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 = mean_squared_error(y_true, y_pred, multioutput=[0.4, 0.6], squared=False)
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)
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")
err_msg = ("multioutput is expected to be 'raw_values' "
"or 'uniform_average' but we got 'variance_weighted' instead.")
with pytest.raises(ValueError, match=err_msg):
mean_pinball_loss(y_true, y_pred, multioutput="variance_weighted")
with pytest.raises(ValueError, match=err_msg):
d2_pinball_score(y_true, y_pred, multioutput="variance_weighted")
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_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_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(mean_squared_error([0.0], [0.0], squared=False), 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])
# 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)
power = 0.5
with pytest.raises(ValueError,
match="is only defined for power<=0 and power>=1"):
mean_tweedie_deviance([0.0], [0.0], power=power)
with pytest.raises(ValueError,
match="is only defined for power<=0 and power>=1"):
d2_tweedie_score([0.0] * 2, [0.0] * 2, power=power)
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 = mean_squared_error(y_true, y_pred, squared=False)
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)
# 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)