = 1.0) and check r2 improved (it should because irrelevent features + noise)
poly_LASSO = Poly(parameters=param,
basis=basis,
method='elastic-net',
sampling_args={
'mesh': 'user-defined',
'sample-points': X_train,
'sample-outputs': y_train.reshape(-1, 1)
},
solver_args={
'param1': 0.015,
'param2': 1.0
})
poly_LASSO.set_model()
_, r2_LASSO = poly_LASSO.get_polyscore(X_test=X_test, y_test=y_test)
self.assertTrue(r2_LASSO > r2_OLS)
# Finally, check LASSO has shrunk irrelevent Poly coefficients
coeffs = poly_LASSO.get_coefficients().squeeze()
ideal_coeffs = 3 #As tensor-grid, order=1, relevent_dims=2
idx = np.abs(coeffs).argsort()[::-1]
irrelevent_coeffs = np.sum(np.abs(
coeffs[idx[ideal_coeffs:]])) / np.sum(np.abs(coeffs))
self.assertTrue(irrelevent_coeffs < 1e-5,
msg='irrelevent_coeffs = %.2e' % irrelevent_coeffs)