def testPmfNonIntegerCounts(self):
p = [[0.1, 0.2, 0.7]]
n = [[5.]]
with self.test_session():
# No errors with integer n.
multinom = multinomial.Multinomial(total_count=n,
probs=p,
validate_args=True)
multinom.prob([2., 1, 2]).eval()
multinom.prob([3., 0, 2]).eval()
# Counts don't sum to n.
with self.assertRaisesOpError(
"counts must sum to `self.total_count`"):
multinom.prob([2., 3, 2]).eval()
# Counts are non-integers.
x = array_ops.placeholder(dtypes.float32)
with self.assertRaisesOpError(
"cannot contain fractional components."):
multinom.prob(x).eval(feed_dict={x: [1.0, 2.5, 1.5]})
multinom = multinomial.Multinomial(total_count=n,
probs=p,
validate_args=False)
multinom.prob([1., 2., 2.]).eval()
# Non-integer arguments work.
multinom.prob([1.0, 2.5, 1.5]).eval()
def testPmfCountsStretchedInBroadcastWhenLowerRank(self):
with self.test_session():
p = [[0.1, 0.9], [0.7, 0.3]]
counts = [1., 0]
pmf = multinomial.Multinomial(total_count=1., probs=p).prob(counts)
self.assertAllClose(pmf.eval(), [0.1, 0.7])
self.assertEqual(pmf.get_shape(), (2))
def testN(self):
p = [[0.1, 0.2, 0.7], [0.2, 0.3, 0.5]]
n = [[3.], [4]]
with self.test_session():
dist = multinomial.Multinomial(total_count=n, probs=p)
self.assertEqual((2, 1), dist.total_count.get_shape())
self.assertAllClose(n, dist.total_count.eval())
def testP(self):
p = [[0.1, 0.2, 0.7]]
with self.test_session():
dist = multinomial.Multinomial(total_count=3., probs=p)
self.assertEqual((1, 3), dist.probs.get_shape())
self.assertEqual((1, 3), dist.logits.get_shape())
self.assertAllClose(p, dist.probs.eval())
def testSampleUnbiasedNonScalarBatch(self):
with self.test_session() as sess:
dist = multinomial.Multinomial(
total_count=[7., 6., 5.],
logits=math_ops.log(
2. * self._rng.rand(4, 3, 2).astype(np.float32)))
n = int(3e4)
x = dist.sample(n, seed=0)
sample_mean = math_ops.reduce_mean(x, 0)
# Cyclically rotate event dims left.
x_centered = array_ops.transpose(x - sample_mean, [1, 2, 3, 0])
sample_covariance = math_ops.matmul(
x_centered, x_centered, adjoint_b=True) / n
[
sample_mean_,
sample_covariance_,
actual_mean_,
actual_covariance_,
] = sess.run([
sample_mean,
sample_covariance,
dist.mean(),
dist.covariance(),
])
self.assertAllEqual([4, 3, 2], sample_mean.get_shape())
self.assertAllClose(actual_mean_, sample_mean_, atol=0., rtol=0.07)
self.assertAllEqual([4, 3, 2, 2], sample_covariance.get_shape())
self.assertAllClose(actual_covariance_,
sample_covariance_,
atol=0.,
rtol=0.10)
def testSampleUnbiasedScalarBatch(self):
with self.test_session() as sess:
dist = multinomial.Multinomial(
total_count=5.,
logits=math_ops.log(2. * self._rng.rand(4).astype(np.float32)))
n = int(5e3)
x = dist.sample(n, seed=0)
sample_mean = math_ops.reduce_mean(x, 0)
x_centered = x - sample_mean # Already transposed to [n, 2].
sample_covariance = math_ops.matmul(
x_centered, x_centered, adjoint_a=True) / n
[
sample_mean_,
sample_covariance_,
actual_mean_,
actual_covariance_,
] = sess.run([
sample_mean,
sample_covariance,
dist.mean(),
dist.covariance(),
])
self.assertAllEqual([4], sample_mean.get_shape())
self.assertAllClose(actual_mean_, sample_mean_, atol=0., rtol=0.07)
self.assertAllEqual([4, 4], sample_covariance.get_shape())
self.assertAllClose(actual_covariance_,
sample_covariance_,
atol=0.,
rtol=0.10)
def testPmfPStretchedInBroadcastWhenLowerRank(self):
with self.test_session():
p = [0.1, 0.9]
counts = [[1., 0], [0, 1]]
pmf = multinomial.Multinomial(total_count=1., probs=p).prob(counts)
self.assertAllClose([0.1, 0.9], pmf.eval())
self.assertEqual((2), pmf.get_shape())
def testPmfCountsStretchedInBroadcastWhenSameRank(self):
with self.cached_session():
p = [[0.1, 0.9], [0.7, 0.3]]
counts = [[1., 0]]
pmf = multinomial.Multinomial(total_count=1., probs=p).prob(counts)
self.assertAllClose(pmf, [0.1, 0.7])
self.assertEqual((2), pmf.get_shape())
def testPmfBothZeroBatches(self):
with self.test_session():
# Both zero-batches. No broadcast
p = [0.5, 0.5]
counts = [1., 0]
pmf = multinomial.Multinomial(total_count=1., probs=p).prob(counts)
self.assertAllClose(0.5, pmf.eval())
self.assertEqual((), pmf.get_shape())
def testCovarianceMultidimensional(self):
# Shape [3, 5, 4]
p = np.random.dirichlet([.25, .25, .25, .25], [3, 5]).astype(np.float32)
# Shape [6, 3, 3]
p2 = np.random.dirichlet([.3, .3, .4], [6, 3]).astype(np.float32)
ns = np.random.randint(low=1, high=11, size=[3, 5]).astype(np.float32)
ns2 = np.random.randint(low=1, high=11, size=[6, 1]).astype(np.float32)
with self.test_session():
dist = multinomial.Multinomial(ns, p)
dist2 = multinomial.Multinomial(ns2, p2)
covariance = dist.covariance()
covariance2 = dist2.covariance()
self.assertEqual((3, 5, 4, 4), covariance.get_shape())
self.assertEqual((6, 3, 3, 3), covariance2.get_shape())
def testSimpleShapes(self):
with self.test_session():
p = [.1, .3, .6]
dist = multinomial.Multinomial(total_count=1., probs=p)
self.assertEqual(3, dist.event_shape_tensor().eval())
self.assertAllEqual([], dist.batch_shape_tensor().eval())
self.assertEqual(tensor_shape.TensorShape([3]), dist.event_shape)
self.assertEqual(tensor_shape.TensorShape([]), dist.batch_shape)
def testMultinomialMean(self):
with self.test_session():
n = 5.
p = [0.1, 0.2, 0.7]
dist = multinomial.Multinomial(total_count=n, probs=p)
expected_means = 5 * np.array(p, dtype=np.float32)
self.assertEqual((3, ), dist.mean().get_shape())
self.assertAllClose(expected_means, dist.mean().eval())
def testPmfShapeCountsPStretchedN(self):
with self.test_session():
p = [0.1, 0.9]
counts = [3., 2]
n = np.full([4, 3], 5., dtype=np.float32)
pmf = multinomial.Multinomial(total_count=n, probs=p).prob(counts)
pmf.eval()
self.assertEqual((4, 3), pmf.get_shape())
def testComplexShapes(self):
with self.test_session():
p = 0.5 * np.ones([3, 2, 2], dtype=np.float32)
n = [[3., 2], [4, 5], [6, 7]]
dist = multinomial.Multinomial(total_count=n, probs=p)
self.assertEqual(2, dist.event_shape_tensor().eval())
self.assertAllEqual([3, 2], dist.batch_shape_tensor().eval())
self.assertEqual(tensor_shape.TensorShape([2]), dist.event_shape)
self.assertEqual(tensor_shape.TensorShape([3, 2]), dist.batch_shape)
def testLogits(self):
p = np.array([[0.1, 0.2, 0.7]], dtype=np.float32)
logits = np.log(p) - 50.
with self.test_session():
multinom = multinomial.Multinomial(total_count=3., logits=logits)
self.assertEqual((1, 3), multinom.probs.get_shape())
self.assertEqual((1, 3), multinom.logits.get_shape())
self.assertAllClose(p, multinom.probs.eval())
self.assertAllClose(logits, multinom.logits.eval())
def testMultinomialCovariance(self):
with self.test_session():
n = 5.
p = [0.1, 0.2, 0.7]
dist = multinomial.Multinomial(total_count=n, probs=p)
expected_covariances = [[9. / 20, -1 / 10, -7 / 20],
[-1 / 10, 4 / 5, -7 / 10],
[-7 / 20, -7 / 10, 21 / 20]]
self.assertEqual((3, 3), dist.covariance().get_shape())
self.assertAllClose(expected_covariances, dist.covariance().eval())
def testPmfBothZeroBatchesNontrivialN(self):
with self.test_session():
# Both zero-batches. No broadcast
p = [0.1, 0.9]
counts = [3., 2]
dist = multinomial.Multinomial(total_count=5., probs=p)
pmf = dist.prob(counts)
# 5 choose 3 = 5 choose 2 = 10. 10 * (.9)^2 * (.1)^3 = 81/10000.
self.assertAllClose(81. / 10000, pmf.eval())
self.assertEqual((), pmf.get_shape())
def testPmfandCountsAgree(self):
p = [[0.1, 0.2, 0.7]]
n = [[5.]]
with self.test_session():
dist = multinomial.Multinomial(total_count=n, probs=p, validate_args=True)
dist.prob([2., 3, 0]).eval()
dist.prob([3., 0, 2]).eval()
with self.assertRaisesOpError("must be non-negative"):
dist.prob([-1., 4, 2]).eval()
with self.assertRaisesOpError("counts must sum to `self.total_count`"):
dist.prob([3., 3, 0]).eval()
def testNotReparameterized(self):
total_count = constant_op.constant(5.0)
p = constant_op.constant([0.2, 0.6])
with backprop.GradientTape() as tape:
tape.watch(total_count)
tape.watch(p)
dist = multinomial.Multinomial(total_count=total_count, probs=p)
samples = dist.sample(100)
grad_total_count, grad_p = tape.gradient(samples, [total_count, p])
self.assertIsNone(grad_total_count)
self.assertIsNone(grad_p)
def testCovarianceFromSampling(self):
# We will test mean, cov, var, stddev on a DirichletMultinomial constructed
# via broadcast between alpha, n.
theta = np.array([[1., 2, 3], [2.5, 4, 0.01]], dtype=np.float32)
theta /= np.sum(theta, 1)[..., array_ops.newaxis]
# Ideally we'd be able to test broadcasting but, the multinomial sampler
# doesn't support different total counts.
n = np.float32(5)
with self.test_session() as sess:
# batch_shape=[2], event_shape=[3]
dist = multinomial.Multinomial(n, theta)
x = dist.sample(int(250e3), seed=1)
sample_mean = math_ops.reduce_mean(x, 0)
x_centered = x - sample_mean[array_ops.newaxis, ...]
sample_cov = math_ops.reduce_mean(
math_ops.matmul(x_centered[..., array_ops.newaxis],
x_centered[..., array_ops.newaxis, :]), 0)
sample_var = array_ops.matrix_diag_part(sample_cov)
sample_stddev = math_ops.sqrt(sample_var)
[
sample_mean_,
sample_cov_,
sample_var_,
sample_stddev_,
analytic_mean,
analytic_cov,
analytic_var,
analytic_stddev,
] = sess.run([
sample_mean,
sample_cov,
sample_var,
sample_stddev,
dist.mean(),
dist.covariance(),
dist.variance(),
dist.stddev(),
])
self.assertAllClose(sample_mean_,
analytic_mean,
atol=0.01,
rtol=0.01)
self.assertAllClose(sample_cov_,
analytic_cov,
atol=0.01,
rtol=0.01)
self.assertAllClose(sample_var_,
analytic_var,
atol=0.01,
rtol=0.01)
self.assertAllClose(sample_stddev_,
analytic_stddev,
atol=0.01,
rtol=0.01)
def testPmfShapeCountsStretchedN(self):
with self.test_session():
# [2, 2, 2]
p = [[[0.1, 0.9], [0.1, 0.9]], [[0.7, 0.3], [0.7, 0.3]]]
# [2, 2]
n = [[3., 3], [3, 3]]
# [2]
counts = [2., 1]
pmf = multinomial.Multinomial(total_count=n, probs=p).prob(counts)
pmf.eval()
self.assertEqual(pmf.get_shape(), (2, 2))
def testMultinomialCovarianceBatch(self):
with self.test_session():
# Shape [2]
n = [5.] * 2
# Shape [4, 1, 2]
p = [[[0.1, 0.9]], [[0.1, 0.9]]] * 2
dist = multinomial.Multinomial(total_count=n, probs=p)
# Shape [2, 2]
inner_var = [[9. / 20, -9 / 20], [-9 / 20, 9 / 20]]
# Shape [4, 2, 2, 2]
expected_covariances = [[inner_var, inner_var]] * 4
self.assertEqual((4, 2, 2, 2), dist.covariance().get_shape())
self.assertAllClose(expected_covariances, dist.covariance().eval())
def testPmfUnderflow(self):
logits = np.array([[-200, 0]], dtype=np.float32)
with self.test_session():
dist = multinomial.Multinomial(total_count=1., logits=logits)
lp = dist.log_prob([1., 0.]).eval()[0]
self.assertAllClose(-200, lp, atol=0, rtol=1e-6)
