def testVarianceAllowNanStatsTrueReturnsNaNforUndefinedBatchMembers(self):
with self.test_session():
# df = 0.5 ==> undefined mean ==> undefined variance.
# df = 1.5 ==> infinite variance.
df = [0.5, 1.5, 3., 5., 7.]
mu = [-2, 0., 1., 3.3, 4.4]
sigma = [5., 4., 3., 2., 1.]
student = student_t.StudentT(df=df,
loc=mu,
scale=sigma,
allow_nan_stats=True)
var = student.variance().eval()
## scipy uses inf for variance when the mean is undefined. When mean is
# undefined we say variance is undefined as well. So test the first
# member of var, making sure it is NaN, then replace with inf and compare
# to scipy.
self.assertTrue(np.isnan(var[0]))
var[0] = np.inf
if not stats:
return
expected_var = [
stats.t.var(d, loc=m, scale=s)
for (d, m, s) in zip(df, mu, sigma)
]
self.assertAllClose(expected_var, var)
def testStudentSampleMultiDimensional(self):
with self.test_session():
batch_size = 7
df = constant_op.constant([[3., 7.]] * batch_size)
mu = constant_op.constant([[3., -3.]] * batch_size)
sigma = constant_op.constant([[math.sqrt(10.), math.sqrt(15.)]] *
batch_size)
df_v = [3., 7.]
mu_v = [3., -3.]
sigma_v = [np.sqrt(10.), np.sqrt(15.)]
n = constant_op.constant(200000)
student = student_t.StudentT(df=df, loc=mu, scale=sigma)
samples = student.sample(n, seed=123456)
sample_values = self.evaluate(samples)
self.assertEqual(samples.get_shape(), (200000, batch_size, 2))
self.assertAllClose(
sample_values[:, 0, 0].mean(), mu_v[0], rtol=1e-2, atol=0)
self.assertAllClose(
sample_values[:, 0, 0].var(),
sigma_v[0]**2 * df_v[0] / (df_v[0] - 2),
rtol=1e-1,
atol=0)
self._checkKLApprox(df_v[0], mu_v[0], sigma_v[0], sample_values[:, 0, 0])
self.assertAllClose(
sample_values[:, 0, 1].mean(), mu_v[1], rtol=1e-2, atol=0)
self.assertAllClose(
sample_values[:, 0, 1].var(),
sigma_v[1]**2 * df_v[1] / (df_v[1] - 2),
rtol=1e-1,
atol=0)
self._checkKLApprox(df_v[0], mu_v[0], sigma_v[0], sample_values[:, 0, 1])
def testMeanAllowNanStatsIsFalseWorksWhenAllBatchMembersAreDefined(self):
mu = [1., 3.3, 4.4]
student = student_t.StudentT(df=[3., 5., 7.],
loc=mu,
scale=[3., 2., 1.])
mean = self.evaluate(student.mean())
self.assertAllClose([1., 3.3, 4.4], mean)
def testPdfOfSampleMultiDims(self):
student = student_t.StudentT(df=[7., 11.], loc=[[5.], [6.]], scale=3.)
self.assertAllEqual([], student.event_shape)
self.assertAllEqual([], self.evaluate(student.event_shape_tensor()))
self.assertAllEqual([2, 2], student.batch_shape)
self.assertAllEqual([2, 2], self.evaluate(student.batch_shape_tensor()))
num = 50000
samples = student.sample(num, seed=123456)
pdfs = student.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.assertNear(5., np.mean(sample_vals[:, 0, :]), err=.03)
self.assertNear(6., np.mean(sample_vals[:, 1, :]), err=.03)
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.assertNear(
stats.t.var(7., loc=0., scale=3.), # loc d.n. effect var
np.var(sample_vals[:, :, 0]),
err=.4)
self.assertNear(
stats.t.var(11., loc=0., scale=3.), # loc d.n. effect var
np.var(sample_vals[:, :, 1]),
err=.4)
def testStudentPDFAndLogPDF(self):
with self.test_session():
batch_size = 6
df = constant_op.constant([3.] * batch_size)
mu = constant_op.constant([7.] * batch_size)
sigma = constant_op.constant([8.] * batch_size)
df_v = 3.
mu_v = 7.
sigma_v = 8.
t = np.array([-2.5, 2.5, 8., 0., -1., 2.], dtype=np.float32)
student = student_t.StudentT(df, loc=mu, scale=-sigma)
log_pdf = student.log_prob(t)
self.assertEquals(log_pdf.get_shape(), (6,))
log_pdf_values = self.evaluate(log_pdf)
pdf = student.prob(t)
self.assertEquals(pdf.get_shape(), (6,))
pdf_values = self.evaluate(pdf)
if not stats:
return
expected_log_pdf = stats.t.logpdf(t, df_v, loc=mu_v, scale=sigma_v)
expected_pdf = stats.t.pdf(t, df_v, loc=mu_v, scale=sigma_v)
self.assertAllClose(expected_log_pdf, log_pdf_values)
self.assertAllClose(np.log(expected_pdf), log_pdf_values)
self.assertAllClose(expected_pdf, pdf_values)
self.assertAllClose(np.exp(expected_log_pdf), pdf_values)
def testStudentCDFAndLogCDF(self):
batch_size = 6
df = constant_op.constant([3.] * batch_size)
mu = constant_op.constant([7.] * batch_size)
sigma = constant_op.constant([-8.] * batch_size)
df_v = 3.
mu_v = 7.
sigma_v = 8.
t = np.array([-2.5, 2.5, 8., 0., -1., 2.], dtype=np.float32)
student = student_t.StudentT(df, loc=mu, scale=sigma)
log_cdf = student.log_cdf(t)
self.assertEquals(log_cdf.get_shape(), (6, ))
log_cdf_values = self.evaluate(log_cdf)
cdf = student.cdf(t)
self.assertEquals(cdf.get_shape(), (6, ))
cdf_values = self.evaluate(cdf)
if not stats:
return
expected_log_cdf = stats.t.logcdf(t, df_v, loc=mu_v, scale=sigma_v)
expected_cdf = stats.t.cdf(t, df_v, loc=mu_v, scale=sigma_v)
self.assertAllClose(expected_log_cdf,
log_cdf_values,
atol=0.,
rtol=1e-5)
self.assertAllClose(np.log(expected_cdf),
log_cdf_values,
atol=0.,
rtol=1e-5)
self.assertAllClose(expected_cdf, cdf_values, atol=0., rtol=1e-5)
self.assertAllClose(np.exp(expected_log_cdf),
cdf_values,
atol=0.,
rtol=1e-5)
def testVarianceAllowNanStatsFalseRaisesForUndefinedBatchMembers(self):
# df <= 1 ==> variance not defined
student = student_t.StudentT(df=1.,
loc=0.,
scale=1.,
allow_nan_stats=False)
with self.assertRaisesOpError("x < y"):
self.evaluate(student.variance())
# df <= 1 ==> variance not defined
student = student_t.StudentT(df=0.5,
loc=0.,
scale=1.,
allow_nan_stats=False)
with self.assertRaisesOpError("x < y"):
self.evaluate(student.variance())
def testStudentLogPDFMultidimensional(self):
with self.test_session():
batch_size = 6
df = constant_op.constant([[1.5, 7.2]] * batch_size)
mu = constant_op.constant([[3., -3.]] * batch_size)
sigma = constant_op.constant([[-math.sqrt(10.), math.sqrt(15.)]] *
batch_size)
df_v = np.array([1.5, 7.2])
mu_v = np.array([3., -3.])
sigma_v = np.array([np.sqrt(10.), np.sqrt(15.)])
t = np.array([[-2.5, 2.5, 4., 0., -1., 2.]], dtype=np.float32).T
student = student_t.StudentT(df, loc=mu, scale=sigma)
log_pdf = student.log_prob(t)
log_pdf_values = self.evaluate(log_pdf)
self.assertEqual(log_pdf.get_shape(), (6, 2))
pdf = student.prob(t)
pdf_values = self.evaluate(pdf)
self.assertEqual(pdf.get_shape(), (6, 2))
if not stats:
return
expected_log_pdf = stats.t.logpdf(t, df_v, loc=mu_v, scale=sigma_v)
expected_pdf = stats.t.pdf(t, df_v, loc=mu_v, scale=sigma_v)
self.assertAllClose(expected_log_pdf, log_pdf_values)
self.assertAllClose(np.log(expected_pdf), log_pdf_values)
self.assertAllClose(expected_pdf, pdf_values)
self.assertAllClose(np.exp(expected_log_pdf), pdf_values)
def testNegativeDofFails(self):
with self.assertRaisesOpError(r"Condition x > 0 did not hold"):
student = student_t.StudentT(df=[2, -5.],
loc=0.,
scale=1.,
validate_args=True,
name="S")
self.evaluate(student.mean())
def testMeanAllowNanStatsIsFalseRaisesWhenBatchMemberIsUndefined(self):
with self.test_session():
mu = [1., 3.3, 4.4]
student = student_t.StudentT(
df=[0.5, 5., 7.], loc=mu, scale=[3., 2., 1.],
allow_nan_stats=False)
with self.assertRaisesOpError("x < y"):
self.evaluate(student.mean())
def testMode(self):
df = [0.5, 1., 3]
mu = [-1, 0., 1]
sigma = [5., 4., 3.]
student = student_t.StudentT(df=df, loc=mu, scale=sigma)
# Test broadcast of mu across shape of df/sigma
mode = self.evaluate(student.mode())
self.assertAllClose([-1., 0, 1], mode)
def testMeanAllowNanStatsIsTrueReturnsNaNForUndefinedBatchMembers(self):
with self.test_session():
mu = [-2, 0., 1., 3.3, 4.4]
sigma = [5., 4., 3., 2., 1.]
student = student_t.StudentT(
df=[0.5, 1., 3., 5., 7.], loc=mu, scale=sigma,
allow_nan_stats=True)
mean = self.evaluate(student.mean())
self.assertAllClose([np.nan, np.nan, 1., 3.3, 4.4], mean)
def testStudentSampleMultipleTimes(self):
with self.test_session():
df = constant_op.constant(4.)
mu = constant_op.constant(3.)
sigma = constant_op.constant(math.sqrt(10.))
n = constant_op.constant(100)
random_seed.set_random_seed(654321)
student = student_t.StudentT(
df=df, loc=mu, scale=sigma, name="student_t1")
samples1 = self.evaluate(student.sample(n, seed=123456))
random_seed.set_random_seed(654321)
student2 = student_t.StudentT(
df=df, loc=mu, scale=sigma, name="student_t2")
samples2 = self.evaluate(student2.sample(n, seed=123456))
self.assertAllClose(samples1, samples2)
def testStudentSampleSmallDfNoNan(self):
df_v = [1e-1, 1e-5, 1e-10, 1e-20]
df = constant_op.constant(df_v)
n = constant_op.constant(200000)
student = student_t.StudentT(df=df, loc=1., scale=1.)
samples = student.sample(n, seed=123456)
sample_values = self.evaluate(samples)
n_val = 200000
self.assertEqual(sample_values.shape, (n_val, 4))
self.assertTrue(np.all(np.logical_not(np.isnan(sample_values))))
def testBroadcastingPdfArgs(self):
def _assert_shape(student, arg, shape):
self.assertEqual(student.log_prob(arg).get_shape(), shape)
self.assertEqual(student.prob(arg).get_shape(), shape)
def _check(student):
_assert_shape(student, 2., (3,))
xs = np.array([2., 3., 4.], dtype=np.float32)
_assert_shape(student, xs, (3,))
xs = np.array([xs])
_assert_shape(student, xs, (1, 3))
xs = xs.T
_assert_shape(student, xs, (3, 3))
_check(student_t.StudentT(df=[2., 3., 4.,], loc=2., scale=1.))
_check(student_t.StudentT(df=7., loc=[2., 3., 4.,], scale=1.))
_check(student_t.StudentT(df=7., loc=3., scale=[2., 3., 4.,]))
def _check2d(student):
_assert_shape(student, 2., (1, 3))
xs = np.array([2., 3., 4.], dtype=np.float32)
_assert_shape(student, xs, (1, 3))
xs = np.array([xs])
_assert_shape(student, xs, (1, 3))
xs = xs.T
_assert_shape(student, xs, (3, 3))
_check2d(student_t.StudentT(df=[[2., 3., 4.,]], loc=2., scale=1.))
_check2d(student_t.StudentT(df=7., loc=[[2., 3., 4.,]], scale=1.))
_check2d(student_t.StudentT(df=7., loc=3., scale=[[2., 3., 4.,]]))
def _check2d_rows(student):
_assert_shape(student, 2., (3, 1))
xs = np.array([2., 3., 4.], dtype=np.float32) # (3,)
_assert_shape(student, xs, (3, 3))
xs = np.array([xs]) # (1,3)
_assert_shape(student, xs, (3, 3))
xs = xs.T # (3,1)
_assert_shape(student, xs, (3, 1))
_check2d_rows(student_t.StudentT(df=[[2.], [3.], [4.]], loc=2., scale=1.))
_check2d_rows(student_t.StudentT(df=7., loc=[[2.], [3.], [4.]], scale=1.))
_check2d_rows(student_t.StudentT(df=7., loc=3., scale=[[2.], [3.], [4.]]))
def testFullyReparameterized(self):
df = constant_op.constant(2.0)
mu = constant_op.constant(1.0)
sigma = constant_op.constant(3.0)
with backprop.GradientTape() as tape:
tape.watch(df)
tape.watch(mu)
tape.watch(sigma)
student = student_t.StudentT(df=df, loc=mu, scale=sigma)
samples = student.sample(100)
grad_df, grad_mu, grad_sigma = tape.gradient(samples, [df, mu, sigma])
self.assertIsNotNone(grad_df)
self.assertIsNotNone(grad_mu)
self.assertIsNotNone(grad_sigma)
def testVarianceAllowNanStatsFalseGivesCorrectValueForDefinedBatchMembers(
self):
# df = 1.5 ==> infinite variance.
df = [1.5, 3., 5., 7.]
mu = [0., 1., 3.3, 4.4]
sigma = [4., 3., 2., 1.]
student = student_t.StudentT(df=df, loc=mu, scale=sigma)
var = self.evaluate(student.variance())
if not stats:
return
expected_var = [
stats.t.var(d, loc=m, scale=s) for (d, m, s) in zip(df, mu, sigma)
]
self.assertAllClose(expected_var, var)
def testStd(self):
# Defined for all batch members.
df = [3.5, 5., 3., 5., 7.]
mu = [-2.2]
sigma = [5., 4., 3., 2., 1.]
student = student_t.StudentT(df=df, loc=mu, scale=sigma)
# Test broadcast of mu across shape of df/sigma
stddev = self.evaluate(student.stddev())
mu *= len(df)
if not stats:
return
expected_stddev = [
stats.t.std(d, loc=m, scale=s) for (d, m, s) in zip(df, mu, sigma)
]
self.assertAllClose(expected_stddev, stddev)
def testStudentSample(self):
df = constant_op.constant(4.)
mu = constant_op.constant(3.)
sigma = constant_op.constant(-math.sqrt(10.))
df_v = 4.
mu_v = 3.
sigma_v = np.sqrt(10.)
n = constant_op.constant(200000)
student = student_t.StudentT(df=df, loc=mu, scale=sigma)
samples = student.sample(n, seed=123456)
sample_values = self.evaluate(samples)
n_val = 200000
self.assertEqual(sample_values.shape, (n_val, ))
self.assertAllClose(sample_values.mean(), mu_v, rtol=0.1, atol=0)
self.assertAllClose(sample_values.var(),
sigma_v**2 * df_v / (df_v - 2),
rtol=0.1,
atol=0)
self._checkKLApprox(df_v, mu_v, sigma_v, sample_values)
def testVarianceAllowNanStatsTrueReturnsNaNforUndefinedBatchMembers(self):
# df = 0.5 ==> undefined mean ==> undefined variance.
# df = 1.5 ==> infinite variance.
df = [0.5, 1.5, 3., 5., 7.]
mu = [-2, 0., 1., 3.3, 4.4]
sigma = [5., 4., 3., 2., 1.]
student = student_t.StudentT(df=df,
loc=mu,
scale=sigma,
allow_nan_stats=True)
var = self.evaluate(student.variance())
if not stats:
return
expected_var = [
stats.t.var(d, loc=m, scale=s) for (d, m, s) in zip(df, mu, sigma)
]
# Slicing off first element due to nan/inf mismatch in different SciPy
# versions.
self.assertAllClose(expected_var[1:], var[1:])
def testStudentEntropy(self):
df_v = np.array([[2., 3., 7.]]) # 1x3
mu_v = np.array([[1., -1, 0]]) # 1x3
sigma_v = np.array([[1., -2., 3.]]).T # transposed => 3x1
student = student_t.StudentT(df=df_v, loc=mu_v, scale=sigma_v)
ent = student.entropy()
ent_values = self.evaluate(ent)
# Help scipy broadcast to 3x3
ones = np.array([[1, 1, 1]])
sigma_bc = np.abs(sigma_v) * ones
mu_bc = ones.T * mu_v
df_bc = ones.T * df_v
if not stats:
return
expected_entropy = stats.t.entropy(np.reshape(df_bc, [-1]),
loc=np.reshape(mu_bc, [-1]),
scale=np.reshape(sigma_bc, [-1]))
expected_entropy = np.reshape(expected_entropy, df_bc.shape)
self.assertAllClose(expected_entropy, ent_values)
def testPdfOfSample(self):
student = student_t.StudentT(df=3., loc=np.pi, scale=1.)
num = 20000
samples = student.sample(num, seed=123456)
pdfs = student.prob(samples)
mean = student.mean()
mean_pdf = student.prob(student.mean())
sample_vals, pdf_vals, mean_val, mean_pdf_val = self.evaluate(
[samples, pdfs, student.mean(), mean_pdf])
self.assertEqual(samples.get_shape(), (num,))
self.assertEqual(pdfs.get_shape(), (num,))
self.assertEqual(mean.get_shape(), ())
self.assertNear(np.pi, np.mean(sample_vals), err=0.02)
self.assertNear(np.pi, mean_val, err=1e-6)
# Verify integral over sample*pdf ~= 1.
# Tolerance increased since eager was getting a value of 1.002041.
self._assertIntegral(sample_vals, pdf_vals, err=3e-3)
if not stats:
return
self.assertNear(stats.t.pdf(np.pi, 3., loc=np.pi), mean_pdf_val, err=1e-6)
def testPdfOfSample(self):
with self.test_session() as sess:
student = student_t.StudentT(df=3., loc=np.pi, scale=1.)
num = 20000
samples = student.sample(num, seed=123456)
pdfs = student.prob(samples)
mean = student.mean()
mean_pdf = student.prob(student.mean())
sample_vals, pdf_vals, mean_val, mean_pdf_val = sess.run(
[samples, pdfs, student.mean(), mean_pdf])
self.assertEqual(samples.get_shape(), (num, ))
self.assertEqual(pdfs.get_shape(), (num, ))
self.assertEqual(mean.get_shape(), ())
self.assertNear(np.pi, np.mean(sample_vals), err=0.02)
self.assertNear(np.pi, mean_val, err=1e-6)
# Verify integral over sample*pdf ~= 1.
self._assertIntegral(sample_vals, pdf_vals, err=2e-3)
if not stats:
return
self.assertNear(stats.t.pdf(np.pi, 3., loc=np.pi),
mean_pdf_val,
err=1e-6)
def __init__(self,
df,
loc=None,
scale_identity_multiplier=None,
scale_diag=None,
scale_tril=None,
scale_perturb_factor=None,
scale_perturb_diag=None,
validate_args=False,
allow_nan_stats=True,
name="VectorStudentT"):
"""Instantiates the vector Student's t-distributions on `R^k`.
The `batch_shape` is the broadcast between `df.batch_shape` and
`Affine.batch_shape` where `Affine` is constructed from `loc` and
`scale_*` arguments.
The `event_shape` is the event shape of `Affine.event_shape`.
Args:
df: Floating-point `Tensor`. The degrees of freedom of the
distribution(s). `df` must contain only positive values. Must be
scalar if `loc`, `scale_*` imply non-scalar batch_shape or must have the
same `batch_shape` implied by `loc`, `scale_*`.
loc: Floating-point `Tensor`. If this is set to `None`, no `loc` is
applied.
scale_identity_multiplier: floating point rank 0 `Tensor` representing a
scaling done to the identity matrix. When `scale_identity_multiplier =
scale_diag=scale_tril = None` then `scale += IdentityMatrix`. Otherwise
no scaled-identity-matrix is added to `scale`.
scale_diag: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ..., k], which represents a k x k
diagonal matrix. When `None` no diagonal term is added to `scale`.
scale_tril: Floating-point `Tensor` representing the diagonal matrix.
`scale_diag` has shape [N1, N2, ..., k, k], which represents a k x k
lower triangular matrix. When `None` no `scale_tril` term is added to
`scale`. The upper triangular elements above the diagonal are ignored.
scale_perturb_factor: Floating-point `Tensor` representing factor matrix
with last two dimensions of shape `(k, r)`. When `None`, no rank-r
update is added to `scale`.
scale_perturb_diag: Floating-point `Tensor` representing the diagonal
matrix. `scale_perturb_diag` has shape [N1, N2, ..., r], which
represents an r x r Diagonal matrix. When `None` low rank updates will
take the form `scale_perturb_factor * scale_perturb_factor.T`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
"""
parameters = dict(locals())
graph_parents = [
df, loc, scale_identity_multiplier, scale_diag, scale_tril,
scale_perturb_factor, scale_perturb_diag
]
with ops.name_scope(name) as name:
with ops.name_scope("init", values=graph_parents):
# The shape of the _VectorStudentT distribution is governed by the
# relationship between df.batch_shape and affine.batch_shape. In
# pseudocode the basic procedure is:
# if df.batch_shape is scalar:
# if affine.batch_shape is not scalar:
# # broadcast distribution.sample so
# # it has affine.batch_shape.
# self.batch_shape = affine.batch_shape
# else:
# if affine.batch_shape is scalar:
# # let affine broadcasting do its thing.
# self.batch_shape = df.batch_shape
# All of the above magic is actually handled by TransformedDistribution.
# Here we really only need to collect the affine.batch_shape and decide
# what we're going to pass in to TransformedDistribution's
# (override) batch_shape arg.
affine = bijectors.Affine(
shift=loc,
scale_identity_multiplier=scale_identity_multiplier,
scale_diag=scale_diag,
scale_tril=scale_tril,
scale_perturb_factor=scale_perturb_factor,
scale_perturb_diag=scale_perturb_diag,
validate_args=validate_args)
distribution = student_t.StudentT(
df=df,
loc=array_ops.zeros([], dtype=affine.dtype),
scale=array_ops.ones([], dtype=affine.dtype))
batch_shape, override_event_shape = (
distribution_util.shapes_from_loc_and_scale(
affine.shift, affine.scale))
override_batch_shape = distribution_util.pick_vector(
distribution.is_scalar_batch(), batch_shape,
constant_op.constant([], dtype=dtypes.int32))
super(_VectorStudentT,
self).__init__(distribution=distribution,
bijector=affine,
batch_shape=override_batch_shape,
event_shape=override_event_shape,
validate_args=validate_args,
name=name)
self._parameters = parameters
