def _cdf(self, x):
# CDF is the probability that the Poisson variable is less or equal to x.
# For fractional x, the CDF is equal to the CDF at n = floor(x).
# For negative x, the CDF is zero, but tf.igammac gives NaNs, so we impute
# the values and handle this case explicitly.
n = tf.maximum(tf.floor(x), 0.)
cdf = tf.igammac(1. + n, self.rate)
return tf.where(tf.broadcast_to(tf.less(x, 0.), tf.shape(cdf)),
tf.zeros_like(cdf), cdf)
def _cdf(self, x):
# CDF is the probability that the Poisson variable is less or equal to x.
# For fractional x, the CDF is equal to the CDF at n = floor(x).
# For negative x, the CDF is zero, but tf.igammac gives NaNs, so we impute
# the values and handle this case explicitly.
safe_x = tf.maximum(x if self.interpolate_nondiscrete else tf.floor(x), 0.)
cdf = tf.igammac(1. + safe_x, self.rate)
return tf.where(tf.broadcast_to(x < 0., tf.shape(cdf)),
tf.zeros_like(cdf),
cdf)
def testPoissonCdfContinuousRelaxation(self):
batch_size = 12
lam = tf.constant([3.0] * batch_size)
x = np.array([-3., -0.5, 0., 2., 2.2, 3., 3.1, 4., 5., 5.5, 6.,
7.]).astype(np.float32)
expected_continuous_cdf = tf.igammac(1. + x, lam)
expected_continuous_cdf = tf.where(
x >= 0., expected_continuous_cdf,
tf.zeros_like(expected_continuous_cdf))
expected_continuous_log_cdf = tf.log(expected_continuous_cdf)
poisson = self._make_poisson(rate=lam, interpolate_nondiscrete=True)
log_cdf = poisson.log_cdf(x)
self.assertEqual(log_cdf.shape, (batch_size, ))
self.assertAllClose(self.evaluate(log_cdf),
self.evaluate(expected_continuous_log_cdf))
cdf = poisson.cdf(x)
self.assertEqual(cdf.shape, (batch_size, ))
self.assertAllClose(self.evaluate(cdf),
self.evaluate(expected_continuous_cdf))
def testPoissonCdfContinuousRelaxation(self):
batch_size = 12
lam = tf.constant([3.0] * batch_size)
x = np.array(
[-3., -0.5, 0., 2., 2.2, 3., 3.1, 4., 5., 5.5, 6., 7.]).astype(
np.float32)
expected_continuous_cdf = tf.igammac(1. + x, lam)
expected_continuous_cdf = tf.where(x >= 0.,
expected_continuous_cdf,
tf.zeros_like(expected_continuous_cdf))
expected_continuous_log_cdf = tf.log(expected_continuous_cdf)
poisson = self._make_poisson(rate=lam, interpolate_nondiscrete=True)
log_cdf = poisson.log_cdf(x)
self.assertEqual(log_cdf.shape, (batch_size,))
self.assertAllClose(self.evaluate(log_cdf),
self.evaluate(expected_continuous_log_cdf))
cdf = poisson.cdf(x)
self.assertEqual(cdf.shape, (batch_size,))
self.assertAllClose(self.evaluate(cdf),
self.evaluate(expected_continuous_cdf))
def _cdf(self, x):
x = self._maybe_assert_valid_sample(x)
# Note that igammac returns the upper regularized incomplete gamma
# function Q(a, x), which is what we want for the CDF.
return tf.igammac(self.concentration, self.rate / x)
def test_Igammac(self):
t = tf.igammac(*self.random((3, 3), (3, 3)))
self.check(t)
import tensorflow as tf """tf.igammac(a,x,name=None) 功能：计算gamma(a,x)/gamma(a),gamma(a,x)=\intergral_from_x_to_inf t^(a-1)*exp^(-t)dt。 输入：x为张量，可以为`float32`, `float64`类型。""" a = tf.constant(1, tf.float64) x = tf.constant([[-1, 0, 1, 2, 3]], tf.float64) z = tf.igammac(a, x) sess = tf.Session() print(sess.run(z)) sess.close() # z==>[[ nan 1. 0.36787944 0.13533528 0.04978707]]
def _cdf(self, x): x = self._maybe_assert_valid_sample(x) # Note that igammac returns the upper regularized incomplete gamma # function Q(a, x), which is what we want for the CDF. return tf.igammac(self.concentration, self.rate / x)
def _cdf(self, x):
if self.validate_args:
x = distribution_util.embed_check_nonnegative_integer_form(x)
return tf.igammac(1. + x, self.rate)
def GO_Gamma_v2(x, alpha):
# x sim Gamma(alpha, 1)
x = tf.cast(x, tf.float64)
alpha = tf.cast(alpha, tf.float64)
logx = tf.log(x)
ex_gamma_xa = tf.exp(x + tf.lgamma(alpha) + (1. - alpha) * logx)
psi_m_log = tf.digamma(alpha + 1.) - logx
igamma_up_reg = tf.igammac(alpha, x)
# Part 1
indx1 = tf.where(x <= 1e-2)
x_indx1 = tf.gather_nd(x, indx1)
alpha_indx1 = tf.gather_nd(alpha, indx1)
GO_Gamma_alpha_value1 = tf.exp(x_indx1) * x_indx1 / alpha_indx1 * (
tf.gather_nd(psi_m_log, indx1) +
x_indx1 / tf.pow(alpha_indx1 + 1., 2) -
tf.pow(x_indx1 / (alpha_indx1 + 2.), 2) +
0.5 * tf.pow(x_indx1, 3) / tf.pow(alpha_indx1 + 3., 2)
)
# Part 2
N_alpha = tf.round(tf.exp(
- 0.488484605941243044124888683654717169702053070068359375 * tf.log(alpha)
+ 1.6948389987594634220613443176262080669403076171875
))
indx2 = tf.where(tf.logical_and(
tf.logical_and(x > 1e-2, alpha <= 3.),
(x <= (alpha + N_alpha * tf.sqrt(alpha)))
))
KK = 15
kk = tf.cast(tf.range(1, KK + 1), tf.float64)
x_indx2 = tf.gather_nd(x, indx2)
alpha_indx2 = tf.gather_nd(alpha, indx2)
GO_Gamma_alpha_value2 = tf.gather_nd(ex_gamma_xa, indx2) * (
-tf.gather_nd(psi_m_log, indx2) * tf.gather_nd(igamma_up_reg, indx2) +
(
tf.digamma(alpha_indx2 + KK + 1.) - tf.gather_nd(logx, indx2) -
tf.reduce_sum(
tf.igammac(tf.expand_dims(alpha_indx2, 1) + tf.expand_dims(kk, 0), tf.expand_dims(x_indx2, 1)) /
(tf.expand_dims(alpha_indx2, 1) + tf.expand_dims(kk, 0))
, 1)
)
)
# Part 2_1
indx2_1 = tf.where(tf.logical_and(
tf.logical_and(x > 1e-2, alpha <= 3.),
(x > (alpha + N_alpha * tf.sqrt(alpha)))
))
KK = 15
kk = tf.cast(tf.range(1, KK + 1), tf.float64)
x_indx2_1 = tf.gather_nd(x, indx2_1)
alpha_indx2_1 = tf.gather_nd(alpha, indx2_1)
GO_Gamma_alpha_value2_1 = tf.gather_nd(ex_gamma_xa, indx2_1) * (
-tf.gather_nd(psi_m_log, indx2_1) * tf.gather_nd(igamma_up_reg, indx2_1) +
(
tf.digamma(alpha_indx2_1 + KK + 1.) - tf.gather_nd(logx, indx2_1) -
tf.reduce_sum(
tf.igammac(tf.expand_dims(alpha_indx2_1, 1) + tf.expand_dims(kk, 0),
tf.expand_dims(x_indx2_1, 1)) /
(tf.expand_dims(alpha_indx2_1, 1) + tf.expand_dims(kk, 0))
, 1)
)
)
GO_Gamma_alpha_value2_1 = tf.maximum(
GO_Gamma_alpha_value2_1,
1. / alpha_indx2_1 - tf.gather_nd(ex_gamma_xa, indx2_1) *
tf.gather_nd(psi_m_log, indx2_1) * tf.gather_nd(igamma_up_reg, indx2_1)
)
# Part 3
indx3 = tf.where(
tf.logical_and(
tf.logical_and(x > 1e-2, alpha > 3.),
alpha <= 500.
)
)
KK = 10
kk = tf.cast(tf.range(1, KK + 1), tf.float64)
x_indx3 = tf.gather_nd(x, indx3)
alpha_indx3 = tf.gather_nd(alpha, indx3)
x_l = alpha_indx3 - tf.log(alpha_indx3) * tf.sqrt(alpha_indx3)
logx_l = tf.log(x_l)
ex_gamma_xa_l = tf.exp(x_l + tf.lgamma(alpha_indx3) + (1. - alpha_indx3) * logx_l)
psi_m_log_l = tf.digamma(alpha_indx3 + 1.) - logx_l
igamma_low_reg_l = tf.igamma(alpha_indx3, x_l)
# igamma_up_reg_l = tf.igammac(alpha_indx3, x_l)
# f_l = ex_gamma_xa_l * (
# -psi_m_log_l * igamma_up_reg_l +
# (tf.digamma(alpha_indx3 + KK + 1.) - logx_l -
# tf.reduce_sum(
# tf.igammac(tf.expand_dims(alpha_indx3, 1) + tf.expand_dims(kk, 0), tf.expand_dims(x_l, 1)) /
# (tf.expand_dims(alpha_indx3, 1) + tf.expand_dims(kk, 0))
# , 1))
# )
f_l = ex_gamma_xa_l * (
psi_m_log_l * igamma_low_reg_l +
tf.reduce_sum(
tf.igamma(tf.expand_dims(alpha_indx3, 1) + tf.expand_dims(kk, 0), tf.expand_dims(x_l, 1)) /
(tf.expand_dims(alpha_indx3, 1) + tf.expand_dims(kk, 0))
, 1)
)
g_l = (1. + (1. - alpha_indx3) / x_l) * f_l + (
-ex_gamma_xa_l / x_l * igamma_low_reg_l + (psi_m_log_l +
tf.reduce_sum(
tf.exp(
tf.expand_dims(kk, 0) * tf.log(tf.expand_dims(x_l, 1)) +
tf.lgamma(tf.expand_dims(alpha_indx3, 1)) -
tf.lgamma(
tf.expand_dims(alpha_indx3, 1) + tf.expand_dims(kk,
0) + 1.)
)
, 1))
)
x_m = alpha_indx3
f_m = 1. + 0.167303227226226980395296095593948848545551300048828125 / \
(
tf.pow(x_m, 1.0008649793164192676186985409003682434558868408203125) -
0.07516433982238841793321881823430885560810565948486328125
)
x_r = 2. * alpha_indx3 - x_l
f_r = 1. / alpha_indx3 - tf.exp(x_r + tf.lgamma(alpha_indx3) + (1. - alpha_indx3) * tf.log(x_r)) * (
(tf.digamma(alpha_indx3 + 1.) - tf.log(x_r)) * tf.igammac(alpha_indx3, x_r)
)
lambda_r = tf.exp(
959.627335718427275423891842365264892578125 / (
tf.pow(alpha_indx3, 1.324768828487964622553363369661383330821990966796875) +
142.427456986662718918523751199245452880859375
)
- 13.01439996187340142341781756840646266937255859375
)
x_mat_i = tf.concat([tf.expand_dims(x_l, 1), tf.expand_dims(x_m, 1), tf.expand_dims(x_r, 1)], 1)
x_mat_bar_i = x_mat_i - tf.expand_dims(alpha_indx3, 1)
x_mat_hat_i = tf.sqrt(x_mat_i) - tf.sqrt(tf.expand_dims(alpha_indx3, 1))
f_mat_i = tf.concat([tf.expand_dims(f_l, 1), tf.expand_dims(f_m, 1), tf.expand_dims(f_r, 1)], 1)
lambda_mat_i = tf.concat([tf.expand_dims(tf.ones_like(alpha_indx3), 1),
tf.expand_dims(tf.ones_like(alpha_indx3), 1),
tf.expand_dims(lambda_r, 1)
], 1)
x_mat_j = tf.expand_dims(x_l, 1)
g_mat_j = tf.expand_dims(g_l, 1)
lambda_mat_j = tf.expand_dims(tf.ones_like(alpha_indx3), 1)
A = tf.reduce_sum(lambda_mat_i * tf.pow(x_mat_bar_i, 2), 1) + tf.reduce_sum(lambda_mat_j, 1)
B = tf.reduce_sum(lambda_mat_i * x_mat_bar_i * x_mat_hat_i, 1) + \
tf.reduce_sum(lambda_mat_j / 2. / tf.sqrt(x_mat_j), 1)
C = tf.reduce_sum(lambda_mat_i * x_mat_bar_i, 1)
D = tf.reduce_sum(lambda_mat_i * tf.pow(x_mat_hat_i, 2), 1) + tf.reduce_sum(lambda_mat_j / 4. / x_mat_j, 1)
E = tf.reduce_sum(lambda_mat_i * x_mat_hat_i, 1)
F = tf.reduce_sum(lambda_mat_i, 1)
G = tf.reduce_sum(lambda_mat_i * x_mat_bar_i * f_mat_i, 1) + tf.reduce_sum(lambda_mat_j * g_mat_j, 1)
H = tf.reduce_sum(lambda_mat_i * x_mat_hat_i * f_mat_i, 1) + \
tf.reduce_sum(lambda_mat_j / 2. / tf.sqrt(x_mat_j) * g_mat_j, 1)
I = tf.reduce_sum(lambda_mat_i * f_mat_i, 1)
Z = F * tf.pow(B, 2) - 2. * B * C * E + D * tf.pow(C, 2) + A * tf.pow(E, 2) - A * D * F
a_cor = 1. / Z * (G * (tf.pow(E, 2) - D * F) + H * (B * F - C * E) - I * (B * E - C * D))
b_cor = 1. / Z * (G * (B * F - C * E) + H * (tf.pow(C, 2) - A * F) - I * (B * C - A * E))
c_cor = 1. / Z * (-G * (B * E - C * D) + I * (tf.pow(B, 2) - A * D) - H * (B * C - A * E))
GO_Gamma_alpha_value3 = a_cor * (x_indx3 - alpha_indx3) + b_cor * (tf.sqrt(x_indx3) - tf.sqrt(alpha_indx3)) + c_cor
GO_Gamma_alpha_value3 = tf.maximum(
GO_Gamma_alpha_value3,
1. / alpha_indx3 - tf.gather_nd(ex_gamma_xa, indx3) *
tf.gather_nd(psi_m_log, indx3) * tf.gather_nd(igamma_up_reg, indx3)
)
# Part 4
# indx4 = tf.where(
# tf.logical_and(
# tf.logical_and(x > 1e-2, alpha > 500.),
# (x <= (alpha + 2. * tf.log(alpha) * tf.sqrt(alpha)))
# )
# )
indx4 = tf.where(
tf.logical_and(x > 1e-2, alpha > 500.)
)
x_indx4 = tf.gather_nd(x, indx4)
alpha_indx4 = tf.gather_nd(alpha, indx4)
f_m_large = 1. + 0.167303227226226980395296095593948848545551300048828125 / \
(
tf.pow(alpha_indx4, 1.0008649793164192676186985409003682434558868408203125) -
0.07516433982238841793321881823430885560810565948486328125
)
g_m_large = 0.54116502161502622048061539317131973803043365478515625 * \
tf.pow(alpha_indx4, -1.010274491769996618728555404231883585453033447265625)
GO_Gamma_alpha_value4 = f_m_large + g_m_large * (x_indx4 - alpha_indx4)
# Part 4_1
# indx4_1 = tf.where(
# tf.logical_and(
# tf.logical_and(x > 1e-2, alpha > 500.),
# (x > (alpha + 2. * tf.log(alpha) * tf.sqrt(alpha)))
# )
# )
# alpha_indx4_1 = tf.gather_nd(alpha, indx4_1)
# GO_Gamma_alpha_value4_1 = 1. / alpha_indx4_1 - tf.gather_nd(ex_gamma_xa, indx4_1) * \
# tf.gather_nd(psi_m_log, indx4_1) * tf.gather_nd(igamma_up_reg, indx4_1)
# Summerize
GO_Gamma_alpha = tf.sparse_to_dense(indx1, x.shape, GO_Gamma_alpha_value1) + \
tf.sparse_to_dense(indx2, x.shape, GO_Gamma_alpha_value2) + \
tf.sparse_to_dense(indx2_1, x.shape, GO_Gamma_alpha_value2_1) + \
tf.sparse_to_dense(indx3, x.shape, GO_Gamma_alpha_value3) + \
tf.sparse_to_dense(indx4, x.shape, GO_Gamma_alpha_value4)
# + \
# tf.sparse_to_dense(indx4_1, x.shape, GO_Gamma_alpha_value4_1)
GO_Gamma_alpha = tf.cast(GO_Gamma_alpha, tf.float32)
return GO_Gamma_alpha # , x_l, x_r, f_l, f_m, f_r, g_l
tf.gather() tf.gather_nd() tf.gather_v2() tf.get_summary_op() tf.gradients() tf.boolean_mask() tf.sparse_mask() tf.sequence_mask() tf.random_gamma() tf.digamma() tf.igamma() tf.lgamma() tf.polygamma() tf.igammac() tf.tensor_shape.as_shape() # gfile tf.gfile.Copy() tf.gfile.DeleteRecursively() tf.gfile.Exists() tf.gfile.Glob() tf.gfile.IsDirectory() tf.gfile.ListDirectory() tf.gfile.MakeDirs() tf.gfile.MkDir() tf.gfile.Remove() tf.gfile.Rename() tf.gfile.Stat()
def _cdf(self, x):
if self.validate_args:
x = distribution_util.embed_check_nonnegative_integer_form(x)
return tf.igammac(1. + x, self.rate)