def test_log1psquare(self, x, expected_y, expected_dy_dx):
x = tf.convert_to_tensor(x)
with tf.GradientTape() as tape:
tape.watch(x)
y = numeric.log1psquare(x)
dy_dx = tape.gradient(y, x)
y, dy_dx = self.evaluate([y, dy_dx])
self.assertAllClose(expected_y, y)
self.assertAllClose(expected_dy_dx, dy_dx)
def test_log1psquare(self, x, expected_y, expected_dy_dx):
x = tf.convert_to_tensor(x)
with tf.GradientTape() as tape:
tape.watch(x)
y = numeric.log1psquare(x)
dy_dx = tape.gradient(y, x)
y, dy_dx = self.evaluate([y, dy_dx])
self.assertAllClose(expected_y, y)
self.assertAllClose(expected_dy_dx, dy_dx)
def log_prob(x, df, loc, scale):
"""Compute log probability of Student T distribution.
Note that scale can be negative.
Args:
x: Floating-point `Tensor`. Where to compute the log probabilities.
df: Floating-point `Tensor`. The degrees of freedom of the
distribution(s). `df` must contain only positive values.
loc: Floating-point `Tensor`; the location(s) of the distribution(s).
scale: Floating-point `Tensor`; the scale(s) of the distribution(s).
Returns:
A `Tensor` with shape broadcast according to the arguments.
"""
# Writing `y` this way reduces XLA mem copies.
y = (x - loc) * (tf.math.rsqrt(df) / scale)
log_unnormalized_prob = -0.5 * (df + 1.) * log1psquare(y)
log_normalization = (tf.math.log(tf.abs(scale)) + 0.5 * tf.math.log(df) +
0.5 * np.log(np.pi) +
tfp_math.log_gamma_difference(0.5, 0.5 * df))
return log_unnormalized_prob - log_normalization