def testBatesPDFonNaNs(self):
for b in [tfd.Bates(1, 0, 1), tfd.Bates(4, -10, -8)]:
values_with_nans = [
np.nan, -1., np.nan, 0., np.nan, .5, np.nan, 1., np.nan, 2.,
np.nan
]
values = [
v if i % 2 != 0 else 0. for i, v in enumerate(values_with_nans)
]
probs = self.evaluate(b.log_prob(values))
probs_with_nans = self.evaluate(b.log_prob(values_with_nans))
should_be_nan = [
probs_with_nans[i] for i, v in enumerate(values_with_nans)
if np.isnan(v)
]
self.assertAllNan(should_be_nan)
lhs = [
probs[i] for i, v in enumerate(values_with_nans)
if not np.isnan(v)
]
rhs = [
probs_with_nans[i] for i, v in enumerate(values_with_nans)
if not np.isnan(v)
]
self.assertAllEqual(lhs, rhs)
def testBatesInfs(self):
b = tfd.Bates(1., 0., 1., validate_args=True)
values_with_infs = [-np.inf, 0.5, np.inf]
self.assertAllClose([0., 1., 0.],
self.evaluate(b.prob(values_with_infs)))
self.assertAllClose([0., .5, 1.],
self.evaluate(b.cdf(values_with_infs)))
def testBatesCDFLowTotalCount(self):
ns = np.array([1., 2.])
ls = np.array([0., 1.])
hs = np.array([1., 3.])
b = tfd.Bates(total_count=tf.expand_dims(ns, -1),
low=ls,
high=hs,
validate_args=True)
self.assertAllEqual([2, 2], self.evaluate(b.batch_shape_tensor()))
xs = np.array([0., .25, .5, 1.1, 1.5, 2.])
cdfs = b.cdf(tf.reshape(xs, (6, 1, 1)))
self.assertAllEqual([6, 2, 2], self.evaluate(tf.shape(cdfs)))
def expected_cdf(n, l, h, x):
if n == 1:
left = right = (x - l) / (h - l)
elif n == 2:
left = 2 * np.power((x - l) / (h - l), 2)
right = 1 - 2 * np.power((h - x) / (h - l), 2)
else:
raise ValueError('Compute your own damn cdfs')
return np.where(
x < l, 0,
np.where(x > h, 1, np.where(x < (l + h) / 2., left, right)))
expected = [[[expected_cdf(n, l, h, x) for l, h in zip(ls, hs)]
for n in ns] for x in xs]
self.assertAllClose(expected, self.evaluate(cdfs))
def testBatesVariables(self):
n0 = np.array([1., 2.])
l0 = np.array([0., 1.])
h0 = np.array([1., 11.])
n = tf.Variable(n0)
l = tf.Variable(l0)
h = tf.Variable(h0)
d = tfd.Bates(total_count=n, low=l, high=h, validate_args=True)
self.evaluate([v.initializer for v in d.variables])
self.evaluate(d.prob([.5, 1.]))
self.evaluate(n.assign(-n0))
with self.assertRaisesOpError('`total_count` must be positive.'):
self.evaluate(d.prob([.5, 1.]))
self.evaluate(n.assign(n0))
self.evaluate(d.prob([.5, 1.]))
self.evaluate(n.assign(n0 / 2.))
with self.assertRaisesOpError('`total_count` must be integer-valued.'):
self.evaluate(d.prob([.5, 1.]))
self.evaluate(n.assign(n0))
self.evaluate(d.prob([.5, 1.]))
self.evaluate(n.assign([1000., 2000.]))
with self.assertRaisesOpError(
'`total_count` > .* is numerically unstable.'):
self.evaluate(d.prob([.5, 1.]))
self.evaluate(n.assign(n0))
self.evaluate(d.prob([.5, 1.]))
self.evaluate(l.assign(h0))
with self.assertRaisesOpError('`low` must be less than `high`'):
self.evaluate(d.prob([.5, 1.]))
self.evaluate(l.assign(l0))
self.evaluate(d.prob([.5, 1.]))
def testBatesPDFLowTotalCount(self):
ns = np.array([1., 2.])
lss = np.array([[0., -1.], [-10., -1.]])
hss = np.array([[1., 3.], [-9., 0.]])
b = tfd.Bates(total_count=tf.reshape(ns, (2, 1, 1)),
low=lss,
high=hss,
validate_args=True)
self.assertAllEqual([2, 2, 2], self.evaluate(b.batch_shape_tensor()))
xs = np.array([0., .25, .5, 1.1, 1.5, 2.])
probs = b.prob(tf.reshape(xs, (6, 1, 1, 1)))
self.assertAllEqual([6, 2, 2, 2], self.evaluate(tf.shape(probs)))
def expected_pdf(n, l, h, x):
if n == 1:
left = right = 1. / (h - l)
elif n == 2:
left = np.power(2 / (h - l), 2) * (x - l)
right = np.power(2 / (h - l), 2) * (h - x)
else:
raise ValueError('Compute your own damn pdfs')
return np.where(
x < l, 0,
np.where(x > h, 0, np.where(x < (l + h) / 2., left, right)))
expected = [[[[expected_pdf(n, l, h, x) for l, h in zip(ls, hs)]
for ls, hs in zip(lss, hss)] for n in ns] for x in xs]
self.assertAllClose(expected, self.evaluate(probs))
def testBatesNaNs(self):
b = tfd.Bates(1., 0., 1., validate_args=True)
values_with_nans = [-1., 0., .5, 1., np.nan, 2.]
with self.assertRaisesRegex(ValueError, '`value` must not be NaN'):
self.evaluate(b.prob(values_with_nans))
with self.assertRaisesRegex(ValueError, '`value` must not be NaN'):
self.evaluate(b.cdf(values_with_nans))
def testBatesMean(self):
# TODO(b/157666350): Turn this into a hypothesis test.
bounds = np.array([[0., 1.], [1., 2.], [-2., -1.], [10., 20.]])
b = tfd.Bates(total_count=10.,
low=bounds[..., 0],
high=bounds[..., 1],
validate_args=True)
self.assertAllClose(bounds.mean(1), self.evaluate(b.mean()))
def testBatesParamsNoBatch(self):
n = 8.
l = -11.
h = -5.
b = tfd.Bates(total_count=n, low=l, high=h, validate_args=True)
self.assertAllClose(n, self.evaluate(b.total_count))
self.assertAllClose(l, self.evaluate(b.low))
self.assertAllClose(h, self.evaluate(b.high))
self.assertAllEqual([], self.evaluate(b.batch_shape_tensor()))
def testBatesParamsBatch(self):
n = tf.ones((2, 1, 3), dtype=tf.float32)
l = tf.zeros((2, 2, 1), dtype=tf.float32)
h = tf.constant(3, dtype=tf.float32)
b = tfd.Bates(total_count=n, low=l, high=h, validate_args=True)
self.assertAllClose(n, self.evaluate(b.total_count))
self.assertAllClose(l, self.evaluate(b.low))
self.assertAllClose(h, self.evaluate(b.high))
self.assertAllEqual([2, 2, 3], self.evaluate(b.batch_shape_tensor()))
def testBatesInvalidShapes(self):
n = np.ones((2, 3))
l = np.zeros((2, 2))
with self.assertRaisesRegex(
ValueError,
'Arguments `total_count`, `low` and `high` must have compatible shapes'
):
d = tfd.Bates(total_count=n, low=l, validate_args=True)
self.evaluate(d.prob(1.))
def testBatesVariance(self):
ns = np.array([1., 2., 10.])
lss = np.array([[-10., -2.], [-10., 0.]])
hss = np.array([[-1., 0.], [10., 100.]])
b = tfd.Bates(total_count=tf.reshape(ns, (3, 1, 1)),
low=lss,
high=hss,
validate_args=True)
expected = [[[np.power(h - l, 2) / (12 * n) for l, h in zip(ls, hs)]
for ls, hs in zip(lss, hss)] for n in ns]
self.assertAllClose(self.evaluate(b.variance()), expected)
def testBatesStableTotalCountWarning(self):
bad = max(bates.BATES_TOTAL_COUNT_STABILITY_LIMITS.values()) + 10.
d = tfd.Bates(total_count=bad, validate_args=False)
with self.captureWritesToStream(sys.stderr) as captured:
self.evaluate(d.prob(1.))
self.assertRegex(captured.contents(),
'Bates PDF/CDF is unstable for `total_count` >')
with self.captureWritesToStream(sys.stderr) as captured:
self.evaluate(d.cdf(1.))
self.assertRegex(captured.contents(),
'Bates PDF/CDF is unstable for `total_count` >')
def testBatesPDFisNormalized(self, total_count, bounds):
low, high = tf.cast(bounds[0],
tf.float64), tf.cast(bounds[1], tf.float64)
d = tfd.Bates(total_count=total_count, low=low, high=high)
# This is about as high as JAX can go and still finish in time.
nx = 100
x = tf.linspace(low, high, nx)
y = self.evaluate(d.prob(x))
dx = self.evaluate(x[1] - x[0])
self.assertAllClose(scipy.integrate.simps(y=y, dx=dx),
1.,
atol=5e-05,
rtol=5e-05)
def testBatesSampleStatistics(self):
# TODO(b/157666350): Turn this into a hypothesis test.
bounds = np.array([[0., 1.], [1., 2.], [-2., -1.], [10., 20.]])
b = tfd.Bates(total_count=10.,
low=bounds[..., 0],
high=bounds[..., 1],
validate_args=True)
samples = b.sample(1e6, seed=test_util.test_seed())
self.assertAllClose(self.evaluate(b.mean()),
np.mean(self.evaluate(samples), axis=0),
atol=1e-03,
rtol=1e-03)
self.assertAllClose(self.evaluate(b.variance()),
np.var(self.evaluate(samples), axis=0),
atol=1e-03,
rtol=1e-03)
def testBatesCDFHighTotalCount(self):
# Compute with exact integer arithmetic.
def exact(n, nx):
fractional = sum(
fractions.Fraction((-1)**k * (nx - k)**n * math.factorial(n),
math.factorial(n - k) * math.factorial(k))
for k in range(nx + 1)) * fractions.Fraction(
1, math.factorial(n))
return fractional.numerator / fractional.denominator
tests = [(48, .25), (48, .5), (48, .75), (50, 0.02), (50, .48),
(50, .52), (50, .98)]
for n, x in tests:
nx_ = n * x
nx = int(nx_)
self.assertAllClose(nx_, nx)
b = tfd.Bates(total_count=n, low=tf.cast(0, tf.float64))
val = b.cdf(tf.cast(x, tf.float64))
self.assertAllEqual([], self.evaluate(tf.shape(val)))
self.assertAllClose(self.evaluate(val), exact(n, nx))
def testBatesIntegralTotalCount(self):
with self.assertRaisesOpError('`total_count` must be integer-valued.'):
d = tfd.Bates(total_count=1.5, validate_args=True)
self.evaluate(d.prob(1.))
def testBatesStableTotalCount(self):
bad = max(bates.BATES_TOTAL_COUNT_STABILITY_LIMITS.values()) + 10.
with self.assertRaisesOpError(
'`total_count` > .* is numerically unstable'):
d = tfd.Bates(total_count=bad, validate_args=True)
self.evaluate(d.prob(1.))
def testBatesIntegralTotalCount(self):
msg = '`total_count` must be representable as a 32-bit integer.'
with self.assertRaisesOpError(msg):
d = tfd.Bates(total_count=1.5, validate_args=True)
self.evaluate(d.prob(1.))
def testBatesNonNegTotalCount(self):
ns = [0., -1.]
for n in ns:
with self.assertRaisesOpError('`total_count` must be positive.'):
d = tfd.Bates(total_count=n, validate_args=True)
self.evaluate(d.prob(1.))
def testBatesLowLtHigh(self):
bounds = [(-1., -1.), (0., 0.), (-1., -1.1), (1.1, 1.)]
for l, h in bounds:
with self.assertRaisesOpError('`low` must be less than `high`'):
d = tfd.Bates(total_count=1, low=l, high=h, validate_args=True)
self.evaluate(d.prob(1.))
def make_shapeless_bates(self, total_count, low, high):
return tfd.Bates(total_count=self.shapeless(total_count),
low=self.shapeless(low),
high=self.shapeless(high))
def testEmpty(self):
d = tfd.Bates(total_count=tf.zeros([0]))
self.evaluate(d.log_prob(d.sample(seed=test_util.test_seed())))
