def testLaplaceLaplaceKL(self):
batch_size = 6
event_size = 3
a_loc = np.array([[0.5] * event_size] * batch_size, dtype=np.float32)
a_scale = np.array([[0.1] * event_size] * batch_size, dtype=np.float32)
b_loc = np.array([[0.4] * event_size] * batch_size, dtype=np.float32)
b_scale = np.array([[0.2] * event_size] * batch_size, dtype=np.float32)
a = laplace_lib.Laplace(loc=a_loc, scale=a_scale)
b = laplace_lib.Laplace(loc=b_loc, scale=b_scale)
distance = tf.abs(a_loc - b_loc)
ratio = a_scale / b_scale
true_kl = (-tf.log(ratio) - 1 + distance / b_scale +
ratio * tf.exp(-distance / a_scale))
kl = kl_divergence(a, b)
x = a.sample(int(1e4), seed=0)
kl_sample = tf.reduce_mean(a.log_prob(x) - b.log_prob(x), 0)
true_kl_, kl_, kl_sample_ = self.evaluate([true_kl, kl, kl_sample])
self.assertAllEqual(true_kl_, kl_)
self.assertAllClose(true_kl_, kl_sample_, atol=0., rtol=1e-1)
zero_kl = kl_divergence(a, a)
true_zero_kl_, zero_kl_ = self.evaluate([tf.zeros_like(true_kl), zero_kl])
self.assertAllEqual(true_zero_kl_, zero_kl_)
def testLaplaceNonPositiveInitializationParamsRaises(self):
loc_v = tf.constant(0.0, name="loc")
scale_v = tf.constant(-1.0, name="scale")
with self.assertRaisesOpError("Condition x > 0 did not hold element-wise"):
laplace = laplace_lib.Laplace(
loc=loc_v, scale=scale_v, validate_args=True)
self.evaluate(laplace.mean())
loc_v = tf.constant(1.0, name="loc")
scale_v = tf.constant(0.0, name="scale")
with self.assertRaisesOpError("Condition x > 0 did not hold element-wise"):
laplace = laplace_lib.Laplace(
loc=loc_v, scale=scale_v, validate_args=True)
self.evaluate(laplace.mean())
def testLaplacePdfOfSampleMultiDims(self):
laplace = laplace_lib.Laplace(loc=[7., 11.], scale=[[5.], [6.]])
num = 50000
samples = laplace.sample(num, seed=137)
pdfs = laplace.prob(samples)
sample_vals, pdf_vals = self.evaluate([samples, pdfs])
self.assertEqual(samples.get_shape(), (num, 2, 2))
self.assertEqual(pdfs.get_shape(), (num, 2, 2))
self._assertIntegral(sample_vals[:, 0, 0], pdf_vals[:, 0, 0], err=0.02)
self._assertIntegral(sample_vals[:, 0, 1], pdf_vals[:, 0, 1], err=0.02)
self._assertIntegral(sample_vals[:, 1, 0], pdf_vals[:, 1, 0], err=0.02)
self._assertIntegral(sample_vals[:, 1, 1], pdf_vals[:, 1, 1], err=0.02)
if not stats:
return
self.assertAllClose(stats.laplace.mean([[7., 11.], [7., 11.]],
scale=np.array([[5., 5.],
[6., 6.]])),
sample_vals.mean(axis=0),
rtol=0.05,
atol=0.)
self.assertAllClose(stats.laplace.var([[7., 11.], [7., 11.]],
scale=np.array([[5., 5.],
[6., 6.]])),
sample_vals.var(axis=0),
rtol=0.05,
atol=0.)
def testLaplaceSampleMultiDimensional(self):
loc_v = np.array([np.arange(1, 101, dtype=np.float32)]) # 1 x 100
scale_v = np.array([np.arange(1, 11, dtype=np.float32)]).T # 10 x 1
laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
n = 10000
samples = laplace.sample(n, seed=137)
sample_values = self.evaluate(samples)
self.assertEqual(samples.get_shape(), (n, 10, 100))
self.assertEqual(sample_values.shape, (n, 10, 100))
zeros = np.zeros_like(loc_v + scale_v) # 10 x 100
loc_bc = loc_v + zeros
scale_bc = scale_v + zeros
if not stats:
return
self.assertAllClose(sample_values.mean(axis=0),
stats.laplace.mean(loc_bc, scale=scale_bc),
rtol=0.35,
atol=0.)
self.assertAllClose(sample_values.var(axis=0),
stats.laplace.var(loc_bc, scale=scale_bc),
rtol=0.10,
atol=0.)
fails = 0
trials = 0
for ai, a in enumerate(np.reshape(loc_v, [-1])):
for bi, b in enumerate(np.reshape(scale_v, [-1])):
s = sample_values[:, bi, ai]
trials += 1
fails += 0 if self._kstest(a, b, s) else 1
self.assertLess(fails, trials * 0.03)
def testLaplaceShape(self):
loc = tf.constant([3.0] * 5)
scale = tf.constant(11.0)
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
self.assertEqual(self.evaluate(laplace.batch_shape_tensor()), (5, ))
self.assertEqual(laplace.batch_shape, tf.TensorShape([5]))
self.assertAllEqual(self.evaluate(laplace.event_shape_tensor()), [])
self.assertEqual(laplace.event_shape, tf.TensorShape([]))
def testLaplaceEntropy(self):
loc_v = np.array([1.0, 3.0, 2.5])
scale_v = np.array([1.0, 4.0, 5.0])
laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
self.assertEqual(laplace.entropy().get_shape(), (3, ))
if not stats:
return
expected_entropy = stats.laplace.entropy(loc_v, scale=scale_v)
self.assertAllClose(self.evaluate(laplace.entropy()), expected_entropy)
def testLaplaceStd(self):
loc_v = np.array([1.0, 3.0, 2.5])
scale_v = np.array([1.0, 4.0, 5.0])
laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
self.assertEqual(laplace.stddev().shape, (3,))
if not stats:
return
expected_stddev = stats.laplace.std(loc_v, scale=scale_v)
self.assertAllClose(self.evaluate(laplace.stddev()), expected_stddev)
def testLaplaceFullyReparameterized(self):
loc = tf.constant(4.0)
scale = tf.constant(3.0)
with backprop.GradientTape() as tape:
tape.watch(loc)
tape.watch(scale)
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
samples = laplace.sample(100)
grad_loc, grad_scale = tape.gradient(samples, [loc, scale])
self.assertIsNotNone(grad_loc)
self.assertIsNotNone(grad_scale)
def testLaplaceLogSurvivalFunction(self):
batch_size = 6
loc = tf.constant([2.0] * batch_size)
scale = tf.constant([3.0] * batch_size)
loc_v = 2.0
scale_v = 3.0
x = np.array([-2.5, 2.5, -4.0, 0.1, 1.0, 2.0], dtype=np.float32)
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
sf = laplace.log_survival_function(x)
self.assertEqual(sf.get_shape(), (6, ))
if not stats:
return
expected_sf = stats.laplace.logsf(x, loc_v, scale=scale_v)
self.assertAllClose(self.evaluate(sf), expected_sf)
def testLaplaceCDF(self):
batch_size = 6
loc = tf.constant([2.0] * batch_size)
scale = tf.constant([3.0] * batch_size)
loc_v = 2.0
scale_v = 3.0
x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
cdf = laplace.cdf(x)
self.assertEqual(cdf.get_shape(), (6, ))
if not stats:
return
expected_cdf = stats.laplace.cdf(x, loc_v, scale=scale_v)
self.assertAllClose(self.evaluate(cdf), expected_cdf)
def testLaplaceLogPDF(self):
batch_size = 6
loc = tf.constant([2.0] * batch_size)
scale = tf.constant([3.0] * batch_size)
loc_v = 2.0
scale_v = 3.0
x = np.array([2.5, 2.5, 4.0, 0.1, 1.0, 2.0], dtype=np.float32)
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
log_pdf = laplace.log_prob(x)
self.assertEqual(log_pdf.shape, (6,))
if not stats:
return
expected_log_pdf = stats.laplace.logpdf(x, loc_v, scale=scale_v)
self.assertAllClose(self.evaluate(log_pdf), expected_log_pdf)
pdf = laplace.prob(x)
self.assertEqual(pdf.shape, (6,))
self.assertAllClose(self.evaluate(pdf), np.exp(expected_log_pdf))
def testLaplaceLogPDFMultidimensionalBroadcasting(self):
batch_size = 6
loc = tf.constant([[2.0, 4.0]] * batch_size)
scale = tf.constant(3.0)
loc_v = np.array([2.0, 4.0])
scale_v = 3.0
x = np.array([[2.5, 2.5, 4.0, 0.1, 1.0, 2.0]], dtype=np.float32).T
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
log_pdf = laplace.log_prob(x)
log_pdf_values = self.evaluate(log_pdf)
self.assertEqual(log_pdf.get_shape(), (6, 2))
pdf = laplace.prob(x)
pdf_values = self.evaluate(pdf)
self.assertEqual(pdf.get_shape(), (6, 2))
if not stats:
return
expected_log_pdf = stats.laplace.logpdf(x, loc_v, scale=scale_v)
self.assertAllClose(log_pdf_values, expected_log_pdf)
self.assertAllClose(pdf_values, np.exp(expected_log_pdf))
def testLaplaceSample(self):
loc_v = 4.0
scale_v = 3.0
loc = tf.constant(loc_v)
scale = tf.constant(scale_v)
n = 100000
laplace = laplace_lib.Laplace(loc=loc, scale=scale)
samples = laplace.sample(n, seed=137)
sample_values = self.evaluate(samples)
self.assertEqual(samples.get_shape(), (n, ))
self.assertEqual(sample_values.shape, (n, ))
if not stats:
return
self.assertAllClose(sample_values.mean(),
stats.laplace.mean(loc_v, scale=scale_v),
rtol=0.05,
atol=0.)
self.assertAllClose(sample_values.var(),
stats.laplace.var(loc_v, scale=scale_v),
rtol=0.05,
atol=0.)
self.assertTrue(self._kstest(loc_v, scale_v, sample_values))
def testLaplaceMode(self):
loc_v = np.array([0.5, 3.0, 2.5])
scale_v = np.array([1.0, 4.0, 5.0])
laplace = laplace_lib.Laplace(loc=loc_v, scale=scale_v)
self.assertEqual(laplace.mode().get_shape(), (3, ))
self.assertAllClose(self.evaluate(laplace.mode()), loc_v)
def __init__(self,
loc=None,
scale=None,
validate_args=False,
allow_nan_stats=True,
name="VectorLaplaceLinearOperator"):
"""Construct Vector Laplace distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and `scale`
arguments.
The `event_shape` is given by last dimension of the matrix implied by
`scale`. The last dimension of `loc` (if provided) must broadcast with this.
Recall that `covariance = 2 * scale @ scale.T`.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
scale: Instance of `LinearOperator` with same `dtype` as `loc` and shape
`[B1, ..., Bb, k, k]`.
validate_args: Python `bool`, default `False`. Whether to validate input
with asserts. If `validate_args` is `False`, and the inputs are
invalid, correct behavior is not guaranteed.
allow_nan_stats: Python `bool`, default `True`. If `False`, raise an
exception if a statistic (e.g. mean/mode/etc...) is undefined for any
batch member If `True`, batch members with valid parameters leading to
undefined statistics will return NaN for this statistic.
name: The name to give Ops created by the initializer.
Raises:
ValueError: if `scale` is unspecified.
TypeError: if not `scale.dtype.is_floating`
"""
parameters = dict(locals())
if scale is None:
raise ValueError("Missing required `scale` parameter.")
if not dtype_util.is_floating(scale.dtype):
raise TypeError("`scale` parameter must have floating-point dtype.")
with tf.name_scope(name):
# Since expand_dims doesn't preserve constant-ness, we obtain the
# non-dynamic value if possible.
loc = loc if loc is None else tf.convert_to_tensor(
loc, name="loc", dtype=scale.dtype)
batch_shape, event_shape = distribution_util.shapes_from_loc_and_scale(
loc, scale)
super(VectorLaplaceLinearOperator, self).__init__(
distribution=laplace.Laplace(
loc=tf.zeros([], dtype=scale.dtype),
scale=tf.ones([], dtype=scale.dtype)),
bijector=affine_linear_operator_bijector.AffineLinearOperator(
shift=loc, scale=scale, validate_args=validate_args),
batch_shape=batch_shape,
event_shape=event_shape,
validate_args=validate_args,
name=name)
self._parameters = parameters