def test_asymmetric_error(quantile):
"""Test quantile regression for asymmetric distributed targets."""
n_samples = 1000
rng = np.random.RandomState(42)
X = np.concatenate(
(
np.abs(rng.randn(n_samples)[:, None]),
-rng.randint(2, size=(n_samples, 1)),
),
axis=1,
)
intercept = 1.23
coef = np.array([0.5, -2])
# Take care that X @ coef + intercept > 0
assert np.min(X @ coef + intercept) > 0
# For an exponential distribution with rate lambda, e.g. exp(-lambda * x),
# the quantile at level q is:
# quantile(q) = - log(1 - q) / lambda
# scale = 1/lambda = -quantile(q) / log(1 - q)
y = rng.exponential(
scale=-(X @ coef + intercept) / np.log(1 - quantile), size=n_samples
)
model = QuantileRegressor(
quantile=quantile,
alpha=0,
solver="highs",
).fit(X, y)
# This test can be made to pass with any solver but in the interest
# of sparing continuous integration resources, the test is performed
# with the fastest solver only.
assert model.intercept_ == approx(intercept, rel=0.2)
assert_allclose(model.coef_, coef, rtol=0.6)
assert_allclose(np.mean(model.predict(X) > y), quantile, atol=1e-2)
# Now compare to Nelder-Mead optimization with L1 penalty
alpha = 0.01
model.set_params(alpha=alpha).fit(X, y)
model_coef = np.r_[model.intercept_, model.coef_]
def func(coef):
loss = mean_pinball_loss(y, X @ coef[1:] + coef[0], alpha=quantile)
L1 = np.sum(np.abs(coef[1:]))
return loss + alpha * L1
res = minimize(
fun=func,
x0=[1, 0, -1],
method="Nelder-Mead",
tol=1e-12,
options={"maxiter": 2000},
)
assert func(model_coef) == approx(func(res.x))
assert_allclose(model.intercept_, res.x[0])
assert_allclose(model.coef_, res.x[1:])
assert_allclose(np.mean(model.predict(X) > y), quantile, atol=1e-2)
def test_quantile_sample_weight():
# test that with unequal sample weights we still estimate weighted fraction
n = 1000
X, y = make_regression(n_samples=n, n_features=5, random_state=0, noise=10.0)
weight = np.ones(n)
# when we increase weight of upper observations,
# estimate of quantile should go up
weight[y > y.mean()] = 100
quant = QuantileRegressor(quantile=0.5, alpha=1e-8, solver_options={"lstsq": False})
quant.fit(X, y, sample_weight=weight)
fraction_below = np.mean(y < quant.predict(X))
assert fraction_below > 0.5
weighted_fraction_below = np.average(y < quant.predict(X), weights=weight)
assert weighted_fraction_below == approx(0.5, abs=3e-2)
def test_quantile_estimates_calibration(q):
# Test that model estimates percentage of points below the prediction
X, y = make_regression(n_samples=1000, n_features=20, random_state=0, noise=1.0)
quant = QuantileRegressor(
quantile=q,
alpha=0,
solver_options={"lstsq": False},
).fit(X, y)
assert np.mean(y < quant.predict(X)) == approx(q, abs=1e-2)
def test_quantile_equals_huber_for_low_epsilon(fit_intercept):
X, y = make_regression(n_samples=100, n_features=20, random_state=0, noise=1.0)
alpha = 1e-4
huber = HuberRegressor(
epsilon=1 + 1e-4, alpha=alpha, fit_intercept=fit_intercept
).fit(X, y)
quant = QuantileRegressor(alpha=alpha, fit_intercept=fit_intercept).fit(X, y)
assert_allclose(huber.coef_, quant.coef_, atol=1e-1)
if fit_intercept:
assert huber.intercept_ == approx(quant.intercept_, abs=1e-1)
# check that we still predict fraction
assert np.mean(y < quant.predict(X)) == approx(0.5, abs=1e-1)
def test_sparse_input(sparse_format, solver, fit_intercept):
"""Test that sparse and dense X give same results."""
X, y = make_regression(n_samples=100, n_features=20, random_state=1, noise=1.0)
X_sparse = sparse_format(X)
alpha = 1e-4
quant_dense = QuantileRegressor(alpha=alpha, fit_intercept=fit_intercept).fit(X, y)
quant_sparse = QuantileRegressor(
alpha=alpha, fit_intercept=fit_intercept, solver=solver
).fit(X_sparse, y)
assert_allclose(quant_sparse.coef_, quant_dense.coef_, rtol=1e-2)
if fit_intercept:
assert quant_sparse.intercept_ == approx(quant_dense.intercept_)
# check that we still predict fraction
assert 0.45 <= np.mean(y < quant_sparse.predict(X_sparse)) <= 0.55
def get_calibration(train_approximation_distances, train_target_distances,
val_approximation_distances, val_target_distances,
quantile):
qr = QuantileRegressor(quantile=quantile, alpha=0, solver='highs')
qr.fit(train_approximation_distances.reshape(-1, 1),
train_target_distances)
predicted_target_distances = qr.predict(
val_approximation_distances.reshape(-1, 1)).squeeze()
num_leq = 0
for predicted_target, val_target in zip(predicted_target_distances,
val_target_distances):
if val_target <= predicted_target:
num_leq += 1
return num_leq / len(val_target_distances), predicted_target_distances