def test_mixture_ppf_adversarial():
# Make a mixture with one very improbable distribution and one dominant
mixture = LogisticMixture(
[Logistic(10, 3), Logistic(5, 5)], [1.8629593e-29, 1.0])
assert mixture.ppf(0.5) == pytest.approx(5.0, rel=1e-3)
assert mixture.ppf(0.01) == pytest.approx(-17.9755, rel=1e-3)
assert mixture.ppf(0.001) == pytest.approx(-29.5337, rel=1e-3)
assert mixture.ppf(0.99) == pytest.approx(27.9755, rel=1e-3)
assert mixture.ppf(0.999) == pytest.approx(39.5337, rel=1e-3)
def test_mixture_ppf_adversarial():
# Make a mixture with one very improbable distribution and one dominant
mixture = LogisticMixture([Logistic(10, 3), Logistic(5, 5)], [1.8629593e-29, 1.0])
assert mixture.ppf(0.5) == pytest.approx(5.0, rel=1e-3)
assert mixture.ppf(0.01) == pytest.approx(-17.9755, rel=1e-3)
assert mixture.ppf(0.001) == pytest.approx(-29.5337, rel=1e-3)
assert mixture.ppf(0.99) == pytest.approx(27.9755, rel=1e-3)
assert mixture.ppf(0.999) == pytest.approx(39.5337, rel=1e-3)
# Make a mixture with hugely overlapping distributions
mixture = LogisticMixture(
[
Logistic(4000000.035555004, 200000.02),
Logistic(4000000.0329152746, 200000.0),
],
[0.5, 0.5],
)
assert mixture.ppf(0.5) == pytest.approx(4000000.0342351394, rel=1e-3)
assert mixture.ppf(0.01) == pytest.approx(3080976.018257023, rel=1e-3)
assert mixture.ppf(0.001) == pytest.approx(2618649.009437881, rel=1e-3)
assert mixture.ppf(0.99) == pytest.approx(4919024.050213255, rel=1e-3)
assert mixture.ppf(0.999) == pytest.approx(5381351.059032397, rel=1e-3)
def test_truncated_ppf(xscale: Scale):
normed_test_loc = 0.5
normed_test_s = 0.1
test_loc = xscale.denormalize_point(normed_test_loc)
test_s = normed_test_s * xscale.width
normed_baseline_dist = scipy.stats.logistic(normed_test_loc, normed_test_s)
def ppf_through_cdf(dist, q):
return scipy.optimize.bisect(lambda x: dist.cdf(x) - q,
dist.ppf(0.0001),
dist.ppf(0.9999),
maxiter=1000)
# No bounds
dist_w_no_bounds = Truncate(Logistic(loc=test_loc, s=test_s, scale=xscale))
for x in np.linspace(0.01, 0.99, 8):
assert dist_w_no_bounds.ppf(x) == pytest.approx(float(
xscale.denormalize_point(normed_baseline_dist.ppf(x))),
rel=0.001)
# Floor
dist_w_floor = Truncate(
Logistic(loc=test_loc, s=test_s, scale=xscale),
floor=xscale.denormalize_point(0.5),
)
mix_w_floor = LogisticMixture(
components=[
Truncate( # type: ignore
Logistic(test_loc, s=test_s, scale=xscale),
floor=xscale.denormalize_point(0.5),
)
],
probs=[1.0],
)
for x in np.linspace(0.01, 0.99, 8):
assert dist_w_floor.ppf(x) == pytest.approx(float(mix_w_floor.ppf(x)),
rel=0.001)
assert dist_w_floor.ppf(x) == pytest.approx(float(
ppf_through_cdf(dist_w_floor, x)),
rel=0.001)
# Ceiling
dist_w_ceiling = Truncate(
Logistic(loc=test_loc, s=test_s, scale=xscale),
ceiling=xscale.denormalize_point(0.8),
)
mix_w_ceiling = LogisticMixture(
components=[
Truncate( # type: ignore
Logistic(test_loc, s=test_s, scale=xscale),
ceiling=xscale.denormalize_point(0.8),
)
],
probs=[1.0],
)
for x in np.linspace(0.01, 0.99, 8):
assert dist_w_ceiling.ppf(x) == pytest.approx(float(
mix_w_ceiling.ppf(x)),
rel=0.001)
assert dist_w_ceiling.ppf(x) == pytest.approx(float(
ppf_through_cdf(dist_w_ceiling, x)),
rel=0.001)
# Floor and Ceiling
dist_w_floor_and_ceiling = Truncate(
Logistic(loc=test_loc, s=test_s, scale=xscale),
floor=xscale.denormalize_point(0.2),
ceiling=xscale.denormalize_point(0.8),
)
mix_w_floor_and_ceiling = LogisticMixture(
components=[
Truncate( # type: ignore
Logistic(test_loc, s=test_s, scale=xscale),
floor=xscale.denormalize_point(0.2),
ceiling=xscale.denormalize_point(0.8),
)
],
probs=[1.0],
)
for x in np.linspace(0.01, 0.99, 8):
assert dist_w_floor_and_ceiling.ppf(x) == pytest.approx(float(
mix_w_floor_and_ceiling.ppf(x)),
rel=0.001)
assert dist_w_floor_and_ceiling.ppf(x) == pytest.approx(float(
ppf_through_cdf(dist_w_floor_and_ceiling, x)),
rel=0.001)
