def _test_ridge_loo(filter_):
# test that can work with both dense or sparse matrices
n_samples = X_diabetes.shape[0]
ret = []
ridge_gcv = _RidgeGCV(fit_intercept=False)
ridge = Ridge(fit_intercept=False)
# generalized cross-validation (efficient leave-one-out)
K, v, Q = ridge_gcv._pre_compute(X_diabetes, y_diabetes)
errors, c = ridge_gcv._errors(v, Q, y_diabetes, 1.0)
values, c = ridge_gcv._values(K, v, Q, y_diabetes, 1.0)
# brute-force leave-one-out: remove one example at a time
errors2 = []
values2 = []
for i in range(n_samples):
sel = np.arange(n_samples) != i
X_new = X_diabetes[sel]
y_new = y_diabetes[sel]
ridge.fit(X_new, y_new)
value = ridge.predict([X_diabetes[i]])[0]
error = (y_diabetes[i] - value) ** 2
errors2.append(error)
values2.append(value)
# check that efficient and brute-force LOO give same results
assert_almost_equal(errors, errors2)
assert_almost_equal(values, values2)
# check best alpha
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
best_alpha = ridge_gcv.best_alpha
ret.append(best_alpha)
# check that we get same best alpha with custom loss_func
ridge_gcv2 = _RidgeGCV(fit_intercept=False, loss_func=mean_squared_error)
ridge_gcv2.fit(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv2.best_alpha, best_alpha)
# check that we get same best alpha with sample weights
ridge_gcv.fit(filter_(X_diabetes), y_diabetes,
sample_weight=np.ones(n_samples))
assert_equal(ridge_gcv.best_alpha, best_alpha)
# simulate several responses
Y = np.vstack((y_diabetes, y_diabetes)).T
ridge_gcv.fit(filter_(X_diabetes), Y)
Y_pred = ridge_gcv.predict(filter_(X_diabetes))
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
y_pred = ridge_gcv.predict(filter_(X_diabetes))
assert_array_almost_equal(np.vstack((y_pred, y_pred)).T,
Y_pred, decimal=5)
return ret
def _test_ridge_loo(filter_):
# test that can work with both dense or sparse matrices
n_samples = X_diabetes.shape[0]
ret = []
ridge_gcv = _RidgeGCV(fit_intercept=False)
ridge = Ridge(fit_intercept=False)
# generalized cross-validation (efficient leave-one-out)
K, v, Q = ridge_gcv._pre_compute(X_diabetes, y_diabetes)
errors, c = ridge_gcv._errors(v, Q, y_diabetes, 1.0)
values, c = ridge_gcv._values(K, v, Q, y_diabetes, 1.0)
# brute-force leave-one-out: remove one example at a time
errors2 = []
values2 = []
for i in range(n_samples):
sel = np.arange(n_samples) != i
X_new = X_diabetes[sel]
y_new = y_diabetes[sel]
ridge.fit(X_new, y_new)
value = ridge.predict([X_diabetes[i]])[0]
error = (y_diabetes[i] - value)**2
errors2.append(error)
values2.append(value)
# check that efficient and brute-force LOO give same results
assert_almost_equal(errors, errors2)
assert_almost_equal(values, values2)
# check best alpha
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
best_alpha = ridge_gcv.best_alpha
ret.append(best_alpha)
# check that we get same best alpha with custom loss_func
ridge_gcv2 = _RidgeGCV(fit_intercept=False, loss_func=mean_square_error)
ridge_gcv2.fit(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv2.best_alpha, best_alpha)
# check that we get same best alpha with sample weights
ridge_gcv.fit(filter_(X_diabetes),
y_diabetes,
sample_weight=np.ones(n_samples))
assert_equal(ridge_gcv.best_alpha, best_alpha)
# simulate several responses
Y = np.vstack((y_diabetes, y_diabetes)).T
ridge_gcv.fit(filter_(X_diabetes), Y)
Y_pred = ridge_gcv.predict(filter_(X_diabetes))
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
y_pred = ridge_gcv.predict(filter_(X_diabetes))
assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=5)
return ret
def _test_ridge_loo(filter_):
# test that can work with both dense or sparse matrices
n_samples = X_diabetes.shape[0]
ret = []
fit_intercept = filter_ == DENSE_FILTER
ridge_gcv = _RidgeGCV(fit_intercept=fit_intercept)
# check best alpha
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
alpha_ = ridge_gcv.alpha_
ret.append(alpha_)
# check that we get same best alpha with custom loss_func
f = ignore_warnings
scoring = make_scorer(mean_squared_error, greater_is_better=False)
ridge_gcv2 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv2.fit)(filter_(X_diabetes), y_diabetes)
assert ridge_gcv2.alpha_ == pytest.approx(alpha_)
# check that we get same best alpha with custom score_func
func = lambda x, y: -mean_squared_error(x, y)
scoring = make_scorer(func)
ridge_gcv3 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv3.fit)(filter_(X_diabetes), y_diabetes)
assert ridge_gcv3.alpha_ == pytest.approx(alpha_)
# check that we get same best alpha with a scorer
scorer = get_scorer('neg_mean_squared_error')
ridge_gcv4 = RidgeCV(fit_intercept=False, scoring=scorer)
ridge_gcv4.fit(filter_(X_diabetes), y_diabetes)
assert ridge_gcv4.alpha_ == pytest.approx(alpha_)
# check that we get same best alpha with sample weights
if filter_ == DENSE_FILTER:
ridge_gcv.fit(filter_(X_diabetes),
y_diabetes,
sample_weight=np.ones(n_samples))
assert ridge_gcv.alpha_ == pytest.approx(alpha_)
# simulate several responses
Y = np.vstack((y_diabetes, y_diabetes)).T
ridge_gcv.fit(filter_(X_diabetes), Y)
Y_pred = ridge_gcv.predict(filter_(X_diabetes))
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
y_pred = ridge_gcv.predict(filter_(X_diabetes))
assert_allclose(np.vstack((y_pred, y_pred)).T, Y_pred, rtol=1e-5)
return ret
def _test_ridge_loo(filter_):
# test that can work with both dense or sparse matrices
n_samples = X_diabetes.shape[0]
ret = []
fit_intercept = filter_ == DENSE_FILTER
ridge_gcv = _RidgeGCV(fit_intercept=fit_intercept)
# check best alpha
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
alpha_ = ridge_gcv.alpha_
ret.append(alpha_)
# check that we get same best alpha with custom loss_func
f = ignore_warnings
scoring = make_scorer(mean_squared_error, greater_is_better=False)
ridge_gcv2 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv2.fit)(filter_(X_diabetes), y_diabetes)
assert ridge_gcv2.alpha_ == pytest.approx(alpha_)
# check that we get same best alpha with custom score_func
func = lambda x, y: -mean_squared_error(x, y)
scoring = make_scorer(func)
ridge_gcv3 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv3.fit)(filter_(X_diabetes), y_diabetes)
assert ridge_gcv3.alpha_ == pytest.approx(alpha_)
# check that we get same best alpha with a scorer
scorer = get_scorer('neg_mean_squared_error')
ridge_gcv4 = RidgeCV(fit_intercept=False, scoring=scorer)
ridge_gcv4.fit(filter_(X_diabetes), y_diabetes)
assert ridge_gcv4.alpha_ == pytest.approx(alpha_)
# check that we get same best alpha with sample weights
if filter_ == DENSE_FILTER:
ridge_gcv.fit(filter_(X_diabetes), y_diabetes,
sample_weight=np.ones(n_samples))
assert ridge_gcv.alpha_ == pytest.approx(alpha_)
# simulate several responses
Y = np.vstack((y_diabetes, y_diabetes)).T
ridge_gcv.fit(filter_(X_diabetes), Y)
Y_pred = ridge_gcv.predict(filter_(X_diabetes))
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
y_pred = ridge_gcv.predict(filter_(X_diabetes))
assert_allclose(np.vstack((y_pred, y_pred)).T,
Y_pred, rtol=1e-5)
return ret
def test_compute_covariance(shape, uniform_weights):
rng = np.random.RandomState(0)
X = rng.randn(*shape)
if uniform_weights:
sw = np.ones(X.shape[0])
else:
sw = rng.chisquare(1, shape[0])
sqrt_sw = np.sqrt(sw)
X_mean = np.average(X, axis=0, weights=sw)
X_centered = (X - X_mean) * sqrt_sw[:, None]
true_covariance = X_centered.T.dot(X_centered)
X_sparse = sp.csr_matrix(X * sqrt_sw[:, None])
gcv = _RidgeGCV(fit_intercept=True)
computed_cov, computed_mean = gcv._compute_covariance(X_sparse, sqrt_sw)
assert_allclose(X_mean, computed_mean)
assert_allclose(true_covariance, computed_cov)
def test_compute_covariance(shape, uniform_weights):
rng = np.random.RandomState(0)
X = rng.randn(*shape)
if uniform_weights:
sw = np.ones(X.shape[0])
else:
sw = rng.chisquare(1, shape[0])
sqrt_sw = np.sqrt(sw)
X_mean = np.average(X, axis=0, weights=sw)
X_centered = (X - X_mean) * sqrt_sw[:, None]
true_covariance = X_centered.T.dot(X_centered)
X_sparse = sp.csr_matrix(X * sqrt_sw[:, None])
gcv = _RidgeGCV(fit_intercept=True)
computed_cov, computed_mean = gcv._compute_covariance(X_sparse, sqrt_sw)
assert_allclose(X_mean, computed_mean)
assert_allclose(true_covariance, computed_cov)
def test_errors_and_values_svd_helper():
ridgecv = _RidgeGCV()
rng = check_random_state(42)
alpha = 1.
for n, p in zip((5, 10), (12, 6)):
y = rng.randn(n)
v = rng.randn(p)
U = rng.randn(n, p)
UT_y = U.T.dot(y)
G_diag, c = ridgecv._errors_and_values_svd_helper(alpha, y, v, U, UT_y)
# test that helper function behaves as expected
out, c_ = ridgecv._errors_svd(alpha, y, v, U, UT_y)
np.testing.assert_array_equal(out, (c / G_diag)**2)
np.testing.assert_array_equal(c, c)
out, c_ = ridgecv._values_svd(alpha, y, v, U, UT_y)
np.testing.assert_array_equal(out, y - (c / G_diag))
np.testing.assert_array_equal(c_, c)
def test_errors_and_values_helper():
ridgecv = _RidgeGCV()
rng = check_random_state(42)
alpha = 1.
n = 5
y = rng.randn(n)
v = rng.randn(n)
Q = rng.randn(len(v), len(v))
QT_y = Q.T.dot(y)
G_diag, c = ridgecv._errors_and_values_helper(alpha, y, v, Q, QT_y)
# test that helper function behaves as expected
out, c_ = ridgecv._errors(alpha, y, v, Q, QT_y)
np.testing.assert_array_equal(out, (c / G_diag)**2)
np.testing.assert_array_equal(c, c)
out, c_ = ridgecv._values(alpha, y, v, Q, QT_y)
np.testing.assert_array_equal(out, y - (c / G_diag))
np.testing.assert_array_equal(c_, c)
def test_errors_and_values_svd_helper():
ridgecv = _RidgeGCV()
rng = check_random_state(42)
alpha = 1.
for n, p in zip((5, 10), (12, 6)):
y = rng.randn(n)
v = rng.randn(p)
U = rng.randn(n, p)
UT_y = U.T.dot(y)
G_diag, c = ridgecv._errors_and_values_svd_helper(alpha, y, v, U, UT_y)
# test that helper function behaves as expected
out, c_ = ridgecv._errors_svd(alpha, y, v, U, UT_y)
np.testing.assert_array_equal(out, (c / G_diag) ** 2)
np.testing.assert_array_equal(c, c)
out, c_ = ridgecv._values_svd(alpha, y, v, U, UT_y)
np.testing.assert_array_equal(out, y - (c / G_diag))
np.testing.assert_array_equal(c_, c)
def test_errors_and_values_helper():
ridgecv = _RidgeGCV()
rng = check_random_state(42)
alpha = 1.
n = 5
y = rng.randn(n)
v = rng.randn(n)
Q = rng.randn(len(v), len(v))
QT_y = Q.T.dot(y)
G_diag, c = ridgecv._errors_and_values_helper(alpha, y, v, Q, QT_y)
# test that helper function behaves as expected
out, c_ = ridgecv._errors(alpha, y, v, Q, QT_y)
np.testing.assert_array_equal(out, (c / G_diag) ** 2)
np.testing.assert_array_equal(c, c)
out, c_ = ridgecv._values(alpha, y, v, Q, QT_y)
np.testing.assert_array_equal(out, y - (c / G_diag))
np.testing.assert_array_equal(c_, c)
def _test_ridge_loo(filter_):
# test that can work with both dense or sparse matrices
n_samples = X_diabetes.shape[0]
ret = []
ridge_gcv = _RidgeGCV(fit_intercept=False)
ridge = Ridge(alpha=1.0, fit_intercept=False)
# generalized cross-validation (efficient leave-one-out)
decomp = ridge_gcv._pre_compute(X_diabetes, y_diabetes)
errors, c = ridge_gcv._errors(1.0, y_diabetes, *decomp)
values, c = ridge_gcv._values(1.0, y_diabetes, *decomp)
# brute-force leave-one-out: remove one example at a time
errors2 = []
values2 = []
for i in range(n_samples):
sel = np.arange(n_samples) != i
X_new = X_diabetes[sel]
y_new = y_diabetes[sel]
ridge.fit(X_new, y_new)
value = ridge.predict([X_diabetes[i]])[0]
error = (y_diabetes[i] - value) ** 2
errors2.append(error)
values2.append(value)
# check that efficient and brute-force LOO give same results
assert_almost_equal(errors, errors2)
assert_almost_equal(values, values2)
# generalized cross-validation (efficient leave-one-out,
# SVD variation)
decomp = ridge_gcv._pre_compute_svd(X_diabetes, y_diabetes)
errors3, c = ridge_gcv._errors_svd(ridge.alpha, y_diabetes, *decomp)
values3, c = ridge_gcv._values_svd(ridge.alpha, y_diabetes, *decomp)
# check that efficient and SVD efficient LOO give same results
assert_almost_equal(errors, errors3)
assert_almost_equal(values, values3)
# check best alpha
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
alpha_ = ridge_gcv.alpha_
ret.append(alpha_)
# check that we get same best alpha with custom loss_func
f = ignore_warnings
scoring = make_scorer(mean_squared_error, greater_is_better=False)
ridge_gcv2 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv2.fit)(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv2.alpha_, alpha_)
# check that we get same best alpha with custom score_func
func = lambda x, y: -mean_squared_error(x, y)
scoring = make_scorer(func)
ridge_gcv3 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv3.fit)(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv3.alpha_, alpha_)
# check that we get same best alpha with a scorer
scorer = get_scorer('mean_squared_error')
ridge_gcv4 = RidgeCV(fit_intercept=False, scoring=scorer)
ridge_gcv4.fit(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv4.alpha_, alpha_)
# check that we get same best alpha with sample weights
ridge_gcv.fit(filter_(X_diabetes), y_diabetes,
sample_weight=np.ones(n_samples))
assert_equal(ridge_gcv.alpha_, alpha_)
# simulate several responses
Y = np.vstack((y_diabetes, y_diabetes)).T
ridge_gcv.fit(filter_(X_diabetes), Y)
Y_pred = ridge_gcv.predict(filter_(X_diabetes))
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
y_pred = ridge_gcv.predict(filter_(X_diabetes))
assert_array_almost_equal(np.vstack((y_pred, y_pred)).T,
Y_pred, decimal=5)
return ret
def _test_ridge_loo(filter_):
# test that can work with both dense or sparse matrices
n_samples = X_diabetes.shape[0]
ret = []
ridge_gcv = _RidgeGCV(fit_intercept=False)
ridge = Ridge(alpha=1.0, fit_intercept=False)
# generalized cross-validation (efficient leave-one-out)
decomp = ridge_gcv._pre_compute(X_diabetes, y_diabetes)
errors, c = ridge_gcv._errors(1.0, y_diabetes, *decomp)
values, c = ridge_gcv._values(1.0, y_diabetes, *decomp)
# brute-force leave-one-out: remove one example at a time
errors2 = []
values2 = []
for i in range(n_samples):
sel = np.arange(n_samples) != i
X_new = X_diabetes[sel]
y_new = y_diabetes[sel]
ridge.fit(X_new, y_new)
value = ridge.predict([X_diabetes[i]])[0]
error = (y_diabetes[i] - value)**2
errors2.append(error)
values2.append(value)
# check that efficient and brute-force LOO give same results
assert_almost_equal(errors, errors2)
assert_almost_equal(values, values2)
# generalized cross-validation (efficient leave-one-out,
# SVD variation)
decomp = ridge_gcv._pre_compute_svd(X_diabetes, y_diabetes)
errors3, c = ridge_gcv._errors_svd(ridge.alpha, y_diabetes, *decomp)
values3, c = ridge_gcv._values_svd(ridge.alpha, y_diabetes, *decomp)
# check that efficient and SVD efficient LOO give same results
assert_almost_equal(errors, errors3)
assert_almost_equal(values, values3)
# check best alpha
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
alpha_ = ridge_gcv.alpha_
ret.append(alpha_)
# check that we get same best alpha with custom loss_func
f = ignore_warnings
scoring = make_scorer(mean_squared_error, greater_is_better=False)
ridge_gcv2 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv2.fit)(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv2.alpha_, alpha_)
# check that we get same best alpha with custom score_func
func = lambda x, y: -mean_squared_error(x, y)
scoring = make_scorer(func)
ridge_gcv3 = RidgeCV(fit_intercept=False, scoring=scoring)
f(ridge_gcv3.fit)(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv3.alpha_, alpha_)
# check that we get same best alpha with a scorer
scorer = get_scorer('mean_squared_error')
ridge_gcv4 = RidgeCV(fit_intercept=False, scoring=scorer)
ridge_gcv4.fit(filter_(X_diabetes), y_diabetes)
assert_equal(ridge_gcv4.alpha_, alpha_)
# check that we get same best alpha with sample weights
ridge_gcv.fit(filter_(X_diabetes),
y_diabetes,
sample_weight=np.ones(n_samples))
assert_equal(ridge_gcv.alpha_, alpha_)
# simulate several responses
Y = np.vstack((y_diabetes, y_diabetes)).T
ridge_gcv.fit(filter_(X_diabetes), Y)
Y_pred = ridge_gcv.predict(filter_(X_diabetes))
ridge_gcv.fit(filter_(X_diabetes), y_diabetes)
y_pred = ridge_gcv.predict(filter_(X_diabetes))
assert_array_almost_equal(np.vstack((y_pred, y_pred)).T, Y_pred, decimal=5)
return ret