def test_log_pdf(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
ergoLogisticMixture = LogisticMixture(
components=[
Logistic(
loc=xscale.denormalize_point(0.2),
s=0.5 * xscale.width,
scale=xscale,
),
Logistic(loc=test_loc, s=test_s, scale=xscale),
],
probs=[1.8629593e-29, 1.0],
)
ergoLogistic = Logistic(loc=test_loc, s=test_s, scale=xscale)
## Test PDF
normed_scipydist = scipy.stats.logistic(normed_test_loc, normed_test_s)
for x in np.linspace(0, 1, 10):
denormalized_x = xscale.denormalize_point(x)
assert (normed_scipydist.pdf(x) / xscale.width == pytest.approx(
float(ergoLogistic.pdf(denormalized_x)), rel=1e-3) ==
pytest.approx(float(ergoLogisticMixture.pdf(denormalized_x)),
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)
def test_logistic_mixture_normalization():
mixture = LogisticMixture([Logistic(-40, 1), Logistic(50, 10)], [0.5, 0.5])
for scale_min, scale_max in [(0, 10), (10, 100), (-10, 10), (-100, -10)]:
assert (mixture.normalize(scale_min,
scale_max).denormalize(scale_min,
scale_max) == mixture)
normalized = mixture.normalize(-50, 50)
assert normalized == LogisticMixture(
[Logistic(0.1, 0.01), Logistic(1, 0.1)], [0.5, 0.5])
def test_percentiles_from_mixture():
mixture = LogisticMixture(
components=[Logistic(loc=1, scale=0.1),
Logistic(loc=2, scale=0.1)],
probs=[0.5, 0.5],
)
conditions = mixture.percentiles(percentiles=[0.1, 0.5, 0.9])
for condition in conditions:
if condition.max == 0.5:
assert condition.p == pytest.approx(1.5, rel=0.01)
return conditions
def test_cdf(xscale: Scale):
scipydist_normed = scipy.stats.logistic(0.5, 0.05)
true_loc = xscale.denormalize_point(0.5)
true_s = 0.05 * xscale.width
ergodist = Logistic(loc=true_loc, s=true_s, scale=xscale)
for x in np.linspace(0, 1, 10):
assert scipydist_normed.cdf(x) == pytest.approx(float(
ergodist.cdf(xscale.denormalize_point(x))),
rel=1e-3)
# TODO: consider a better approach for log scale
if isinstance(xscale, LogScale):
for x in np.linspace(xscale.low, xscale.high, 10):
assert scipydist_normed.cdf(
xscale.normalize_point(x)) == pytest.approx(float(
ergodist.cdf(x)),
rel=1e-3)
else:
scipydist_true = scipy.stats.logistic(true_loc, true_s)
for x in np.linspace(xscale.low, xscale.high, 10):
assert scipydist_true.cdf(x) == pytest.approx(float(
ergodist.cdf(x)),
rel=1e-3)
def test_logistic_mixture_normalization():
scale = Scale(-50, 50)
scalex2 = Scale(-100, 100)
mixture = LogisticMixture(
components=[Logistic(-40, 1, scale),
Logistic(50, 10, scale)],
probs=[0.5, 0.5],
)
mixturex2 = LogisticMixture(
components=[Logistic(-80, 2, scalex2),
Logistic(100, 20, scalex2)],
probs=[0.5, 0.5],
)
assert mixturex2 == mixture.normalize().denormalize(scalex2)
assert mixture == mixturex2.normalize().denormalize(scale)
normalized = (mixture.normalize()
) # not necessary to normalize but here for readability
assert normalized == LogisticMixture(
[Logistic(0.1, 0.01, Scale(0, 1)),
Logistic(1, 0.1, Scale(0, 1))],
[0.5, 0.5],
)
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_pdf(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
ergoLogisticMixture = LogisticMixture(
components=[
Logistic(
loc=xscale.denormalize_point(0.2),
s=0.5 * xscale.width,
scale=xscale,
),
Logistic(loc=test_loc, s=test_s, scale=xscale),
],
probs=[1.8629593e-29, 1.0],
)
ergoLogistic = Logistic(loc=test_loc, s=test_s, scale=xscale)
## Make sure it integrates to 1
_xs = xscale.denormalize_points(np.linspace(0, 1, 100))
densities_logistic = np.array([float(ergoLogistic.pdf(x)) for x in _xs])
densities_mixture = np.array(
[float(ergoLogisticMixture.pdf(x)) for x in _xs])
auc_logistic = float(trapz(densities_logistic, x=_xs))
auc_mixture = float(trapz(densities_mixture, x=_xs))
assert (1 == pytest.approx(auc_logistic, abs=0.03) == pytest.approx(
auc_mixture, abs=0.03))
if not isinstance(xscale, LogScale):
scipydist = scipy.stats.logistic(test_loc, test_s)
for x in np.linspace(xscale.denormalize_point(0),
xscale.denormalize_point(1), 10):
assert (scipydist.pdf(x) == pytest.approx(
float(ergoLogistic.pdf(x)), rel=1e-3) == pytest.approx(
float(ergoLogisticMixture.pdf(x)), 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)
def test_cdf():
jax_dist = Logistic(loc=10, scale=1)
original_dist = jax_dist.rv()
for x in range(5, 15):
assert jax_dist.cdf(x) == pytest.approx(original_dist.cdf(x), rel=0.1)