def test_local_sigm_times_exp(self):
"""
Test the `local_sigm_times_exp` optimization.
exp(x) * sigm(-x) -> sigm(x)
exp(-x) * sigm(x) -> sigm(-x)
"""
def match(func, ops):
# print [node.op.scalar_op for node in func.maker.fgraph.toposort()]
assert [node.op for node in func.maker.fgraph.toposort()] == ops
m = self.get_mode(excluding=["local_elemwise_fusion", "inplace"])
x, y = tensor.vectors("x", "y")
f = theano.function([x], sigmoid(-x) * tensor.exp(x), mode=m)
match(f, [sigmoid])
f = theano.function([x], sigmoid(x) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid])
f = theano.function([x], -(-(-(sigmoid(x)))) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid, tensor.neg])
f = theano.function(
[x, y], (sigmoid(x) * sigmoid(-y) * -tensor.exp(-x) * tensor.exp(x * y) * tensor.exp(y)), mode=m
)
match(f, [sigmoid, tensor.mul, tensor.neg, tensor.exp, sigmoid, tensor.mul])
def Generate_theta_p(x, s, I, N, K, prod_f):
#print(s,N,len(x))
T = len(x)
D = len(x[0])
s = [one_hot(ss, N) for ss in s]
# x = [[xt for _ in range(N)] for xt in x]
x = np.array(x)
s = np.array(s)
model = pm.Model()
with model:
# Priors for unknown model parameters
theta = pm.Normal("theta", mu=0, sigma=1, shape=(D, K)) / np.sqrt(
K * D)
p_list = []
for t in range(T):
#print(prod_f)
#print(np.transpose(theta))
wt = dot(dot(prod_f, transpose(theta)), x[t])
swt = s[t] * wt
sum_sw = sum(swt)
p = exp(swt) / (1 + sum_sw)
p0 = 1 / (1 + sum_sw)
p_list.append(concatenate(([p0], p)))
I_obs = pm.Categorical("I_obs", p=stack(p_list, axis=0), observed=I)
with model:
step = pm.Metropolis()
trace1 = pm.sample(tune=2000, chains=1, step=step)
return trace1["theta"][-1]
def test_local_sigm_times_exp(self):
"""
Test the `local_sigm_times_exp` optimization.
exp(x) * sigm(-x) -> sigm(x)
exp(-x) * sigm(x) -> sigm(-x)
"""
def match(func, ops):
# print [node.op.scalar_op for node in func.maker.fgraph.toposort()]
assert [node.op for node in func.maker.fgraph.toposort()] == ops
m = self.get_mode(excluding=['local_elemwise_fusion', 'inplace'])
x, y = tensor.vectors('x', 'y')
f = theano.function([x], sigmoid(-x) * tensor.exp(x), mode=m)
match(f, [sigmoid])
assert check_stack_trace(f, ops_to_check=sigmoid)
f = theano.function([x], sigmoid(x) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid])
assert check_stack_trace(f, ops_to_check=sigmoid)
f = theano.function([x], -(-(-(sigmoid(x)))) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid, tensor.neg])
# assert check_stack_trace(f, ops_to_check=sigmoid)
f = theano.function([x, y],
(sigmoid(x) * sigmoid(-y) * -tensor.exp(-x) *
tensor.exp(x * y) * tensor.exp(y)),
mode=m)
topo = f.maker.fgraph.toposort()
for op, nb in [(sigmoid, 2), (tensor.mul, 2), (tensor.neg, 1),
(tensor.exp, 1)]:
assert sum([n.op == op for n in topo]) == nb
def test_local_sigm_times_exp(self):
"""
Test the `local_sigm_times_exp` optimization.
exp(x) * sigm(-x) -> sigm(x)
exp(-x) * sigm(x) -> sigm(-x)
"""
def match(func, ops):
# print [node.op.scalar_op for node in func.maker.fgraph.toposort()]
assert [node.op for node in func.maker.fgraph.toposort()] == ops
m = self.get_mode(excluding=['local_elemwise_fusion', 'inplace'])
x, y = tensor.vectors('x', 'y')
f = theano.function([x], sigmoid(-x) * tensor.exp(x), mode=m)
match(f, [sigmoid])
f = theano.function([x], sigmoid(x) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid])
f = theano.function([x], -(-(-(sigmoid(x)))) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid, tensor.neg])
f = theano.function(
[x, y],
(sigmoid(x) * sigmoid(-y) * -tensor.exp(-x) *
tensor.exp(x * y) * tensor.exp(y)),
mode=m)
match(f, [sigmoid, tensor.mul, tensor.neg, tensor.exp, sigmoid,
tensor.mul])
def test_local_sigm_times_exp(self):
"""
Test the `local_sigm_times_exp` optimization.
exp(x) * sigm(-x) -> sigm(x)
exp(-x) * sigm(x) -> sigm(-x)
"""
def match(func, ops):
# print [node.op.scalar_op for node in func.maker.fgraph.toposort()]
assert [node.op for node in func.maker.fgraph.toposort()] == ops
m = self.get_mode(excluding=['local_elemwise_fusion', 'inplace'])
x, y = tensor.vectors('x', 'y')
f = theano.function([x], sigmoid(-x) * tensor.exp(x), mode=m)
match(f, [sigmoid])
assert check_stack_trace(f, ops_to_check=sigmoid)
f = theano.function([x], sigmoid(x) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid])
assert check_stack_trace(f, ops_to_check=sigmoid)
f = theano.function([x], -(-(-(sigmoid(x)))) * tensor.exp(-x), mode=m)
match(f, [tensor.neg, sigmoid, tensor.neg])
# assert check_stack_trace(f, ops_to_check=sigmoid)
f = theano.function(
[x, y],
(sigmoid(x) * sigmoid(-y) * -tensor.exp(-x) *
tensor.exp(x * y) * tensor.exp(y)), mode=m)
topo = f.maker.fgraph.toposort()
for op, nb in [(sigmoid, 2), (tensor.mul, 2),
(tensor.neg, 1), (tensor.exp, 1)]:
assert sum([n.op == op for n in topo]) == nb
def local_exp_over_1_plus_exp(node):
"""
exp(x)/(1+exp(x)) -> sigm(x)
c/(1+exp(x)) -> c*sigm(-x)
"""
# this optimization should be done for numerical stability
# so we don't care to check client counts
if node.op == tensor.true_div:
# find all the exp() terms in the numerator
num, denom = node.inputs
num_exp_x, num_rest, num_neg = partition_num_or_denom(num, is_exp)
denom_1pexp, denom_rest, denom_neg = partition_num_or_denom(
denom, is_1pexp)
sigmoids = []
for t in denom_1pexp:
if t in num_exp_x:
# case: exp(x) /(1+exp(x))
sigmoids.append(sigmoid(t))
del num_exp_x[num_exp_x.index(t)]
else:
# case: 1/(1+exp(x))
sigmoids.append(sigmoid(-t))
copy_stack_trace(node.outputs[0], sigmoids[-1])
if not sigmoids: # we didn't find any. abort
return
# put the new numerator together
new_num = sigmoids + [tensor.exp(t) for t in num_exp_x] + num_rest
if len(new_num) == 1:
new_num = new_num[0]
else:
new_num = tensor.mul(*new_num)
if num_neg ^ denom_neg:
new_num = -new_num
copy_stack_trace(num, new_num)
if len(denom_rest) == 0:
return [new_num]
elif len(denom_rest) == 1:
out = new_num / denom_rest[0]
else:
out = new_num / tensor.mul(*denom_rest)
copy_stack_trace(node.outputs[0], out)
return [out]
def local_exp_over_1_plus_exp(node):
"""
exp(x)/(1+exp(x)) -> sigm(x)
c/(1+exp(x)) -> c*sigm(-x)
"""
# this optimization should be done for numerical stability
# so we don't care to check client counts
if node.op == tensor.true_div:
# find all the exp() terms in the numerator
num, denom = node.inputs
num_exp_x, num_rest, num_neg = partition_num_or_denom(num, is_exp)
denom_1pexp, denom_rest, \
denom_neg = partition_num_or_denom(denom, is_1pexp)
sigmoids = []
for t in denom_1pexp:
if t in num_exp_x:
# case: exp(x) /(1+exp(x))
sigmoids.append(sigmoid(t))
del num_exp_x[num_exp_x.index(t)]
else:
# case: 1/(1+exp(x))
sigmoids.append(sigmoid(-t))
copy_stack_trace(node.outputs[0], sigmoids[-1])
if not sigmoids: # we didn't find any. abort
return
# put the new numerator together
new_num = sigmoids + [tensor.exp(t) for t in num_exp_x] + num_rest
if len(new_num) == 1:
new_num = new_num[0]
else:
new_num = tensor.mul(*new_num)
if num_neg ^ denom_neg:
new_num = -new_num
copy_stack_trace(num, new_num)
if len(denom_rest) == 0:
return [new_num]
elif len(denom_rest) == 1:
out = new_num / denom_rest[0]
else:
out = new_num / tensor.mul(*denom_rest)
copy_stack_trace(node.outputs[0], out)
return [out]