def test_transformed_distribution() -> None:
zero = nd.zeros(1)
one = nd.ones(1)
# If Y = -log(U) with U ~ Uniform(0, 1), then Y ~ Exponential(1)
exponential = TransformedDistribution(
Uniform(zero, one),
bijection.log,
bijection.AffineTransformation(scale=-1 * one),
)
# For Y ~ Exponential(1), P(Y) = e^{-x) ==> log P(Y) = -x
assert exponential.log_prob(1 * one).asscalar() == -1.0
assert exponential.log_prob(2 * one).asscalar() == -2.0
# If Y ~ Exponential(1), then U = 1 - e^{-Y} has Uniform(0, 1) distribution
uniform = TransformedDistribution(
exponential,
bijection.AffineTransformation(scale=-1 * one),
bijection.log.inverse_bijection(), # == bijection.exp
bijection.AffineTransformation(loc=one, scale=-1 * one),
)
# For U ~ Uniform(0, 1), log P(U) = 0
assert uniform.log_prob(0.5 * one).asscalar() == 0
assert uniform.log_prob(0.2 * one).asscalar() == 0
def test_transformed_distribution(serialize_fn) -> None:
zero = nd.zeros(1)
one = nd.ones(1)
# If Y = -log(U) with U ~ Uniform(0, 1), then Y ~ Exponential(1)
exponential = TransformedDistribution(
Uniform(zero, one),
[bijection.log,
bijection.AffineTransformation(scale=-1 * one)],
)
exponential = serialize_fn(exponential)
# For Y ~ Exponential(1), P(Y) = e^{-x) ==> log P(Y) = -x
assert exponential.log_prob(1 * one).asscalar() == -1.0
assert exponential.log_prob(2 * one).asscalar() == -2.0
v = np.linspace(0, 5, 101)
assert np.allclose(exponential.cdf(nd.array(v)).asnumpy(), exp_cdf(v))
level = np.linspace(1.0e-5, 1.0 - 1.0e-5, 101)
qs_calc = exponential.quantile(nd.array(level)).asnumpy()[:, 0]
qs_theo = exp_quantile(level)
assert np.allclose(qs_calc, qs_theo, atol=1.0e-2)
# If Y ~ Exponential(1), then U = 1 - e^{-Y} has Uniform(0, 1) distribution
uniform = TransformedDistribution(
exponential,
[
bijection.AffineTransformation(scale=-1 * one),
bijection.log.inverse_bijection(), # == bijection.exp
bijection.AffineTransformation(loc=one, scale=-1 * one),
],
)
uniform = serialize_fn(uniform)
# For U ~ Uniform(0, 1), log P(U) = 0
assert uniform.log_prob(0.5 * one).asscalar() == 0
assert uniform.log_prob(0.2 * one).asscalar() == 0
v = np.linspace(0, 1, 101)
assert np.allclose(uniform.cdf(nd.array(v)).asnumpy(), v)
qs_calc = uniform.quantile(nd.array(level)).asnumpy()[:, 0]
assert np.allclose(qs_calc, level, atol=1.0e-2)
def test_DistributionForecast():
forecast = DistributionForecast(
distribution=Uniform(low=mx.nd.array([0.0, 0.0]),
high=mx.nd.array([1.0, 2.0])),
start_date=START_DATE,
freq=FREQ,
)
def percentile(value):
return f"p{int(round(value * 100)):02d}"
for quantile in QUANTILES:
test_cases = [quantile, str(quantile), percentile(quantile)]
for quant_pred in map(forecast.quantile, test_cases):
expected = quantile * np.array([1.0, 2.0])
assert np.allclose(
quant_pred, expected
), f"Expected {quantile} quantile {quantile}. Obtained {quant_pred}."
pred_length = 2
assert forecast.prediction_length == pred_length
assert len(forecast.index) == pred_length
assert forecast.index[0] == pd.Timestamp(START_DATE)
START_DATE = pd.Timestamp(2017, 1, 1, 12)
FREQ = "1D"
FORECASTS = {
"QuantileForecast":
QuantileForecast(
forecast_arrays=QUANTILES.reshape(-1, 1),
start_date=START_DATE,
forecast_keys=np.array(QUANTILES, str),
freq=FREQ,
),
"SampleForecast":
SampleForecast(samples=SAMPLES, start_date=START_DATE, freq=FREQ),
"DistributionForecast":
DistributionForecast(
distribution=Uniform(low=mx.nd.zeros(1), high=mx.nd.ones(1)),
start_date=START_DATE,
freq=FREQ,
),
}
@pytest.mark.parametrize("name", FORECASTS.keys())
def test_Forecast(name):
forecast = FORECASTS[name]
def percentile(value):
return f"p{int(round(value * 100)):02d}"
num_samples, pred_length = SAMPLES.shape
Laplace(mu=mx.nd.zeros(shape=(3, 4, 5)),
b=mx.nd.ones(shape=(3, 4, 5))),
(3, 4, 5),
(),
),
(
NegativeBinomial(
mu=mx.nd.zeros(shape=(3, 4, 5)),
alpha=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
Uniform(
low=-mx.nd.ones(shape=(3, 4, 5)),
high=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
PiecewiseLinear(
gamma=mx.nd.ones(shape=(3, 4, 5)),
slopes=mx.nd.ones(shape=(3, 4, 5, 10)),
knot_spacings=mx.nd.ones(shape=(3, 4, 5, 10)) / 10,
),
(3, 4, 5),
(),
),
(
MixtureDistribution(
START_DATE = pd.Timestamp(2017, 1, 1, 12)
FREQ = "1D"
FORECASTS = {
"QuantileForecast":
QuantileForecast(
forecast_arrays=QUANTILES.reshape(-1, 1),
start_date=START_DATE,
forecast_keys=np.array(QUANTILES, str),
freq=FREQ,
),
"SampleForecast":
SampleForecast(samples=SAMPLES, start_date=START_DATE, freq=FREQ),
"DistributionForecast":
DistributionForecast(
distribution=Uniform(low=mx.nd.zeros(1), high=mx.nd.ones(1)),
start_date=START_DATE,
freq=FREQ,
),
}
@pytest.mark.parametrize("name", FORECASTS.keys())
def test_Forecast(name):
forecast = FORECASTS[name]
def percentile(value):
return f"p{int(round(value * 100)):02d}"
num_samples, pred_length = SAMPLES.shape
StudentT(
mu=mx.nd.zeros(shape=BATCH_SHAPE),
sigma=mx.nd.ones(shape=BATCH_SHAPE),
nu=mx.nd.ones(shape=BATCH_SHAPE),
),
Dirichlet(alpha=mx.nd.ones(shape=BATCH_SHAPE)),
Laplace(
mu=mx.nd.zeros(shape=BATCH_SHAPE), b=mx.nd.ones(shape=BATCH_SHAPE)
),
NegativeBinomial(
mu=mx.nd.zeros(shape=BATCH_SHAPE),
alpha=mx.nd.ones(shape=BATCH_SHAPE),
),
Poisson(rate=mx.nd.ones(shape=BATCH_SHAPE)),
Uniform(
low=-mx.nd.ones(shape=BATCH_SHAPE),
high=mx.nd.ones(shape=BATCH_SHAPE),
),
PiecewiseLinear(
gamma=mx.nd.ones(shape=BATCH_SHAPE),
slopes=mx.nd.ones(shape=(3, 4, 5, 10)),
knot_spacings=mx.nd.ones(shape=(3, 4, 5, 10)) / 10,
),
MixtureDistribution(
mixture_probs=mx.nd.stack(
0.2 * mx.nd.ones(shape=BATCH_SHAPE),
0.8 * mx.nd.ones(shape=BATCH_SHAPE),
axis=-1,
),
components=[
Gaussian(
mu=mx.nd.zeros(shape=BATCH_SHAPE),