def get_base_rate(self, base_rate_type="uniform"):
base_rate, annealable_params = RBM.get_base_rate(self, base_rate_type)
#annealable_params.append(self.beta) # Seems to work better without annealing self.beta (see unit tests)
if base_rate_type == "uniform":
def compute_lnZ(self):
# Since biases and weights are all 0, there are $2^input_size$ different
# visible neuron's states having the following energy
# $\sum_{z=1}^H \sum_{h \in \{0,1\}^z} \exp(-\beta z \ln(2))$
r = T.exp((1-self.beta) * T.log(2)) # Ratio of a geometric serie
lnZ = T.log((r - r**(self.hidden_size+1)) / (1-r))
return (self.input_size * T.log(2) + # ln(2^input_size)
lnZ) # $ln( \sum_{z=1}^H \sum_{h \in \{0,1\}^z} \exp(-\beta z \ln(2)) )$
elif base_rate_type == "c":
def compute_lnZ(self):
# Since the hidden biases (but not the visible ones) and the weights are all 0
r = T.exp((1-self.beta) * T.log(2)) # Ratio of a geometric serie
lnZ = T.log((r - r**(self.hidden_size+1)) / (1-r))
return (lnZ + # $ln( \sum_{z=1}^H \sum_{h \in \{0,1\}^z} \exp(-\beta z \ln(2)) )$
T.sum(T.nnet.softplus(self.c)))
elif base_rate_type == "b":
raise NotImplementedError()
import types
base_rate.compute_lnZ = types.MethodType(compute_lnZ, base_rate)
return base_rate, annealable_params
def get_base_rate(self, base_rate_type="uniform"):
base_rate, annealable_params = RBM.get_base_rate(self, base_rate_type)
#annealable_params.append(self.beta) # Seems to work better without annealing self.beta (see unit tests)
if base_rate_type == "uniform":
def compute_lnZ(self):
# Since biases and weights are all 0, there are $2^input_size$ different
# visible neuron's states having the following energy
# $\sum_{z=1}^H \sum_{h \in \{0,1\}^z} \exp(-\beta z \ln(2))$
r = T.exp((1-self.beta) * T.log(2)) # Ratio of a geometric serie
lnZ = T.log(r / (1-r)) # Convergence of the geometric serie
return (self.input_size * T.log(2) + # ln(2^input_size)
lnZ) # $ln( \sum_{z=1}^H \sum_{h \in \{0,1\}^z} \exp(-\beta z \ln(2)) )$
elif base_rate_type == "c":
def compute_lnZ(self):
# Since the hidden biases (but not the visible ones) and the weights are all 0
r = T.exp((1-self.beta) * T.log(2)) # Ratio of a geometric serie
lnZ = T.log(r / (1-r)) # Convergence of the geometric serie
return (lnZ + # $ln( \sum_{z=1}^H \sum_{h \in \{0,1\}^z} \exp(-\beta z \ln(2)) )$
T.sum(T.nnet.softplus(self.c)))
elif base_rate_type == "b":
raise NotImplementedError()
import types
base_rate.compute_lnZ = types.MethodType(compute_lnZ, base_rate)
return base_rate, annealable_params
class Test_RBM(unittest.TestCase):
def setUp(self):
self.input_size = 4
self.hidden_size = 3
self.batch_size = 100
rng = np.random.RandomState(42)
self.W = rng.randn(self.hidden_size,
self.input_size).astype(config.floatX)
self.b = rng.randn(self.hidden_size).astype(config.floatX)
self.c = rng.randn(self.input_size).astype(config.floatX)
self.model = RBM(input_size=self.input_size,
hidden_size=self.hidden_size)
self.model.W.set_value(self.W)
self.model.b.set_value(self.b)
self.model.c.set_value(self.c)
def test_free_energy(self):
v = T.matrix('v')
h = T.matrix('h')
logsumexp_E = theano.function([v, h], -logsumexp(-self.model.E(v, h)))
v1 = np.random.rand(1, self.input_size).astype(config.floatX)
H = cartesian([(0, 1)] * self.hidden_size, dtype=config.floatX)
Fv = logsumexp_E(v1, H) # Marginalization over $\bh$
v = T.matrix('v')
free_energy = theano.function([v], self.model.free_energy(v))
assert_array_almost_equal(free_energy(v1), [Fv])
v2 = np.tile(v1, (self.batch_size, 1))
assert_array_almost_equal(free_energy(v2), [Fv] * self.batch_size)
def test_marginalize_over_v(self):
v = T.matrix('v')
h = T.matrix('h')
E = theano.function([v, h], -logsumexp(-self.model.E(v, h)))
h1 = np.random.rand(1, self.hidden_size).astype(config.floatX)
V = cartesian([(0, 1)] * self.input_size, dtype=config.floatX)
expected_energy = E(V, h1)
h = T.matrix('h')
marginalize_over_v = theano.function([h],
self.model.marginalize_over_v(h))
assert_array_almost_equal(marginalize_over_v(h1), [expected_energy])
h2 = np.tile(h1, (self.batch_size, 1))
assert_array_almost_equal(marginalize_over_v(h2),
[expected_energy] * self.batch_size)
def test_compute_lnZ(self):
v = T.matrix('v')
h = T.matrix('h')
lnZ = theano.function([v, h], logsumexp(-self.model.E(v, h)))
V = cartesian([(0, 1)] * self.input_size, dtype=config.floatX)
H = cartesian([(0, 1)] * self.hidden_size, dtype=config.floatX)
lnZ_using_free_energy = theano.function(
[v], logsumexp(-self.model.free_energy(v)))
assert_equal(lnZ_using_free_energy(V), lnZ(V, H))
lnZ_using_marginalize_over_v = theano.function(
[h], logsumexp(-self.model.marginalize_over_v(h)))
assert_almost_equal(lnZ_using_marginalize_over_v(H),
lnZ(V, H),
decimal=6)
def test_base_rate(self):
# All binary combinaisons for V and H.
V = cartesian([(0, 1)] * self.input_size, dtype=config.floatX)
H = cartesian([(0, 1)] * self.hidden_size, dtype=config.floatX)
base_rates = []
# Add the uniform base rate, i.e. all parameters of the model are set to 0.
base_rates.append(self.model.get_base_rate())
# Add the base rate where visible biases are the ones from the model.
base_rates.append(self.model.get_base_rate('c'))
# Add the base rate where hidden biases are the ones from the model.
base_rates.append(self.model.get_base_rate('b')) # Not implemented
for base_rate, anneable_params in base_rates:
base_rate_lnZ = base_rate.compute_lnZ().eval().astype(
config.floatX)
brute_force_lnZ = logsumexp(-base_rate.E(V, H)).eval()
assert_almost_equal(brute_force_lnZ.astype(config.floatX),
base_rate_lnZ,
decimal=6)
theano_lnZ = logsumexp(-base_rate.free_energy(V), axis=0).eval()
assert_almost_equal(theano_lnZ.astype(config.floatX),
base_rate_lnZ,
decimal=6)
theano_lnZ = logsumexp(-base_rate.marginalize_over_v(H)).eval()
assert_almost_equal(theano_lnZ.astype(config.floatX),
base_rate_lnZ,
decimal=6)
@npt.dec.slow
def test_binomial_from_uniform_cpu(self):
#Test using numpy
rng = np.random.RandomState(42)
probs = rng.rand(10)
seed = 1337
nb_samples = 1000000
rng = np.random.RandomState(seed)
success1 = np.zeros(len(probs))
for i in range(nb_samples):
success1 += rng.binomial(n=1, p=probs)
rng = np.random.RandomState(seed)
success2 = np.zeros(len(probs))
for i in range(nb_samples):
success2 += (rng.rand(len(probs)) < probs).astype('int')
success1 = success1 / nb_samples
success2 = success2 / nb_samples
assert_array_almost_equal(success1, success2)
#Test using Theano's default RandomStreams
theano_rng = RandomStreams(1337)
rng_bin = theano_rng.binomial(size=probs.shape,
n=1,
p=probs,
dtype=theano.config.floatX)
success1 = np.zeros(len(probs))
for i in range(nb_samples):
success1 += rng_bin.eval()
theano_rng = RandomStreams(1337)
rng_bin = theano_rng.uniform(size=probs.shape,
dtype=theano.config.floatX) < probs
success2 = np.zeros(len(probs))
for i in range(nb_samples):
success2 += rng_bin.eval()
assert_array_almost_equal(success1 / nb_samples, success2 / nb_samples)
#Test using Theano's sandbox MRG RandomStreams
theano_rng = MRG_RandomStreams(1337)
success1 = theano_rng.binomial(size=probs.shape,
n=1,
p=probs,
dtype=theano.config.floatX)
theano_rng = MRG_RandomStreams(1337)
success2 = theano_rng.uniform(size=probs.shape,
dtype=theano.config.floatX) < probs
assert_array_equal(success1.eval(), success2.eval())
def test_gradients_auto_vs_manual(self):
rng = np.random.RandomState(42)
batch_size = 5
input_size = 10
rbm = RBM(input_size=input_size,
hidden_size=32,
CDk=1,
rng=np.random.RandomState(42))
W = (rng.rand(rbm.hidden_size, rbm.input_size) > 0.5).astype(
theano.config.floatX)
rbm.W = theano.shared(value=W.astype(theano.config.floatX),
name='b',
borrow=True)
b = (rng.rand(rbm.hidden_size) > 0.5).astype(theano.config.floatX)
rbm.b = theano.shared(value=b.astype(theano.config.floatX),
name='b',
borrow=True)
c = (rng.rand(rbm.input_size) > 0.5).astype(theano.config.floatX)
rbm.c = theano.shared(value=c.astype(theano.config.floatX),
name='c',
borrow=True)
params = [rbm.W, rbm.b, rbm.c]
chain_start = T.matrix('start')
chain_end = T.matrix('end')
chain_start_value = (rng.rand(batch_size, input_size) > 0.5).astype(
theano.config.floatX)
chain_end_value = (rng.rand(batch_size, input_size) > 0.5).astype(
theano.config.floatX)
chain_start.tag.test_value = chain_start_value
chain_end.tag.test_value = chain_end_value
### Computing gradients using automatic differentation ###
cost = T.mean(rbm.free_energy(chain_start)) - T.mean(
rbm.free_energy(chain_end))
gparams_auto = T.grad(cost, params, consider_constant=[chain_end])
### Computing gradients manually ###
h = rbm.sample_h_given_v(chain_start, return_probs=True)
_h = rbm.sample_h_given_v(chain_end, return_probs=True)
grad_W = (T.dot(chain_end.T, _h) -
T.dot(chain_start.T, h)).T / batch_size
grad_b = T.mean(_h - h, 0)
grad_c = T.mean(chain_end - chain_start, 0)
gparams_manual = [grad_W, grad_b, grad_c]
grad_W.name, grad_b.name, grad_c.name = "grad_W", "grad_b", "grad_c"
for gparam_auto, gparam_manual in zip(gparams_auto, gparams_manual):
param1 = gparam_auto.eval({
chain_start: chain_start_value,
chain_end: chain_end_value
})
param2 = gparam_manual.eval({
chain_start: chain_start_value,
chain_end: chain_end_value
})
assert_array_almost_equal(param1,
param2,
err_msg=gparam_manual.name)
class Test_RBM(unittest.TestCase):
def setUp(self):
self.input_size = 4
self.hidden_size = 3
self.batch_size = 100
rng = np.random.RandomState(42)
self.W = rng.randn(self.hidden_size, self.input_size).astype(config.floatX)
self.b = rng.randn(self.hidden_size).astype(config.floatX)
self.c = rng.randn(self.input_size).astype(config.floatX)
self.model = RBM(input_size=self.input_size,
hidden_size=self.hidden_size)
self.model.W.set_value(self.W)
self.model.b.set_value(self.b)
self.model.c.set_value(self.c)
def test_free_energy(self):
v = T.matrix('v')
h = T.matrix('h')
logsumexp_E = theano.function([v, h], -logsumexp(-self.model.E(v, h)))
v1 = np.random.rand(1, self.input_size).astype(config.floatX)
H = cartesian([(0, 1)] * self.hidden_size, dtype=config.floatX)
Fv = logsumexp_E(v1, H) # Marginalization over $\bh$
v = T.matrix('v')
free_energy = theano.function([v], self.model.free_energy(v))
assert_array_almost_equal(free_energy(v1), [Fv])
v2 = np.tile(v1, (self.batch_size, 1))
assert_array_almost_equal(free_energy(v2), [Fv]*self.batch_size)
def test_marginalize_over_v(self):
v = T.matrix('v')
h = T.matrix('h')
E = theano.function([v, h], -logsumexp(-self.model.E(v, h)))
h1 = np.random.rand(1, self.hidden_size).astype(config.floatX)
V = cartesian([(0, 1)] * self.input_size, dtype=config.floatX)
expected_energy = E(V, h1)
h = T.matrix('h')
marginalize_over_v = theano.function([h], self.model.marginalize_over_v(h))
assert_array_almost_equal(marginalize_over_v(h1), [expected_energy])
h2 = np.tile(h1, (self.batch_size, 1))
assert_array_almost_equal(marginalize_over_v(h2), [expected_energy]*self.batch_size)
def test_compute_lnZ(self):
v = T.matrix('v')
h = T.matrix('h')
lnZ = theano.function([v, h], logsumexp(-self.model.E(v, h)))
V = cartesian([(0, 1)] * self.input_size, dtype=config.floatX)
H = cartesian([(0, 1)] * self.hidden_size, dtype=config.floatX)
lnZ_using_free_energy = theano.function([v], logsumexp(-self.model.free_energy(v)))
assert_equal(lnZ_using_free_energy(V), lnZ(V, H))
lnZ_using_marginalize_over_v = theano.function([h], logsumexp(-self.model.marginalize_over_v(h)))
assert_almost_equal(lnZ_using_marginalize_over_v(H), lnZ(V, H), decimal=6)
def test_base_rate(self):
# All binary combinaisons for V and H.
V = cartesian([(0, 1)] * self.input_size, dtype=config.floatX)
H = cartesian([(0, 1)] * self.hidden_size, dtype=config.floatX)
base_rates = []
# Add the uniform base rate, i.e. all parameters of the model are set to 0.
base_rates.append(self.model.get_base_rate())
# Add the base rate where visible biases are the ones from the model.
base_rates.append(self.model.get_base_rate('c'))
# Add the base rate where hidden biases are the ones from the model.
base_rates.append(self.model.get_base_rate('b')) # Not implemented
for base_rate, anneable_params in base_rates:
base_rate_lnZ = base_rate.compute_lnZ().eval().astype(config.floatX)
brute_force_lnZ = logsumexp(-base_rate.E(V, H)).eval()
assert_almost_equal(brute_force_lnZ.astype(config.floatX), base_rate_lnZ, decimal=6)
theano_lnZ = logsumexp(-base_rate.free_energy(V), axis=0).eval()
assert_almost_equal(theano_lnZ.astype(config.floatX), base_rate_lnZ, decimal=6)
theano_lnZ = logsumexp(-base_rate.marginalize_over_v(H)).eval()
assert_almost_equal(theano_lnZ.astype(config.floatX), base_rate_lnZ, decimal=6)
@npt.dec.slow
def test_binomial_from_uniform_cpu(self):
#Test using numpy
rng = np.random.RandomState(42)
probs = rng.rand(10)
seed = 1337
nb_samples = 1000000
rng = np.random.RandomState(seed)
success1 = np.zeros(len(probs))
for i in range(nb_samples):
success1 += rng.binomial(n=1, p=probs)
rng = np.random.RandomState(seed)
success2 = np.zeros(len(probs))
for i in range(nb_samples):
success2 += (rng.rand(len(probs)) < probs).astype('int')
success1 = success1 / nb_samples
success2 = success2 / nb_samples
assert_array_almost_equal(success1, success2)
#Test using Theano's default RandomStreams
theano_rng = RandomStreams(1337)
rng_bin = theano_rng.binomial(size=probs.shape, n=1, p=probs, dtype=theano.config.floatX)
success1 = np.zeros(len(probs))
for i in range(nb_samples):
success1 += rng_bin.eval()
theano_rng = RandomStreams(1337)
rng_bin = theano_rng.uniform(size=probs.shape, dtype=theano.config.floatX) < probs
success2 = np.zeros(len(probs))
for i in range(nb_samples):
success2 += rng_bin.eval()
assert_array_almost_equal(success1/nb_samples, success2/nb_samples)
#Test using Theano's sandbox MRG RandomStreams
theano_rng = MRG_RandomStreams(1337)
success1 = theano_rng.binomial(size=probs.shape, n=1, p=probs, dtype=theano.config.floatX)
theano_rng = MRG_RandomStreams(1337)
success2 = theano_rng.uniform(size=probs.shape, dtype=theano.config.floatX) < probs
assert_array_equal(success1.eval(), success2.eval())
def test_gradients_auto_vs_manual(self):
rng = np.random.RandomState(42)
batch_size = 5
input_size = 10
rbm = RBM(input_size=input_size,
hidden_size=32,
CDk=1,
rng=np.random.RandomState(42))
W = (rng.rand(rbm.hidden_size, rbm.input_size) > 0.5).astype(theano.config.floatX)
rbm.W = theano.shared(value=W.astype(theano.config.floatX), name='b', borrow=True)
b = (rng.rand(rbm.hidden_size) > 0.5).astype(theano.config.floatX)
rbm.b = theano.shared(value=b.astype(theano.config.floatX), name='b', borrow=True)
c = (rng.rand(rbm.input_size) > 0.5).astype(theano.config.floatX)
rbm.c = theano.shared(value=c.astype(theano.config.floatX), name='c', borrow=True)
params = [rbm.W, rbm.b, rbm.c]
chain_start = T.matrix('start')
chain_end = T.matrix('end')
chain_start_value = (rng.rand(batch_size, input_size) > 0.5).astype(theano.config.floatX)
chain_end_value = (rng.rand(batch_size, input_size) > 0.5).astype(theano.config.floatX)
chain_start.tag.test_value = chain_start_value
chain_end.tag.test_value = chain_end_value
### Computing gradients using automatic differentation ###
cost = T.mean(rbm.free_energy(chain_start)) - T.mean(rbm.free_energy(chain_end))
gparams_auto = T.grad(cost, params, consider_constant=[chain_end])
### Computing gradients manually ###
h = rbm.sample_h_given_v(chain_start, return_probs=True)
_h = rbm.sample_h_given_v(chain_end, return_probs=True)
grad_W = (T.dot(chain_end.T, _h) - T.dot(chain_start.T, h)).T / batch_size
grad_b = T.mean(_h - h, 0)
grad_c = T.mean(chain_end - chain_start, 0)
gparams_manual = [grad_W, grad_b, grad_c]
grad_W.name, grad_b.name, grad_c.name = "grad_W", "grad_b", "grad_c"
for gparam_auto, gparam_manual in zip(gparams_auto, gparams_manual):
param1 = gparam_auto.eval({chain_start: chain_start_value, chain_end: chain_end_value})
param2 = gparam_manual.eval({chain_start: chain_start_value, chain_end: chain_end_value})
assert_array_almost_equal(param1, param2, err_msg=gparam_manual.name)
