def testWorksInDistributionLayerAndNegloglik(self):
"""Test that distribution works as layer and in gradient optimization."""
x = np.random.uniform(size=(100, 1))
y = 2 + -1 * x
lwn = lambertw_f.LambertWNormal(tailweight=0.5, loc=0.2, scale=1.0)
eps = self.evaluate(lwn.sample(x.shape, seed=test_util.test_seed()))
y += eps
def dist_lambda(t):
return lambertw_f.LambertWNormal(
loc=t[..., :1],
scale=1e-3 + tf.math.softplus(t[..., 1:2]),
tailweight=1e-3 + tf.math.softplus(t[..., 2:]))
dist_layer = tfp.layers.DistributionLambda(dist_lambda)
model = tf.keras.Sequential([
tf.keras.layers.Dense(10, "relu"),
tf.keras.layers.Dense(5, "selu"),
tf.keras.layers.Dense(1 + 1 + 1),
dist_layer])
negloglik = lambda y, p_y: -p_y.log_prob(y)
model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=0.01),
loss=negloglik)
model.fit(x, y, epochs=1, verbose=True, batch_size=32, validation_split=0.2)
self.assertGreater(model.history.history["val_loss"][0], -np.Inf)
def testVariance(self, delta, variance_multiplier):
loc = 2.
scale = 3.
lwn = lambertw_f.LambertWNormal(loc=loc, scale=scale, tailweight=delta)
if np.isnan(variance_multiplier):
self.assertAllClose(lwn.variance(), np.nan)
else:
self.assertAllClose(lwn.variance(), scale**2 * variance_multiplier)
def testMeanMode(self, delta, mean_exists):
loc = 2.
scale = 3.
lwn = lambertw_f.LambertWNormal(loc=loc, scale=scale, tailweight=delta)
self.assertAllClose(lwn.mode(), loc)
if mean_exists:
self.assertAllClose(lwn.mean(), loc)
else:
self.assertAllClose(lwn.mean(), np.nan)
def testShapes(self):
loc = tf.ones([2], dtype=tf.float32)
scale = tf.ones([3, 1], dtype=tf.float32)
tailweight = tf.zeros([4, 1, 1], dtype=tf.float32)
lwn = lambertw_f.LambertWNormal(loc=loc,
scale=scale,
tailweight=tailweight,
validate_args=True)
self.assertAllEqual(lwn.batch_shape, [4, 3, 2])
def testProbMethod(self): """Tests that Lambert W pdf is the same as Normal pdf when tail is zero.""" tailweight = 0. loc = 2. scale = 3. lwn = lambertw_f.LambertWNormal(loc=loc, scale=scale, tailweight=tailweight) values = np.random.normal(loc=2., scale=3., size=10) normal_pdf = tfd.Normal(loc, scale).prob(values) lambertw_normal_pdf = lwn.prob(values) self.assertAllClose(normal_pdf, lambertw_normal_pdf)
def testSampleMethod(self):
"""Tests that samples can be correctly transformed into gaussian samples."""
tailweight = .1
loc = 2.
scale = 3.
lwn = lambertw_f.LambertWNormal(loc=loc, scale=scale, tailweight=tailweight)
samples = lwn.sample(100, seed=test_util.test_seed)
self.assertAllEqual(samples.shape, [100])
gaussianized_samples = tfb.LambertWTail(
shift=loc, scale=scale, tailweight=tailweight).inverse(samples)
_, p = stats.normaltest(self.evaluate(gaussianized_samples))
self.assertGreater(p, .05)
def testQuantileMethod(self):
"""Tests that quantiles are correct."""
tailweight = 0.
loc = 2.
scale = 3.
lwn = lambertw_f.LambertWNormal(loc=loc, scale=scale, tailweight=tailweight)
values = np.random.uniform(low=0.0, high=1.0, size=5)
normal_quantiles = tfd.Normal(loc, scale).quantile(values)
transformed_normal_quantiles = tfb.LambertWTail(
shift=loc, scale=scale, tailweight=tailweight)(normal_quantiles)
lambertw_quantiles = lwn.quantile(values)
self.assertAllClose(transformed_normal_quantiles, lambertw_quantiles)
def testCDFMethod(self):
"""Tests that output of the cdf method is correct."""
tailweight = 0.
loc = 2.
scale = 3.
lwn = lambertw_f.LambertWNormal(loc=loc, scale=scale, tailweight=tailweight)
values = np.random.uniform(low=0.0, high=1.0, size=10)
quantiles = tfd.Normal(loc, scale).quantile(values)
heavy_tailed_values = tfb.LambertWTail(
shift=loc, scale=scale, tailweight=tailweight)(quantiles)
lambertw_normal_values = lwn.cdf(heavy_tailed_values)
self.assertAllClose(values, lambertw_normal_values)
def dist_lambda(t):
return lambertw_f.LambertWNormal(
loc=t[..., :1],
scale=1e-3 + tf.math.softplus(t[..., 1:2]),
tailweight=1e-3 + tf.math.softplus(t[..., 2:]))
def testQuantileInverseOfCDF(self, delta): lwn = lambertw_f.LambertWNormal(loc=2., scale=3., tailweight=delta) samples_ = self.evaluate(lwn.sample(5, seed=test_util.test_seed())) cdf_vals = lwn.cdf(samples_) self.assertAllClose(lwn.quantile(cdf_vals), samples_, rtol=1e-4)
