def mcmc(ll, *frvs):
full_observations = dict(observations)
full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, frvs)]))
loglik = -full_log_likelihood(full_observations)
proposals = free_RVs_prop
H = tensor.add(*[tensor.sum(tensor.sqr(p)) for p in proposals])/2. + loglik
# -- this should be an inner loop
g = []
g.append(tensor.grad(loglik, frvs))
proposals = [(p - epsilon*gg[0]/2.) for p, gg in zip(proposals, g)]
rvsp = [(rvs + epsilon*rvp) for rvs,rvp in zip(frvs, proposals)]
full_observations = dict(observations)
full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, rvsp)]))
new_loglik = -full_log_likelihood(full_observations)
gnew = []
gnew.append(tensor.grad(new_loglik, rvsp))
proposals = [(p - epsilon*gn[0]/2.) for p, gn in zip(proposals, gnew)]
# --
Hnew = tensor.add(*[tensor.sum(tensor.sqr(p)) for p in proposals])/2. + new_loglik
dH = Hnew - H
accept = tensor.or_(dH < 0., U < tensor.exp(-dH))
return [tensor.switch(accept, -new_loglik, ll)] + \
[tensor.switch(accept, p, f) for p, f in zip(rvsp, frvs)], \
{}, theano.scan_module.until(accept)
def likelihood_gradient(observations = {}, learning_rate = 0.1):
all_vars = ancestors(list(observations.keys()))
for o in observations:
assert o in all_vars
if not is_raw_rv(o):
raise TypeError(o)
RVs = [v for v in all_vars if is_raw_rv(v)]
free_RVs = [v for v in RVs if v not in observations]
# Instantiate actual values for the different random variables:
params = dict()
for v in free_RVs:
f = theano.function([], v, mode=theano.Mode(linker='py', optimizer=None))
params[v] = theano.shared(f())
# Compute the full log likelihood:
full_observations = dict(observations)
full_observations.update(params)
log_likelihood = full_log_likelihood(full_observations)
# Construct the update equations for learning:
updates = dict()
for frvs in params.values():
updates[frvs] = frvs + learning_rate * tensor.grad(log_likelihood, frvs)
return params, updates, log_likelihood
def test_tt(self):
RVs = dict([(self.D, self.D_data)])
lik = full_log_likelihood(RVs)
lf = theano.function([self.m1, self.m2, self.C], lik)
print lf(1,3,0)
print lf(1,3,1)
def test_tt(self):
RVs = dict([(self.D, self.D_data)])
lik = full_log_likelihood(RVs)
lf = theano.function([self.m1, self.m2, self.C], lik)
print lf(1, 3, 0)
print lf(1, 3, 1)
def mcmc(ll, *frvs):
full_observations = dict(observations)
full_observations.update(
dict([(rv, s) for rv, s in zip(free_RVs, frvs)]))
loglik = -full_log_likelihood(full_observations)
proposals = free_RVs_prop
H = tensor.add(*[tensor.sum(tensor.sqr(p))
for p in proposals]) / 2. + loglik
# -- this should be an inner loop
g = []
g.append(tensor.grad(loglik, frvs))
proposals = [(p - epsilon * gg[0] / 2.) for p, gg in zip(proposals, g)]
rvsp = [(rvs + epsilon * rvp) for rvs, rvp in zip(frvs, proposals)]
full_observations = dict(observations)
full_observations.update(
dict([(rv, s) for rv, s in zip(free_RVs, rvsp)]))
new_loglik = -full_log_likelihood(full_observations)
gnew = []
gnew.append(tensor.grad(new_loglik, rvsp))
proposals = [(p - epsilon * gn[0] / 2.)
for p, gn in zip(proposals, gnew)]
# --
Hnew = tensor.add(*[tensor.sum(tensor.sqr(p))
for p in proposals]) / 2. + new_loglik
dH = Hnew - H
accept = tensor.or_(dH < 0., U < tensor.exp(-dH))
return [tensor.switch(accept, -new_loglik, ll)] + \
[tensor.switch(accept, p, f) for p, f in zip(rvsp, frvs)], \
{}, theano.scan_module.until(accept)
def mcmc(ll, *frvs):
proposals = [s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, frvs)]
proposals_rev = [s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, proposals)]
full_observations = dict(observations)
full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, proposals)]))
new_log_likelihood = full_log_likelihood(full_observations)
logratio = new_log_likelihood - ll \
+ tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals_rev, frvs)]) \
- tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals, proposals)])
accept = tensor.gt(logratio, tensor.log(U))
return [tensor.switch(accept, new_log_likelihood, ll)] + \
[tensor.switch(accept, p, f) for p, f in zip(proposals, frvs)], \
{}, theano.scan_module.until(accept)
def mcmc(ll, *frvs):
proposals = [
s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, frvs)
]
proposals_rev = [
s_rng.local_proposal(v, rvs)
for v, rvs in zip(free_RVs, proposals)
]
full_observations = dict(observations)
full_observations.update(
dict([(rv, s) for rv, s in zip(free_RVs, proposals)]))
new_log_likelihood = full_log_likelihood(full_observations)
logratio = new_log_likelihood - ll \
+ tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals_rev, frvs)]) \
- tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals, proposals)])
accept = tensor.gt(logratio, tensor.log(U))
return [tensor.switch(accept, new_log_likelihood, ll)] + \
[tensor.switch(accept, p, f) for p, f in zip(proposals, frvs)], \
{}, theano.scan_module.until(accept)
def mh2_sample(s_rng, outputs, observations = {}, givens = {}):
all_vars = ancestors(list(observations.keys()) + list(outputs))
for o in observations:
assert o in all_vars
if not is_raw_rv(o):
raise TypeError(o)
RVs = [v for v in all_vars if is_raw_rv(v)]
free_RVs = [v for v in RVs if v not in observations]
free_RVs_state = []
for v in free_RVs:
f = theano.function([], v,
mode=theano.Mode(linker='py', optimizer=None))
free_RVs_state.append(theano.shared(f()))
U = s_rng.uniform(low=0.0, high=1.0)
rr = []
for index in range(len(free_RVs)):
# TODO: why does the compiler crash when we try to expose the likelihood ?
full_observations = dict(observations)
full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)]))
log_likelihood = full_log_likelihood(full_observations)
proposal = s_rng.local_proposal(free_RVs[index], free_RVs_state[index])
proposal_rev = s_rng.local_proposal(free_RVs[index], proposal)
full_observations = dict(observations)
full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)]))
full_observations.update(dict([(free_RVs[index], proposal)]))
new_log_likelihood = full_log_likelihood(full_observations)
bw = tensor.sum(lpdf(proposal_rev, free_RVs_state[index]))
fw = tensor.sum(lpdf(proposal, proposal))
lr = new_log_likelihood-log_likelihood+bw-fw
accept = tensor.gt(lr, tensor.log(U))
updates = {free_RVs_state[index] : tensor.switch(accept, proposal, free_RVs_state[index])}
rr.append(theano.function([], [accept], updates=updates, givens=givens))
# TODO: this exacte amount of samples given back is still wrong
def sampler(nr_samples, burnin = 100, lag = 100):
data = [[] for o in outputs]
for i in range(nr_samples*lag+burnin):
accept = False
while not accept:
index = numpy.random.randint(len(free_RVs))
accept = rr[index]()
if accept and i > burnin and (i-burnin) % lag == 0:
for d, o in zip(data, outputs):
# TODO: this can be optimized
if is_raw_rv(o):
d.append(free_RVs_state[free_RVs.index(o)].get_value())
else:
full_observations = dict(observations)
full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)]))
d.append(evaluate(evaluate_with_assignments(o, full_observations), givens=givens))
data = [numpy.asarray(d).squeeze() for d in data]
return data
return sampler
# Define model
w = s_rng.normal(0, 4, draw_shape=(2, ))
x = tensor.matrix('x')
y = tensor.nnet.sigmoid(tensor.dot(x, w))
t = s_rng.binomial(p=y, draw_shape=(4, ))
# Define data
X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0]],
dtype=theano.config.floatX).T
Y_data = numpy.asarray([1., 1., 0., 0.], dtype=theano.config.floatX)
# Plot full likelihood function
RVs = dict([(t, Y_data)])
lik = full_log_likelihood(RVs)
givens = dict([(x, X_data)])
lik_func = theano.function([w], lik, givens=givens, allow_input_downcast=True)
delta = .1
x_range = numpy.arange(-10.0, 10.0, delta)
y_range = numpy.arange(-10.0, 10.0, delta)
X, Y = numpy.meshgrid(x_range, y_range)
response = []
for xl, yl in zip(X.flatten(), Y.flatten()):
response.append(lik_func([xl, yl]))
pylab.figure(1)
pylab.contour(X, Y, numpy.exp(numpy.asarray(response)).reshape(X.shape), 20)
def mh2_sample(s_rng, outputs, observations={}, givens={}):
all_vars = ancestors(list(observations.keys()) + list(outputs))
for o in observations:
assert o in all_vars
if not is_raw_rv(o):
raise TypeError(o)
RVs = [v for v in all_vars if is_raw_rv(v)]
free_RVs = [v for v in RVs if v not in observations]
free_RVs_state = []
for v in free_RVs:
f = theano.function([],
v,
mode=theano.Mode(linker='py', optimizer=None))
free_RVs_state.append(theano.shared(f()))
U = s_rng.uniform(low=0.0, high=1.0)
rr = []
for index in range(len(free_RVs)):
# TODO: why does the compiler crash when we try to expose the likelihood ?
full_observations = dict(observations)
full_observations.update(
dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)]))
log_likelihood = full_log_likelihood(full_observations)
proposal = s_rng.local_proposal(free_RVs[index], free_RVs_state[index])
proposal_rev = s_rng.local_proposal(free_RVs[index], proposal)
full_observations = dict(observations)
full_observations.update(
dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)]))
full_observations.update(dict([(free_RVs[index], proposal)]))
new_log_likelihood = full_log_likelihood(full_observations)
bw = tensor.sum(lpdf(proposal_rev, free_RVs_state[index]))
fw = tensor.sum(lpdf(proposal, proposal))
lr = new_log_likelihood - log_likelihood + bw - fw
accept = tensor.gt(lr, tensor.log(U))
updates = {
free_RVs_state[index]:
tensor.switch(accept, proposal, free_RVs_state[index])
}
rr.append(theano.function([], [accept], updates=updates,
givens=givens))
# TODO: this exacte amount of samples given back is still wrong
def sampler(nr_samples, burnin=100, lag=100):
data = [[] for o in outputs]
for i in range(nr_samples * lag + burnin):
accept = False
while not accept:
index = numpy.random.randint(len(free_RVs))
accept = rr[index]()
if accept and i > burnin and (i - burnin) % lag == 0:
for d, o in zip(data, outputs):
# TODO: this can be optimized
if is_raw_rv(o):
d.append(
free_RVs_state[free_RVs.index(o)].get_value())
else:
full_observations = dict(observations)
full_observations.update(
dict([
(rv, s)
for rv, s in zip(free_RVs, free_RVs_state)
]))
d.append(
evaluate(evaluate_with_assignments(
o, full_observations),
givens=givens))
data = [numpy.asarray(d).squeeze() for d in data]
return data
return sampler
# Define model
w = s_rng.normal(0, 4, draw_shape=(2,))
x = tensor.matrix("x")
y = tensor.nnet.sigmoid(tensor.dot(x, w))
t = s_rng.binomial(p=y, draw_shape=(4,))
# Define data
X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0]], dtype=theano.config.floatX).T
Y_data = numpy.asarray([1.0, 1.0, 0.0, 0.0], dtype=theano.config.floatX)
# Plot full likelihood function
RVs = dict([(t, Y_data)])
lik = full_log_likelihood(RVs)
givens = dict([(x, X_data)])
lik_func = theano.function([w], lik, givens=givens, allow_input_downcast=True)
delta = 0.1
x_range = numpy.arange(-10.0, 10.0, delta)
y_range = numpy.arange(-10.0, 10.0, delta)
X, Y = numpy.meshgrid(x_range, y_range)
response = []
for xl, yl in zip(X.flatten(), Y.flatten()):
response.append(lik_func([xl, yl]))
pylab.figure(1)
pylab.contour(X, Y, numpy.exp(numpy.asarray(response)).reshape(X.shape), 20)
