def jacobian_det(self, rv_var, rv_value):
a, b = self.param_extract_fn(rv_var)
if a is not None and b is not None:
s = at.softplus(-rv_value)
return at.log(b - a) - 2 * s - rv_value
else:
return rv_value
def make_uw(self, u, w):
if not self.batched:
# u_: d
# w_: d
wu = u.dot(w) # .
mwu = -1.0 + at.softplus(wu) # .
# d + (. - .) * d / .
u_h = u + (mwu - wu) * w / ((w**2).sum() + 1e-10)
return u_h, w
else:
# u_: bxd
# w_: bxd
wu = (u * w).sum(-1, keepdims=True) # bx-
mwu = -1.0 + at.softplus(wu) # bx-
# bxd + (bx- - bx-) * bxd / bx- = bxd
u_h = u + (mwu - wu) * w / ((w**2).sum(-1, keepdims=True) + 1e-10)
return u_h, w
def rho2sigma(rho):
"""
`rho -> sigma` Aesara converter
:math:`mu + sigma*e = mu + log(1+exp(rho))*e`"""
return at.softplus(rho)
def test_accuracy(self):
# Test all aproximations are working (cutoff points are -37, 18, 33.3)
x_test = np.array([-40.0, -17.5, 17.5, 18.5, 40.0])
y_th = aet.softplus(x_test).eval()
y_np = np.log1p(np.exp(x_test))
np.testing.assert_allclose(y_th, y_np, rtol=10e-10)
def jacobian_det(self, rv_var, rv_value):
return -at.softplus(-rv_value)
def backward(self, rv_var, rv_value):
return at.softplus(rv_value)
def log_jac_det(self, value, *inputs):
return -at.softplus(-value)
def backward(self, value, *inputs):
return at.softplus(value)
def make_ab(self, a, b):
a = at.exp(a)
b = -a + at.softplus(b)
return a, b
def log1pexp(x):
"""Return log(1 + exp(x)), also called softplus.
This function is numerically more stable than the naive approach.
"""
return at.softplus(x)
