def dlogp(inputs, gradients):
(g_logp, ) = gradients
cov, delta = inputs
g_logp.tag.test_value = floatX(1.0)
n, k = delta.shape
chol_cov = cholesky(cov)
diag = aet.nlinalg.diag(chol_cov)
ok = aet.all(diag > 0)
chol_cov = aet.switch(ok, chol_cov, aet.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
inner = n * aet.eye(k) - aet.dot(delta_trans.T, delta_trans)
g_cov = solve_upper(chol_cov.T, inner)
g_cov = solve_upper(chol_cov.T, g_cov.T)
tau_delta = solve_upper(chol_cov.T, delta_trans.T)
g_delta = tau_delta.T
g_cov = aet.switch(ok, g_cov, -np.nan)
g_delta = aet.switch(ok, g_delta, -np.nan)
return [-0.5 * g_cov * g_logp, -g_delta * g_logp]
def test_1msigmoid(self):
if not register_local_1msigmoid:
return
m = self.get_mode()
x = fmatrix()
# tests exp_over_1_plus_exp
f = aesara.function([x], 1 - exp(x) / (1 + exp(x)), mode=m)
assert check_stack_trace(f, ops_to_check=[neg, sigmoid_inplace])
assert [node.op for node in f.maker.fgraph.toposort()] == [
neg,
sigmoid_inplace,
]
# tests inv_1_plus_exp
f = aesara.function([x], 1 - aet.fill(x, 1.0) / (1 + exp(-x)), mode=m)
assert check_stack_trace(f, ops_to_check=[neg, sigmoid_inplace])
assert [node.op for node in f.maker.fgraph.toposort()] == [
neg,
sigmoid_inplace,
]
def test_exp_over_1_plus_exp(self):
m = self.get_mode(excluding=["local_elemwise_fusion"])
x = vector()
data = np.random.rand(54).astype(config.floatX)
backup = config.warn__identify_1pexp_bug
config.warn__identify_1pexp_bug = False
try:
# tests exp_over_1_plus_exp
f = aesara.function([x], exp(x) / (1 + exp(x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] == [sigmoid]
f(data)
f = aesara.function([x], exp(x) / (2 + exp(x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [sigmoid]
f(data)
f = aesara.function([x], exp(x) / (1 - exp(x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [sigmoid]
f(data)
f = aesara.function([x], exp(x + 1) / (1 + exp(x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [sigmoid]
f(data)
# tests inv_1_plus_exp
f = aesara.function([x], aet.fill(x, 1.0) / (1 + exp(-x)), mode=m)
# todo: solve issue #4589 first
# assert check_stack_trace(f, ops_to_check=sigmoid)
assert [node.op for node in f.maker.fgraph.toposort()] == [sigmoid]
f(data)
f = aesara.function([x], aet.fill(x, 1.0) / (2 + exp(-x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [sigmoid]
f(data)
f = aesara.function([x], aet.fill(x, 1.0) / (1 - exp(-x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [sigmoid]
f(data)
f = aesara.function([x], aet.fill(x, 1.1) / (1 + exp(-x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [sigmoid]
f(data)
# tests inv_1_plus_exp with neg
f = aesara.function([x], aet.fill(x, -1.0) / (1 + exp(-x)), mode=m)
# todo: solve issue #4589 first
# assert check_stack_trace(
# f, ops_to_check=[sigmoid, neg_inplace])
assert [node.op for node in f.maker.fgraph.toposort()] == [
sigmoid,
neg_inplace,
]
f(data)
f = aesara.function([x], aet.fill(x, -1.0) / (1 - exp(-x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
neg_inplace,
]
f(data)
f = aesara.function([x], aet.fill(x, -1.0) / (2 + exp(-x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
neg_inplace,
]
f(data)
f = aesara.function([x], aet.fill(x, -1.1) / (1 + exp(-x)), mode=m)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
neg_inplace,
]
f(data)
# tests double inv_1_plus_exp with neg
# (-1)(exp(x)) / (1+exp(x))(1+exp(-x))
# = (-1)/(1+exp(-x)) * exp(x)/(1+exp(x))
# = - (sigm(x) * sigm(x))
f = aesara.function(
[x],
(aet.fill(x, -1.0) * exp(x)) / ((1 + exp(x)) * (1 + exp(-x))),
mode=m,
)
# todo: solve issue #4589 first
# assert check_stack_trace(f, ops_to_check=[sigmoid, mul])
assert [node.op
for node in f.maker.fgraph.toposort()] == [sigmoid, mul]
f(data)
f = aesara.function(
[x],
(aet.fill(x, -1.1) * exp(x)) / ((1 + exp(x)) * (1 + exp(-x))),
mode=m,
)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
mul,
neg_inplace,
]
f(data)
f = aesara.function(
[x],
(aet.fill(x, -1.0) * exp(x)) / ((2 + exp(x)) * (1 + exp(-x))),
mode=m,
)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
mul,
neg_inplace,
]
f(data)
f = aesara.function(
[x],
(aet.fill(x, -1.0) * exp(x)) / ((1 + exp(x)) * (2 + exp(-x))),
mode=m,
)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
mul,
neg_inplace,
]
f(data)
f = aesara.function(
[x],
(aet.fill(x, -1.0) * exp(x)) / ((1 + exp(x)) * (1 + exp(x))),
mode=m,
)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
mul,
neg_inplace,
]
f(data)
f = aesara.function(
[x],
(aet.fill(x, -1.0) * exp(x)) / ((1 + exp(x)) * (2 + exp(-x))),
mode=m,
)
assert [node.op for node in f.maker.fgraph.toposort()] != [
sigmoid,
mul,
neg_inplace,
]
f(data)
finally:
# Restore config option.
config.warn__identify_1pexp_bug = backup
def MvNormalLogp():
"""Compute the log pdf of a multivariate normal distribution.
This should be used in MvNormal.logp once Theano#5908 is released.
Parameters
----------
cov: aet.matrix
The covariance matrix.
delta: aet.matrix
Array of deviations from the mean.
"""
cov = aet.matrix("cov")
cov.tag.test_value = floatX(np.eye(3))
delta = aet.matrix("delta")
delta.tag.test_value = floatX(np.zeros((2, 3)))
solve_lower = Solve(A_structure="lower_triangular")
solve_upper = Solve(A_structure="upper_triangular")
cholesky = Cholesky(lower=True, on_error="nan")
n, k = delta.shape
n, k = f(n), f(k)
chol_cov = cholesky(cov)
diag = aet.nlinalg.diag(chol_cov)
ok = aet.all(diag > 0)
chol_cov = aet.switch(ok, chol_cov, aet.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
result = n * k * aet.log(f(2) * np.pi)
result += f(2) * n * aet.sum(aet.log(diag))
result += (delta_trans**f(2)).sum()
result = f(-0.5) * result
logp = aet.switch(ok, result, -np.inf)
def dlogp(inputs, gradients):
(g_logp, ) = gradients
cov, delta = inputs
g_logp.tag.test_value = floatX(1.0)
n, k = delta.shape
chol_cov = cholesky(cov)
diag = aet.nlinalg.diag(chol_cov)
ok = aet.all(diag > 0)
chol_cov = aet.switch(ok, chol_cov, aet.fill(chol_cov, 1))
delta_trans = solve_lower(chol_cov, delta.T).T
inner = n * aet.eye(k) - aet.dot(delta_trans.T, delta_trans)
g_cov = solve_upper(chol_cov.T, inner)
g_cov = solve_upper(chol_cov.T, g_cov.T)
tau_delta = solve_upper(chol_cov.T, delta_trans.T)
g_delta = tau_delta.T
g_cov = aet.switch(ok, g_cov, -np.nan)
g_delta = aet.switch(ok, g_delta, -np.nan)
return [-0.5 * g_cov * g_logp, -g_delta * g_logp]
return OpFromGraph([cov, delta], [logp], grad_overrides=dlogp, inline=True)
def get_moment(cls, rv, size, *rv_inputs):
mean = at.fill(size, rv.Y.mean())
return mean