from itertools import product
import numpy as np
import pytest
from numpy.testing import assert_allclose
from scipy import optimize
from scipy.special import factorial, xlogy
from sklearn.dummy import DummyRegressor
from sklearn.exceptions import UndefinedMetricWarning
from sklearn.metrics import (
d2_absolute_error_score,
d2_pinball_score,
d2_tweedie_score,
explained_variance_score,
make_scorer,
max_error,
mean_absolute_error,
mean_absolute_percentage_error,
mean_pinball_loss,
mean_squared_error,
mean_squared_log_error,
mean_tweedie_deviance,
median_absolute_error,
r2_score,
root_mean_squared_error,
root_mean_squared_log_error,
)
from sklearn.metrics._regression import _check_reg_targets
from sklearn.model_selection import GridSearchCV
from sklearn.utils._testing import (
assert_almost_equal,
assert_array_almost_equal,
assert_array_equal,
)
def test_regression_metrics(n_samples=50):
y_true = np.arange(n_samples)
y_pred = y_true + 1
y_pred_2 = y_true - 1
assert_almost_equal(mean_squared_error(y_true, y_pred), 1.0)
assert_almost_equal(
mean_squared_log_error(y_true, y_pred),
mean_squared_error(np.log(1 + y_true), np.log(1 + y_pred)),
)
assert_almost_equal(mean_absolute_error(y_true, y_pred), 1.0)
assert_almost_equal(mean_pinball_loss(y_true, y_pred), 0.5)
assert_almost_equal(mean_pinball_loss(y_true, y_pred_2), 0.5)
assert_almost_equal(mean_pinball_loss(y_true, y_pred, alpha=0.4), 0.6)
assert_almost_equal(mean_pinball_loss(y_true, y_pred_2, alpha=0.4), 0.4)
assert_almost_equal(median_absolute_error(y_true, y_pred), 1.0)
mape = mean_absolute_percentage_error(y_true, y_pred)
assert np.isfinite(mape)
assert mape > 1e6
assert_almost_equal(max_error(y_true, y_pred), 1.0)
assert_almost_equal(r2_score(y_true, y_pred), 0.995, 2)
assert_almost_equal(r2_score(y_true, y_pred, force_finite=False), 0.995, 2)
assert_almost_equal(explained_variance_score(y_true, y_pred), 1.0)
assert_almost_equal(
explained_variance_score(y_true, y_pred, force_finite=False), 1.0
)
assert_almost_equal(
mean_tweedie_deviance(y_true, y_pred, power=0),
mean_squared_error(y_true, y_pred),
)
assert_almost_equal(
d2_tweedie_score(y_true, y_pred, power=0), r2_score(y_true, y_pred)
)
dev_median = np.abs(y_true - np.median(y_true)).sum()
assert_array_almost_equal(
d2_absolute_error_score(y_true, y_pred),
1 - np.abs(y_true - y_pred).sum() / dev_median,
)
alpha = 0.2
pinball_loss = lambda y_true, y_pred, alpha: alpha * np.maximum(
y_true - y_pred, 0
) + (1 - alpha) * np.maximum(y_pred - y_true, 0)
y_quantile = np.percentile(y_true, q=alpha * 100)
assert_almost_equal(
d2_pinball_score(y_true, y_pred, alpha=alpha),
1
- pinball_loss(y_true, y_pred, alpha).sum()
/ pinball_loss(y_true, y_quantile, alpha).sum(),
)
assert_almost_equal(
d2_absolute_error_score(y_true, y_pred),
d2_pinball_score(y_true, y_pred, alpha=0.5),
)
# Tweedie deviance needs positive y_pred, except for p=0,
# p>=2 needs positive y_true
# results evaluated by sympy
y_true = np.arange(1, 1 + n_samples)
y_pred = 2 * y_true
n = n_samples
assert_almost_equal(
mean_tweedie_deviance(y_true, y_pred, power=-1),
5 / 12 * n * (n**2 + 2 * n + 1),
)
assert_almost_equal(
mean_tweedie_deviance(y_true, y_pred, power=1), (n + 1) * (1 - np.log(2))
)
assert_almost_equal(
mean_tweedie_deviance(y_true, y_pred, power=2), 2 * np.log(2) - 1
)
assert_almost_equal(
mean_tweedie_deviance(y_true, y_pred, power=3 / 2),
((6 * np.sqrt(2) - 8) / n) * np.sqrt(y_true).sum(),
)
assert_almost_equal(
mean_tweedie_deviance(y_true, y_pred, power=3), np.sum(1 / y_true) / (4 * n)
)
dev_mean = 2 * np.mean(xlogy(y_true, 2 * y_true / (n + 1)))
assert_almost_equal(
d2_tweedie_score(y_true, y_pred, power=1),
1 - (n + 1) * (1 - np.log(2)) / dev_mean,
)
dev_mean = 2 * np.log((n + 1) / 2) - 2 / n * np.log(factorial(n))
assert_almost_equal(
d2_tweedie_score(y_true, y_pred, power=2), 1 - (2 * np.log(2) - 1) / dev_mean
)
def test_root_mean_squared_error_multioutput_raw_value():
# non-regression test for
# https://github.com/scikit-learn/scikit-learn/pull/16323
mse = mean_squared_error([[1]], [[10]], multioutput="raw_values")
rmse = root_mean_squared_error([[1]], [[10]], multioutput="raw_values")
assert np.sqrt(mse) == pytest.approx(rmse)
def test_multioutput_regression():
y_true = np.array([[1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 0, 1]])
y_pred = np.array([[0, 0, 0, 1], [1, 0, 1, 1], [0, 0, 0, 1]])
error = mean_squared_error(y_true, y_pred)
assert_almost_equal(error, (1.0 / 3 + 2.0 / 3 + 2.0 / 3) / 4.0)
error = root_mean_squared_error(y_true, y_pred)
assert_almost_equal(error, 0.454, decimal=2)
error = mean_squared_log_error(y_true, y_pred)
assert_almost_equal(error, 0.200, decimal=2)
error = root_mean_squared_log_error(y_true, y_pred)
assert_almost_equal(error, 0.315, decimal=2)
# mean_absolute_error and mean_squared_error are equal because
# it is a binary problem.
error = mean_absolute_error(y_true, y_pred)
assert_almost_equal(error, (1.0 + 2.0 / 3) / 4.0)
error = mean_pinball_loss(y_true, y_pred)
assert_almost_equal(error, (1.0 + 2.0 / 3) / 8.0)
error = np.around(mean_absolute_percentage_error(y_true, y_pred), decimals=2)
assert np.isfinite(error)
assert error > 1e6
error = median_absolute_error(y_true, y_pred)
assert_almost_equal(error, (1.0 + 1.0) / 4.0)
error = r2_score(y_true, y_pred, multioutput="variance_weighted")
assert_almost_equal(error, 1.0 - 5.0 / 2)
error = r2_score(y_true, y_pred, multioutput="uniform_average")
assert_almost_equal(error, -0.875)
score = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="raw_values")
raw_expected_score = [
1
- np.abs(y_true[:, i] - y_pred[:, i]).sum()
/ np.abs(y_true[:, i] - np.median(y_true[:, i])).sum()
for i in range(y_true.shape[1])
]
# in the last case, the denominator vanishes and hence we get nan,
# but since the numerator vanishes as well the expected score is 1.0
raw_expected_score = np.where(np.isnan(raw_expected_score), 1, raw_expected_score)
assert_array_almost_equal(score, raw_expected_score)
score = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="uniform_average")
assert_almost_equal(score, raw_expected_score.mean())
# constant `y_true` with force_finite=True leads to 1. or 0.
yc = [5.0, 5.0]
error = r2_score(yc, [5.0, 5.0], multioutput="variance_weighted")
assert_almost_equal(error, 1.0)
error = r2_score(yc, [5.0, 5.1], multioutput="variance_weighted")
assert_almost_equal(error, 0.0)
# Setting force_finite=False results in the nan for 4th output propagating
error = r2_score(
y_true, y_pred, multioutput="variance_weighted", force_finite=False
)
assert_almost_equal(error, np.nan)
error = r2_score(y_true, y_pred, multioutput="uniform_average", force_finite=False)
assert_almost_equal(error, np.nan)
# Dropping the 4th output to check `force_finite=False` for nominal
y_true = y_true[:, :-1]
y_pred = y_pred[:, :-1]
error = r2_score(y_true, y_pred, multioutput="variance_weighted")
error2 = r2_score(
y_true, y_pred, multioutput="variance_weighted", force_finite=False
)
assert_almost_equal(error, error2)
error = r2_score(y_true, y_pred, multioutput="uniform_average")
error2 = r2_score(y_true, y_pred, multioutput="uniform_average", force_finite=False)
assert_almost_equal(error, error2)
# constant `y_true` with force_finite=False leads to NaN or -Inf.
error = r2_score(
yc, [5.0, 5.0], multioutput="variance_weighted", force_finite=False
)
assert_almost_equal(error, np.nan)
error = r2_score(
yc, [5.0, 6.0], multioutput="variance_weighted", force_finite=False
)
assert_almost_equal(error, -np.inf)
def test_regression_metrics_at_limits():
# Single-sample case
# Note: for r2 and d2_tweedie see also test_regression_single_sample
assert_almost_equal(mean_squared_error([0.0], [0.0]), 0.0)
assert_almost_equal(root_mean_squared_error([0.0], [0.0]), 0.0)
assert_almost_equal(mean_squared_log_error([0.0], [0.0]), 0.0)
assert_almost_equal(mean_absolute_error([0.0], [0.0]), 0.0)
assert_almost_equal(mean_pinball_loss([0.0], [0.0]), 0.0)
assert_almost_equal(mean_absolute_percentage_error([0.0], [0.0]), 0.0)
assert_almost_equal(median_absolute_error([0.0], [0.0]), 0.0)
assert_almost_equal(max_error([0.0], [0.0]), 0.0)
assert_almost_equal(explained_variance_score([0.0], [0.0]), 1.0)
# Perfect cases
assert_almost_equal(r2_score([0.0, 1], [0.0, 1]), 1.0)
assert_almost_equal(d2_pinball_score([0.0, 1], [0.0, 1]), 1.0)
# Non-finite cases
# R² and explained variance have a fix by default for non-finite cases
for s in (r2_score, explained_variance_score):
assert_almost_equal(s([0, 0], [1, -1]), 0.0)
assert_almost_equal(s([0, 0], [1, -1], force_finite=False), -np.inf)
assert_almost_equal(s([1, 1], [1, 1]), 1.0)
assert_almost_equal(s([1, 1], [1, 1], force_finite=False), np.nan)
msg = (
"Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values."
)
with pytest.raises(ValueError, match=msg):
mean_squared_log_error([-1.0], [-1.0])
msg = (
"Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values."
)
with pytest.raises(ValueError, match=msg):
mean_squared_log_error([1.0, 2.0, 3.0], [1.0, -2.0, 3.0])
msg = (
"Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values."
)
with pytest.raises(ValueError, match=msg):
mean_squared_log_error([1.0, -2.0, 3.0], [1.0, 2.0, 3.0])
msg = (
"Root Mean Squared Logarithmic Error cannot be used when targets "
"contain negative values."
)
with pytest.raises(ValueError, match=msg):
root_mean_squared_log_error([1.0, -2.0, 3.0], [1.0, 2.0, 3.0])
# Tweedie deviance error
power = -1.2
assert_allclose(
mean_tweedie_deviance([0], [1.0], power=power), 2 / (2 - power), rtol=1e-3
)
msg = "can only be used on strictly positive y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.0], [0.0], power=power)
with pytest.raises(ValueError, match=msg):
d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
assert_almost_equal(mean_tweedie_deviance([0.0], [0.0], power=0), 0.0, 2)
power = 1.0
msg = "only be used on non-negative y and strictly positive y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.0], [0.0], power=power)
with pytest.raises(ValueError, match=msg):
d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
power = 1.5
assert_allclose(mean_tweedie_deviance([0.0], [1.0], power=power), 2 / (2 - power))
msg = "only be used on non-negative y and strictly positive y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.0], [0.0], power=power)
with pytest.raises(ValueError, match=msg):
d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
power = 2.0
assert_allclose(mean_tweedie_deviance([1.0], [1.0], power=power), 0.00, atol=1e-8)
msg = "can only be used on strictly positive y and y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.0], [0.0], power=power)
with pytest.raises(ValueError, match=msg):
d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
power = 3.0
assert_allclose(mean_tweedie_deviance([1.0], [1.0], power=power), 0.00, atol=1e-8)
msg = "can only be used on strictly positive y and y_pred."
with pytest.raises(ValueError, match=msg):
mean_tweedie_deviance([0.0], [0.0], power=power)
with pytest.raises(ValueError, match=msg):
d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
def test__check_reg_targets():
# All of length 3
EXAMPLES = [
("continuous", [1, 2, 3], 1),
("continuous", [[1], [2], [3]], 1),
("continuous-multioutput", [[1, 1], [2, 2], [3, 1]], 2),
("continuous-multioutput", [[5, 1], [4, 2], [3, 1]], 2),
("continuous-multioutput", [[1, 3, 4], [2, 2, 2], [3, 1, 1]], 3),
]
for (type1, y1, n_out1), (type2, y2, n_out2) in product(EXAMPLES, repeat=2):
if type1 == type2 and n_out1 == n_out2:
y_type, y_check1, y_check2, multioutput = _check_reg_targets(y1, y2, None)
assert type1 == y_type
if type1 == "continuous":
assert_array_equal(y_check1, np.reshape(y1, (-1, 1)))
assert_array_equal(y_check2, np.reshape(y2, (-1, 1)))
else:
assert_array_equal(y_check1, y1)
assert_array_equal(y_check2, y2)
else:
with pytest.raises(ValueError):
_check_reg_targets(y1, y2, None)
def test__check_reg_targets_exception():
invalid_multioutput = "this_value_is_not_valid"
expected_message = (
"Allowed 'multioutput' string values are.+You provided multioutput={!r}".format(
invalid_multioutput
)
)
with pytest.raises(ValueError, match=expected_message):
_check_reg_targets([1, 2, 3], [[1], [2], [3]], invalid_multioutput)
def test_regression_multioutput_array():
y_true = [[1, 2], [2.5, -1], [4.5, 3], [5, 7]]
y_pred = [[1, 1], [2, -1], [5, 4], [5, 6.5]]
mse = mean_squared_error(y_true, y_pred, multioutput="raw_values")
mae = mean_absolute_error(y_true, y_pred, multioutput="raw_values")
pbl = mean_pinball_loss(y_true, y_pred, multioutput="raw_values")
mape = mean_absolute_percentage_error(y_true, y_pred, multioutput="raw_values")
r = r2_score(y_true, y_pred, multioutput="raw_values")
evs = explained_variance_score(y_true, y_pred, multioutput="raw_values")
d2ps = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="raw_values")
evs2 = explained_variance_score(
y_true, y_pred, multioutput="raw_values", force_finite=False
)
assert_array_almost_equal(mse, [0.125, 0.5625], decimal=2)
assert_array_almost_equal(mae, [0.25, 0.625], decimal=2)
assert_array_almost_equal(pbl, [0.25 / 2, 0.625 / 2], decimal=2)
assert_array_almost_equal(mape, [0.0778, 0.2262], decimal=2)
assert_array_almost_equal(r, [0.95, 0.93], decimal=2)
assert_array_almost_equal(evs, [0.95, 0.93], decimal=2)
assert_array_almost_equal(d2ps, [0.833, 0.722], decimal=2)
assert_array_almost_equal(evs2, [0.95, 0.93], decimal=2)
# mean_absolute_error and mean_squared_error are equal because
# it is a binary problem.
y_true = [[0, 0]] * 4
y_pred = [[1, 1]] * 4
mse = mean_squared_error(y_true, y_pred, multioutput="raw_values")
mae = mean_absolute_error(y_true, y_pred, multioutput="raw_values")
pbl = mean_pinball_loss(y_true, y_pred, multioutput="raw_values")
r = r2_score(y_true, y_pred, multioutput="raw_values")
d2ps = d2_pinball_score(y_true, y_pred, multioutput="raw_values")
assert_array_almost_equal(mse, [1.0, 1.0], decimal=2)
assert_array_almost_equal(mae, [1.0, 1.0], decimal=2)
assert_array_almost_equal(pbl, [0.5, 0.5], decimal=2)
assert_array_almost_equal(r, [0.0, 0.0], decimal=2)
assert_array_almost_equal(d2ps, [0.0, 0.0], decimal=2)
r = r2_score([[0, -1], [0, 1]], [[2, 2], [1, 1]], multioutput="raw_values")
assert_array_almost_equal(r, [0, -3.5], decimal=2)
assert np.mean(r) == r2_score(
[[0, -1], [0, 1]], [[2, 2], [1, 1]], multioutput="uniform_average"
)
evs = explained_variance_score(
[[0, -1], [0, 1]], [[2, 2], [1, 1]], multioutput="raw_values"
)
assert_array_almost_equal(evs, [0, -1.25], decimal=2)
evs2 = explained_variance_score(
[[0, -1], [0, 1]],
[[2, 2], [1, 1]],
multioutput="raw_values",
force_finite=False,
)
assert_array_almost_equal(evs2, [-np.inf, -1.25], decimal=2)
# Checking for the condition in which both numerator and denominator is
# zero.
y_true = [[1, 3], [1, 2]]
y_pred = [[1, 4], [1, 1]]
r2 = r2_score(y_true, y_pred, multioutput="raw_values")
assert_array_almost_equal(r2, [1.0, -3.0], decimal=2)
assert np.mean(r2) == r2_score(y_true, y_pred, multioutput="uniform_average")
r22 = r2_score(y_true, y_pred, multioutput="raw_values", force_finite=False)
assert_array_almost_equal(r22, [np.nan, -3.0], decimal=2)
assert_almost_equal(
np.mean(r22),
r2_score(y_true, y_pred, multioutput="uniform_average", force_finite=False),
)
evs = explained_variance_score(y_true, y_pred, multioutput="raw_values")
assert_array_almost_equal(evs, [1.0, -3.0], decimal=2)
assert np.mean(evs) == explained_variance_score(y_true, y_pred)
d2ps = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput="raw_values")
assert_array_almost_equal(d2ps, [1.0, -1.0], decimal=2)
evs2 = explained_variance_score(
y_true, y_pred, multioutput="raw_values", force_finite=False
)
assert_array_almost_equal(evs2, [np.nan, -3.0], decimal=2)
assert_almost_equal(
np.mean(evs2), explained_variance_score(y_true, y_pred, force_finite=False)
)
# Handling msle separately as it does not accept negative inputs.
y_true = np.array([[0.5, 1], [1, 2], [7, 6]])
y_pred = np.array([[0.5, 2], [1, 2.5], [8, 8]])
msle = mean_squared_log_error(y_true, y_pred, multioutput="raw_values")
msle2 = mean_squared_error(
np.log(1 + y_true), np.log(1 + y_pred), multioutput="raw_values"
)
assert_array_almost_equal(msle, msle2, decimal=2)
def test_regression_custom_weights():
y_true = [[1, 2], [2.5, -1], [4.5, 3], [5, 7]]
y_pred = [[1, 1], [2, -1], [5, 4], [5, 6.5]]
msew = mean_squared_error(y_true, y_pred, multioutput=[0.4, 0.6])
rmsew = root_mean_squared_error(y_true, y_pred, multioutput=[0.4, 0.6])
maew = mean_absolute_error(y_true, y_pred, multioutput=[0.4, 0.6])
mapew = mean_absolute_percentage_error(y_true, y_pred, multioutput=[0.4, 0.6])
rw = r2_score(y_true, y_pred, multioutput=[0.4, 0.6])
evsw = explained_variance_score(y_true, y_pred, multioutput=[0.4, 0.6])
d2psw = d2_pinball_score(y_true, y_pred, alpha=0.5, multioutput=[0.4, 0.6])
evsw2 = explained_variance_score(
y_true, y_pred, multioutput=[0.4, 0.6], force_finite=False
)
assert_almost_equal(msew, 0.39, decimal=2)
assert_almost_equal(rmsew, 0.59, decimal=2)
assert_almost_equal(maew, 0.475, decimal=3)
assert_almost_equal(mapew, 0.1668, decimal=2)
assert_almost_equal(rw, 0.94, decimal=2)
assert_almost_equal(evsw, 0.94, decimal=2)
assert_almost_equal(d2psw, 0.766, decimal=2)
assert_almost_equal(evsw2, 0.94, decimal=2)
# Handling msle separately as it does not accept negative inputs.
y_true = np.array([[0.5, 1], [1, 2], [7, 6]])
y_pred = np.array([[0.5, 2], [1, 2.5], [8, 8]])
msle = mean_squared_log_error(y_true, y_pred, multioutput=[0.3, 0.7])
msle2 = mean_squared_error(
np.log(1 + y_true), np.log(1 + y_pred), multioutput=[0.3, 0.7]
)
assert_almost_equal(msle, msle2, decimal=2)
@pytest.mark.parametrize("metric", [r2_score, d2_tweedie_score, d2_pinball_score])
def test_regression_single_sample(metric):
y_true = [0]
y_pred = [1]
warning_msg = "not well-defined with less than two samples."
# Trigger the warning
with pytest.warns(UndefinedMetricWarning, match=warning_msg):
score = metric(y_true, y_pred)
assert np.isnan(score)
def test_tweedie_deviance_continuity():
n_samples = 100
y_true = np.random.RandomState(0).rand(n_samples) + 0.1
y_pred = np.random.RandomState(1).rand(n_samples) + 0.1
assert_allclose(
mean_tweedie_deviance(y_true, y_pred, power=0 - 1e-10),
mean_tweedie_deviance(y_true, y_pred, power=0),
)
# Ws we get closer to the limit, with 1e-12 difference the absolute
# tolerance to pass the below check increases. There are likely
# numerical precision issues on the edges of different definition
# regions.
assert_allclose(
mean_tweedie_deviance(y_true, y_pred, power=1 + 1e-10),
mean_tweedie_deviance(y_true, y_pred, power=1),
atol=1e-6,
)
assert_allclose(
mean_tweedie_deviance(y_true, y_pred, power=2 - 1e-10),
mean_tweedie_deviance(y_true, y_pred, power=2),
atol=1e-6,
)
assert_allclose(
mean_tweedie_deviance(y_true, y_pred, power=2 + 1e-10),
mean_tweedie_deviance(y_true, y_pred, power=2),
atol=1e-6,
)
def test_mean_absolute_percentage_error():
random_number_generator = np.random.RandomState(42)
y_true = random_number_generator.exponential(size=100)
y_pred = 1.2 * y_true
assert mean_absolute_percentage_error(y_true, y_pred) == pytest.approx(0.2)
@pytest.mark.parametrize(
"distribution", ["normal", "lognormal", "exponential", "uniform"]
)
@pytest.mark.parametrize("target_quantile", [0.05, 0.5, 0.75])
def test_mean_pinball_loss_on_constant_predictions(distribution, target_quantile):
if not hasattr(np, "quantile"):
pytest.skip(
"This test requires a more recent version of numpy "
"with support for np.quantile."
)
# Check that the pinball loss is minimized by the empirical quantile.
n_samples = 3000
rng = np.random.RandomState(42)
data = getattr(rng, distribution)(size=n_samples)
# Compute the best possible pinball loss for any constant predictor:
best_pred = np.quantile(data, target_quantile)
best_constant_pred = np.full(n_samples, fill_value=best_pred)
best_pbl = mean_pinball_loss(data, best_constant_pred, alpha=target_quantile)
# Evaluate the loss on a grid of quantiles
candidate_predictions = np.quantile(data, np.linspace(0, 1, 100))
for pred in candidate_predictions:
# Compute the pinball loss of a constant predictor:
constant_pred = np.full(n_samples, fill_value=pred)
pbl = mean_pinball_loss(data, constant_pred, alpha=target_quantile)
# Check that the loss of this constant predictor is greater or equal
# than the loss of using the optimal quantile (up to machine
# precision):
assert pbl >= best_pbl - np.finfo(best_pbl.dtype).eps
# Check that the value of the pinball loss matches the analytical
# formula.
expected_pbl = (pred - data[data < pred]).sum() * (1 - target_quantile) + (
data[data >= pred] - pred
).sum() * target_quantile
expected_pbl /= n_samples
assert_almost_equal(expected_pbl, pbl)
# Check that we can actually recover the target_quantile by minimizing the
# pinball loss w.r.t. the constant prediction quantile.
def objective_func(x):
constant_pred = np.full(n_samples, fill_value=x)
return mean_pinball_loss(data, constant_pred, alpha=target_quantile)
result = optimize.minimize(objective_func, data.mean(), method="Nelder-Mead")
assert result.success
# The minimum is not unique with limited data, hence the large tolerance.
assert result.x == pytest.approx(best_pred, rel=1e-2)
assert result.fun == pytest.approx(best_pbl)
def test_dummy_quantile_parameter_tuning():
# Integration test to check that it is possible to use the pinball loss to
# tune the hyperparameter of a quantile regressor. This is conceptually
# similar to the previous test but using the scikit-learn estimator and
# scoring API instead.
n_samples = 1000
rng = np.random.RandomState(0)
X = rng.normal(size=(n_samples, 5)) # Ignored
y = rng.exponential(size=n_samples)
all_quantiles = [0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95]
for alpha in all_quantiles:
neg_mean_pinball_loss = make_scorer(
mean_pinball_loss,
alpha=alpha,
greater_is_better=False,
)
regressor = DummyRegressor(strategy="quantile", quantile=0.25)
grid_search = GridSearchCV(
regressor,
param_grid=dict(quantile=all_quantiles),
scoring=neg_mean_pinball_loss,
).fit(X, y)
assert grid_search.best_params_["quantile"] == pytest.approx(alpha)
def test_pinball_loss_relation_with_mae():
# Test that mean_pinball loss with alpha=0.5 if half of mean absolute error
rng = np.random.RandomState(714)
n = 100
y_true = rng.normal(size=n)
y_pred = y_true.copy() + rng.uniform(n)
assert (
mean_absolute_error(y_true, y_pred)
== mean_pinball_loss(y_true, y_pred, alpha=0.5) * 2
)
# TODO(1.6): remove this test
@pytest.mark.parametrize("metric", [mean_squared_error, mean_squared_log_error])
def test_mean_squared_deprecation_squared(metric):
"""Check the deprecation warning of the squared parameter"""
depr_msg = "'squared' is deprecated in version 1.4 and will be removed in 1.6."
y_true, y_pred = np.arange(10), np.arange(1, 11)
with pytest.warns(FutureWarning, match=depr_msg):
metric(y_true, y_pred, squared=False)
# TODO(1.6): remove this test
@pytest.mark.filterwarnings("ignore:'squared' is deprecated")
@pytest.mark.parametrize(
"old_func, new_func",
[
(mean_squared_error, root_mean_squared_error),
(mean_squared_log_error, root_mean_squared_log_error),
],
)
def test_rmse_rmsle_parameter(old_func, new_func):
# Check that the new rmse/rmsle function is equivalent to
# the old mse/msle + squared=False function.
y_true = np.array([[1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 0, 1]])
y_pred = np.array([[0, 0, 0, 1], [1, 0, 1, 1], [0, 0, 0, 1]])
y_true = np.array([[0.5, 1], [1, 2], [7, 6]])
y_pred = np.array([[0.5, 2], [1, 2.5], [8, 8]])
sw = np.arange(len(y_true))
expected = old_func(y_true, y_pred, squared=False)
actual = new_func(y_true, y_pred)
assert_allclose(expected, actual)
expected = old_func(y_true, y_pred, sample_weight=sw, squared=False)
actual = new_func(y_true, y_pred, sample_weight=sw)
assert_allclose(expected, actual)
expected = old_func(y_true, y_pred, multioutput="raw_values", squared=False)
actual = new_func(y_true, y_pred, multioutput="raw_values")
assert_allclose(expected, actual)
expected = old_func(
y_true, y_pred, sample_weight=sw, multioutput="raw_values", squared=False
)
actual = new_func(y_true, y_pred, sample_weight=sw, multioutput="raw_values")
assert_allclose(expected, actual)