def test_whitening_preconditioner(self):
X = dot(randn(5, 5), randn(5, 1000)) + randn(5, 1)
Y = dot(randn(2, 2), randn(2, 1000)) + dot(randn(2, 5), X)
wt = WhiteningPreconditioner(X, Y)
# joint covariance
C = cov(vstack(wt(X, Y)), bias=True)
self.assertLess(max(abs(C - eye(7))), 1e-8)
# test inverse
Xw, Yw = wt(X, Y)
Xr, Yr = wt.inverse(Xw, Yw)
self.assertLess(max(abs(Xr - X)), 1e-10)
self.assertLess(max(abs(Yr - Y)), 1e-10)
def test_whitening_preconditioner(self): X = dot(randn(5, 5), randn(5, 1000)) + randn(5, 1) Y = dot(randn(2, 2), randn(2, 1000)) + dot(randn(2, 5), X) wt = WhiteningPreconditioner(X, Y) # joint covariance C = cov(vstack(wt(X, Y)), bias=True) self.assertLess(max(abs(C - eye(7))), 1e-8) # test inverse Xw, Yw = wt(X, Y) Xr, Yr = wt.inverse(Xw, Yw) self.assertLess(max(abs(Xr - X)), 1e-10) self.assertLess(max(abs(Yr - Y)), 1e-10)
class RIDE_BSDS300(object):
"""
Basically the same model as L{RIDE} but for the BSDS300 dataset
where the bottom-right pixel is commonly ignored. This model should
be used in combination with L{PatchRIDE}.
"""
MAX_BATCH_SIZE = 10000
def __init__(self,
num_channels=1,
num_hiddens=10,
num_components=4,
num_scales=4,
num_features=16,
num_layers=1,
nb_size=3,
nonlinearity='TanH',
verbosity=1,
extended=False,
input_mask=None,
output_mask=None):
self.verbosity = verbosity
self.num_channels = num_channels
self.num_hiddens = num_hiddens
self.num_layers = num_layers
self.nonlinearity = nonlinearity
self.extended = extended
self.input_mask, self.output_mask = generate_masks([nb_size] *
num_channels)
if input_mask:
self.input_mask = input_mask
if output_mask:
self.output_mask = output_mask
self.num_channels = sum(self.output_mask)
self.slstm = [None] * num_layers
self.mcgsm = MCGSM(dim_in=num_hiddens,
dim_out=num_channels,
num_components=num_components,
num_scales=num_scales,
num_features=num_features)
self.preconditioner = None
# see PatchRIDE
self._indicators = False
def add_layer(self):
"""
Add another spatial LSTM to the network and reinitialize MCGSM.
"""
self.num_layers += 1
# reinitialize MCGSM
self.mcgsm = MCGSM(dim_in=self.num_hiddens,
dim_out=self.num_channels,
num_components=self.mcgsm.num_components,
num_scales=self.mcgsm.num_scales,
num_features=self.mcgsm.num_features)
# add slot for another layer
self.slstm.append(None)
def _precondition(self, inputs, outputs=None):
"""
Remove any correlations within and between inputs and outputs.
"""
shape = inputs.shape
if outputs is None:
if self.preconditioner is None:
raise RuntimeError('No preconditioning possible.')
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
# avoids memory issues
MAX_SAMPLES = 5000000
if self.preconditioner is None:
inputs_ = inputs
if self._indicators:
# half of the inputs are indicators, don't preprocess them
inputs_ = inputs.copy()
inputs_[inputs.shape[0] // 2:] = randn(
inputs.shape[0] // 2, *inputs.shape[1:])
if inputs.shape[1] > MAX_SAMPLES:
idx = random_select(MAX_SAMPLES, inputs.shape[1])
self.preconditioner = WhiteningPreconditioner(
inputs_[:, idx], outputs[:, idx])
else:
self.preconditioner = WhiteningPreconditioner(
inputs_, outputs)
# precondition
for b in range(0, inputs.shape[1], MAX_SAMPLES):
inputs[:, b:b + MAX_SAMPLES], outputs[:, b:b + MAX_SAMPLES] = \
self.preconditioner(inputs[:, b:b + MAX_SAMPLES], outputs[:, b:b + MAX_SAMPLES])
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _precondition_inverse(self, inputs, outputs=None):
"""
Remove any correlations within and between inputs and outputs.
"""
if self.preconditioner is None:
raise RuntimeError('No preconditioner set.')
shape = inputs.shape
if outputs is None:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner.inverse(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
inputs, outputs = self.preconditioner.inverse(inputs, outputs)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _preprocess(self, images):
"""
Extract causal neighborhoods from images.
"""
def process(image):
inputs, outputs = generate_data_from_image(image, self.input_mask,
self.output_mask)
inputs = asarray(inputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1,
image.shape[1] - self.input_mask.shape[1] + 1, -1),
dtype='float32')
outputs = asarray(outputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1,
image.shape[1] - self.input_mask.shape[1] + 1, -1),
dtype='float32')
return inputs, outputs
inputs, outputs = zip(*mapp(process, images))
return asarray(inputs), asarray(outputs)
def loglikelihood(self, images):
"""
Returns a log-likelihood for each pixel except the bottom-right pixel (in nats).
"""
inputs, outputs = self._preprocess(images)
if self.preconditioner is not None:
if self.verbosity > 0:
print 'Computing Jacobian...'
logjacobian = self.preconditioner.logjacobian(
inputs.reshape(-1, sum(self.input_mask)).T,
outputs.reshape(-1, self.num_channels).T)
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
else:
logjacobian = 0.
# compute hidden unit activations
hiddens = inputs
for l in range(self.num_layers):
# create SLSTM
self.slstm[l] = SLSTM(num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min(
[hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if self.verbosity > 0:
print 'Computing likelihood...'
# evaluate log-likelihood
loglik = self.mcgsm.loglikelihood(
hiddens.reshape(-1, self.num_hiddens).T,
outputs.reshape(-1, self.num_channels).T) + logjacobian
# remove bottom-right pixel
loglik = loglik.reshape(hiddens.shape[0], -1)
loglik = loglik[:, :-1]
return loglik
def evaluate(self, images):
"""
Computes the average negative log-likelihood in bits per pixel.
"""
MAX_IMAGES = 100000
loglik = []
for b in range(0, len(images), MAX_IMAGES):
loglik.append(mean(self.loglikelihood(images[b:b + MAX_IMAGES])))
return -mean(loglik) / log(2.)
def train(self,
images,
batch_size=50,
num_epochs=20,
method='SGD',
train_means=False,
train_top_layer=False,
momentum=0.9,
learning_rate=1.,
decay1=0.9,
decay2=0.999,
precondition=True):
"""
@type images: C{ndarray}/C{list}
@param images: an array or a list of images
"""
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if precondition:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# indicates which layers will be trained
train_layers = [self.num_layers -
1] if train_top_layer else range(self.num_layers)
print 'Creating SLSTMs...'
# create SLSTMs
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=inputs.shape[1],
num_cols=inputs.shape[2],
num_channels=inputs.shape[3] if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=min([batch_size, self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
# compute loss function and its gradient
def f_df(params, idx):
# set model parameters
for l in train_layers:
self.slstm[l].set_parameters(params['slstm'][l])
self.mcgsm._set_parameters(params['mcgsm'],
{'train_means': train_means})
# select batch and compute hidden activations
Y = outputs[idx:idx + batch_size]
H = inputs[idx:idx + batch_size]
for l in range(self.num_layers):
H = self.slstm[l].forward(H)
# form inputs to MCGSM
H_flat = H.reshape(-1, self.num_hiddens).T
Y_flat = Y.reshape(-1, self.num_channels).T
norm_const = -H_flat.shape[1]
# compute gradients
df_dh, _, loglik = self.mcgsm._data_gradient(H_flat, Y_flat)
df_dh = df_dh.T.reshape(*H.shape) / norm_const
# ignore bottom-right pixel (BSDS300)
df_dh[:, -1, -1] = 0.
# average negative log-likelihood
f = sum(loglik) / norm_const
df_dtheta = {}
df_dtheta['slstm'] = [0.] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
if l > min(train_layers):
# derivative with respect to inputs of layer l are derivatives
# of hidden states of layer l - 1
df_dtheta['slstm'][l] = self.slstm[l].backward(
df_dh, force_backward=True)
df_dh = df_dtheta['slstm'][l]['inputs']
del df_dtheta['slstm'][l]['inputs']
else:
# no need to compute derivatives with respect to input units
df_dtheta['slstm'][l] = self.slstm[l].backward(df_dh)
# compute gradient of MCGSM
df_dtheta['mcgsm'] = self.mcgsm._parameter_gradient(
H_flat, Y_flat, parameters={'train_means': train_means
}) * log(2.) * self.mcgsm.dim_out
return f, df_dtheta
# collect current parameters
params = {}
params['slstm'] = [0.] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
params['slstm'][l] = self.slstm[l].parameters()
params['mcgsm'] = self.mcgsm._parameters({'train_means': train_means})
# a start index for each batch
start_indices = range(0, inputs.shape[0] - batch_size + 1, batch_size)
print 'Training...'
if method.upper() == 'SFO':
try:
# optimize using sum-of-functions optimizer
optimizer = SFO(f_df,
params,
start_indices,
display=self.verbosity)
params_opt = optimizer.optimize(num_passes=num_epochs)
# set model parameters
for l in range(self.num_layers):
self.slstm[l].set_parameters(params_opt['slstm'][l])
self.mcgsm._set_parameters(params_opt['mcgsm'],
{'train_means': train_means})
except KeyboardInterrupt:
pass
return optimizer.hist_f_flat
elif method.upper() == 'SGD':
loss = []
diff = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])
}
for l in train_layers:
diff['slstm'][l] = {}
for key in params['slstm'][l]:
diff['slstm'][l][key] = zeros_like(params['slstm'][l][key])
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1,
batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f)
# update SLSTM parameters
for l in train_layers:
for key in params['slstm'][l]:
diff['slstm'][l][key] = momentum * diff['slstm'][
l][key] - df['slstm'][l][key]
params['slstm'][l][key] = params['slstm'][l][
key] + learning_rate * diff['slstm'][l][key]
# update MCGSM parameters
diff['mcgsm'] = momentum * diff['mcgsm'] - df['mcgsm']
params['mcgsm'] = params[
'mcgsm'] + learning_rate * diff['mcgsm']
if self.verbosity > 0:
print '{0:>5} {1:>10.4f} {2:>10.4f}'.format(
n, loss[-1],
mean(loss[-max([10, 20000 // batch_size]):]))
return loss
elif method.upper() == 'ADAM':
loss = []
diff_mean = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])
}
diff_sqrd = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])
}
for l in train_layers:
diff_mean['slstm'][l] = {}
diff_sqrd['slstm'][l] = {}
for key in params['slstm'][l]:
diff_mean['slstm'][l][key] = zeros_like(
params['slstm'][l][key])
diff_sqrd['slstm'][l][key] = zeros_like(
params['slstm'][l][key])
# step counter
t = 1
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1,
batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f)
# include bias correction in step width
step_width = learning_rate / (
1. - power(decay1, t)) * sqrt(1. - power(decay2, t))
t += 1
# update SLSTM parameters
for l in train_layers:
for key in params['slstm'][l]:
diff_mean['slstm'][l][key] = decay1 * diff_mean['slstm'][l][key] \
+ (1. - decay1) * df['slstm'][l][key]
diff_sqrd['slstm'][l][key] = decay2 * diff_sqrd['slstm'][l][key] \
+ (1. - decay2) * square(df['slstm'][l][key])
params['slstm'][l][key] = params['slstm'][l][key] - \
step_width * diff_mean['slstm'][l][key] / (1e-8 + sqrt(diff_sqrd['slstm'][l][key]))
# update MCGSM parameters
diff_mean['mcgsm'] = decay1 * diff_mean['mcgsm'] + (
1. - decay1) * df['mcgsm']
diff_sqrd['mcgsm'] = decay2 * diff_sqrd['mcgsm'] + (
1. - decay2) * square(df['mcgsm'])
params['mcgsm'] = params['mcgsm'] - \
step_width * diff_mean['mcgsm'] / (1e-8 + sqrt(diff_sqrd['mcgsm']))
if self.verbosity > 0:
print '{0:>5} {1:>10.4f} {2:>10.4f}'.format(
n, loss[-1],
mean(loss[-max([10, 20000 // batch_size]):]))
return loss
else:
raise ValueError('Unknown method \'{0}\'.'.format(method))
def finetune(self,
images,
max_iter=1000,
train_means=False,
num_samples_train=500000,
num_samples_valid=100000):
"""
Train MCGSM using L-BFGS while keeping parameters of SLSTM fixed.
@type images: C{ndarray}/C{list}
@param images: an array or a list of images
"""
if images.shape[0] > num_samples_train:
images = images[random_select(num_samples_train, images.shape[0])]
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
print 'Forward...'
for l in range(self.num_layers):
self.slstm[l] = SLSTM(num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min(
[hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
print 'Reshape...'
# remove bottom-right pixels (BSDS300)
hiddens = hiddens.reshape(hiddens.shape[0], -1, self.num_hiddens)
outputs = outputs.reshape(outputs.shape[0], -1, self.num_channels)
hiddens = hiddens[:, :-1]
outputs = outputs[:, :-1]
# form inputs to MCGSM
hiddens = hiddens.reshape(-1, self.num_hiddens).T
outputs = outputs.reshape(-1, self.num_channels).T
print 'Finetuning...'
if hiddens.shape[1] > num_samples_train:
num_samples_valid = min(
[num_samples_valid, hiddens.shape[1] - num_samples_train])
# select subset of data points for finetuning
idx = random_select(num_samples_train + num_samples_valid,
hiddens.shape[1])
if num_samples_valid > 0:
# split data into training and validation set
hiddens_train = asarray(hiddens[:, idx[:num_samples_train]],
order='F')
outputs_train = asarray(outputs[:, idx[:num_samples_train]],
order='F')
hiddens_valid = asarray(hiddens[:, idx[num_samples_train:]],
order='F')
outputs_valid = asarray(outputs[:, idx[num_samples_train:]],
order='F')
# finetune with early stopping based on validation performance
return self.mcgsm.train(hiddens_train,
outputs_train,
hiddens_valid,
outputs_valid,
parameters={
'verbosity': self.verbosity,
'train_means': train_means,
'max_iter': max_iter
})
else:
hiddens = asarray(hiddens[:, idx], order='F')
outputs = asarray(outputs[:, idx], order='F')
return self.mcgsm.train(hiddens,
outputs,
parameters={
'verbosity': self.verbosity,
'train_means': train_means,
'max_iter': max_iter
})
def hidden_states(self, images, return_all=False):
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
for l in range(self.num_layers):
self.slstm[l] = SLSTM(num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min(
[hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if return_all:
return inputs, hiddens, outputs
return hiddens
def sample(self, images, min_values=None, max_values=None):
"""
Sample one or several images.
@type images: C{ndarray}
@param images: an array or a list of images to initialize pixels at boundaries
"""
if min_values is not None:
min_values = asarray(min_values).reshape(1, 1, 1, -1)
if max_values is not None:
max_values = asarray(max_values).reshape(1, 1, 1, -1)
# reshape images into four-dimensional arrays
shape = images.shape
if images.ndim == 2:
images = images[None, :, :, None]
elif images.ndim == 3:
if self.num_channels > 1:
images = images[None]
else:
images = images[:, :, :, None]
# create spatial LSTMs for sampling
slstm = []
for l in range(self.num_layers):
slstm.append(
SLSTM(num_rows=1,
num_cols=1,
num_channels=sum(self.input_mask)
if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=images.shape[0],
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity))
# container for hidden and memory unit activations
hiddens = []
memory = []
for l in range(self.num_layers):
hiddens.append(defaultdict(lambda: 0.))
memory.append(defaultdict(lambda: 0.))
# locate output pixel
for i_off, j_off in zip(range(self.output_mask.shape[0]),
range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
# extract patches from images
patches = images[:, i:i + self.input_mask.shape[0],
j:j + self.input_mask.shape[1]]
# extract causal neighborhoods from patches
inputs = []
for k in range(images.shape[0]):
inputs.append(
generate_data_from_image(patches[k, :, :],
self.input_mask,
self.output_mask)[0])
inputs = asarray(inputs)
inputs = inputs.reshape(inputs.shape[0], 1, 1, -1)
if self.preconditioner:
inputs = self._precondition(inputs)
# set hidden unit activations
for l in range(self.num_layers):
slstm[l].net.blobs['h_init_i_jm1'].data[:] = hiddens[l][i,
j -
1]
slstm[l].net.blobs['h_init_im1_j'].data[:] = hiddens[l][i -
1,
j]
slstm[l].net.blobs['c_init_i_jm1'].data[:] = memory[l][i,
j -
1]
slstm[l].net.blobs['c_init_im1_j'].data[:] = memory[l][i -
1,
j]
# compute hidden unit activations
activations = inputs
for l in range(self.num_layers):
activations = slstm[l].forward(activations)
# store hidden unit activations
for l in range(self.num_layers):
hiddens[l][i,
j] = slstm[l].net.blobs['outputs'].data.copy()
memory[l][i, j] = slstm[l].net.blobs['c_0_0'].data.copy()
for _ in range(10):
# sample MCGSM
outputs = self.mcgsm.sample(hiddens[-1][i, j].reshape(
-1, self.num_hiddens).T)
outputs = outputs.T.reshape(outputs.shape[1], 1, 1,
outputs.shape[0])
if not any(isnan(outputs)):
break
print 'Warning: NaNs detected.'
if self.preconditioner:
inputs, outputs = self._precondition_inverse(
inputs, outputs)
if max_values is not None:
outputs[outputs > max_values] = max_values[
outputs > max_values]
if min_values is not None:
outputs[outputs < min_values] = min_values[
outputs < min_values]
# insert sampled pixels into images
images[:, i + i_off,
j + j_off][self.output_mask[i_off, j_off]] = outputs
return images.reshape(*shape)
def __setstate__(self, state):
self.__dict__ = state
if not hasattr(self, 'nonlinearity'):
self.nonlinearity = 'TanH'
if not hasattr(self, 'extended'):
self.extended = False
class RIDE_BSDS300(object):
"""
Basically the same model as L{RIDE} but for the BSDS300 dataset
where the bottom-right pixel is commonly ignored. This model should
be used in combination with L{PatchRIDE}.
"""
MAX_BATCH_SIZE = 10000
def __init__(self,
num_channels=1,
num_hiddens=10,
num_components=4,
num_scales=4,
num_features=16,
num_layers=1,
nb_size=3,
nonlinearity='TanH',
verbosity=1,
extended=False,
input_mask=None,
output_mask=None):
self.verbosity = verbosity
self.num_channels = num_channels
self.num_hiddens = num_hiddens
self.num_layers = num_layers
self.nonlinearity = nonlinearity
self.extended = extended
self.input_mask, self.output_mask = generate_masks([nb_size] * num_channels)
if input_mask:
self.input_mask = input_mask
if output_mask:
self.output_mask = output_mask
self.num_channels = sum(self.output_mask)
self.slstm = [None] * num_layers
self.mcgsm = MCGSM(
dim_in=num_hiddens,
dim_out=num_channels,
num_components=num_components,
num_scales=num_scales,
num_features=num_features)
self.preconditioner = None
# see PatchRIDE
self._indicators = False
def add_layer(self):
"""
Add another spatial LSTM to the network and reinitialize MCGSM.
"""
self.num_layers += 1
# reinitialize MCGSM
self.mcgsm = MCGSM(
dim_in=self.num_hiddens,
dim_out=self.num_channels,
num_components=self.mcgsm.num_components,
num_scales=self.mcgsm.num_scales,
num_features=self.mcgsm.num_features)
# add slot for another layer
self.slstm.append(None)
def _precondition(self, inputs, outputs=None):
"""
Remove any correlations within and between inputs and outputs.
"""
shape = inputs.shape
if outputs is None:
if self.preconditioner is None:
raise RuntimeError('No preconditioning possible.')
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
# avoids memory issues
MAX_SAMPLES = 5000000
if self.preconditioner is None:
inputs_ = inputs
if self._indicators:
# half of the inputs are indicators, don't preprocess them
inputs_ = inputs.copy()
inputs_[inputs.shape[0] // 2:] = randn(inputs.shape[0] // 2, *inputs.shape[1:])
if inputs.shape[1] > MAX_SAMPLES:
idx = random_select(MAX_SAMPLES, inputs.shape[1])
self.preconditioner = WhiteningPreconditioner(inputs_[:, idx], outputs[:, idx])
else:
self.preconditioner = WhiteningPreconditioner(inputs_, outputs)
# precondition
for b in range(0, inputs.shape[1], MAX_SAMPLES):
inputs[:, b:b + MAX_SAMPLES], outputs[:, b:b + MAX_SAMPLES] = \
self.preconditioner(inputs[:, b:b + MAX_SAMPLES], outputs[:, b:b + MAX_SAMPLES])
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _precondition_inverse(self, inputs, outputs=None):
"""
Remove any correlations within and between inputs and outputs.
"""
if self.preconditioner is None:
raise RuntimeError('No preconditioner set.')
shape = inputs.shape
if outputs is None:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner.inverse(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
inputs, outputs = self.preconditioner.inverse(inputs, outputs)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _preprocess(self, images):
"""
Extract causal neighborhoods from images.
"""
def process(image):
inputs, outputs = generate_data_from_image(
image, self.input_mask, self.output_mask)
inputs = asarray(
inputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1,
image.shape[1] - self.input_mask.shape[1] + 1,
-1), dtype='float32')
outputs = asarray(
outputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1,
image.shape[1] - self.input_mask.shape[1] + 1,
-1), dtype='float32')
return inputs, outputs
inputs, outputs = zip(*mapp(process, images))
return asarray(inputs), asarray(outputs)
def loglikelihood(self, images):
"""
Returns a log-likelihood for each pixel except the bottom-right pixel (in nats).
"""
inputs, outputs = self._preprocess(images)
if self.preconditioner is not None:
if self.verbosity > 0:
print 'Computing Jacobian...'
logjacobian = self.preconditioner.logjacobian(
inputs.reshape(-1, sum(self.input_mask)).T,
outputs.reshape(-1, self.num_channels).T)
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
else:
logjacobian = 0.
# compute hidden unit activations
hiddens = inputs
for l in range(self.num_layers):
# create SLSTM
self.slstm[l] = SLSTM(
num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min([hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if self.verbosity > 0:
print 'Computing likelihood...'
# evaluate log-likelihood
loglik = self.mcgsm.loglikelihood(
hiddens.reshape(-1, self.num_hiddens).T,
outputs.reshape(-1, self.num_channels).T) + logjacobian
# remove bottom-right pixel
loglik = loglik.reshape(hiddens.shape[0], -1)
loglik = loglik[:, :-1]
return loglik
def evaluate(self, images):
"""
Computes the average negative log-likelihood in bits per pixel.
"""
MAX_IMAGES = 100000
loglik = []
for b in range(0, len(images), MAX_IMAGES):
loglik.append(mean(self.loglikelihood(images[b:b + MAX_IMAGES])))
return -mean(loglik) / log(2.)
def train(self, images,
batch_size=50,
num_epochs=20,
method='SGD',
train_means=False,
train_top_layer=False,
momentum=0.9,
learning_rate=1.,
decay1=0.9,
decay2=0.999,
precondition=True):
"""
@type images: C{ndarray}/C{list}
@param images: an array or a list of images
"""
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if precondition:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# indicates which layers will be trained
train_layers = [self.num_layers - 1] if train_top_layer else range(self.num_layers)
print 'Creating SLSTMs...'
# create SLSTMs
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=inputs.shape[1],
num_cols=inputs.shape[2],
num_channels=inputs.shape[3] if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=min([batch_size, self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
# compute loss function and its gradient
def f_df(params, idx):
# set model parameters
for l in train_layers:
self.slstm[l].set_parameters(params['slstm'][l])
self.mcgsm._set_parameters(params['mcgsm'], {'train_means': train_means})
# select batch and compute hidden activations
Y = outputs[idx:idx + batch_size]
H = inputs[idx:idx + batch_size]
for l in range(self.num_layers):
H = self.slstm[l].forward(H)
# form inputs to MCGSM
H_flat = H.reshape(-1, self.num_hiddens).T
Y_flat = Y.reshape(-1, self.num_channels).T
norm_const = -H_flat.shape[1]
# compute gradients
df_dh, _, loglik = self.mcgsm._data_gradient(H_flat, Y_flat)
df_dh = df_dh.T.reshape(*H.shape) / norm_const
# ignore bottom-right pixel (BSDS300)
df_dh[:, -1, -1] = 0.
# average negative log-likelihood
f = sum(loglik) / norm_const
df_dtheta = {}
df_dtheta['slstm'] = [0.] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
if l > min(train_layers):
# derivative with respect to inputs of layer l are derivatives
# of hidden states of layer l - 1
df_dtheta['slstm'][l] = self.slstm[l].backward(df_dh, force_backward=True)
df_dh = df_dtheta['slstm'][l]['inputs']
del df_dtheta['slstm'][l]['inputs']
else:
# no need to compute derivatives with respect to input units
df_dtheta['slstm'][l] = self.slstm[l].backward(df_dh)
# compute gradient of MCGSM
df_dtheta['mcgsm'] = self.mcgsm._parameter_gradient(H_flat, Y_flat,
parameters={'train_means': train_means}) * log(2.) * self.mcgsm.dim_out
return f, df_dtheta
# collect current parameters
params = {}
params['slstm'] = [0.] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
params['slstm'][l] = self.slstm[l].parameters()
params['mcgsm'] = self.mcgsm._parameters({'train_means': train_means})
# a start index for each batch
start_indices = range(
0, inputs.shape[0] - batch_size + 1, batch_size)
print 'Training...'
if method.upper() == 'SFO':
try:
# optimize using sum-of-functions optimizer
optimizer = SFO(f_df, params, start_indices, display=self.verbosity)
params_opt = optimizer.optimize(num_passes=num_epochs)
# set model parameters
for l in range(self.num_layers):
self.slstm[l].set_parameters(params_opt['slstm'][l])
self.mcgsm._set_parameters(params_opt['mcgsm'], {'train_means': train_means})
except KeyboardInterrupt:
pass
return optimizer.hist_f_flat
elif method.upper() == 'SGD':
loss = []
diff = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])}
for l in train_layers:
diff['slstm'][l] = {}
for key in params['slstm'][l]:
diff['slstm'][l][key] = zeros_like(params['slstm'][l][key])
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1, batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f)
# update SLSTM parameters
for l in train_layers:
for key in params['slstm'][l]:
diff['slstm'][l][key] = momentum * diff['slstm'][l][key] - df['slstm'][l][key]
params['slstm'][l][key] = params['slstm'][l][key] + learning_rate * diff['slstm'][l][key]
# update MCGSM parameters
diff['mcgsm'] = momentum * diff['mcgsm'] - df['mcgsm']
params['mcgsm'] = params['mcgsm'] + learning_rate * diff['mcgsm']
if self.verbosity > 0:
print '{0:>5} {1:>10.4f} {2:>10.4f}'.format(
n, loss[-1], mean(loss[-max([10, 20000 // batch_size]):]))
return loss
elif method.upper() == 'ADAM':
loss = []
diff_mean = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])}
diff_sqrd = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])}
for l in train_layers:
diff_mean['slstm'][l] = {}
diff_sqrd['slstm'][l] = {}
for key in params['slstm'][l]:
diff_mean['slstm'][l][key] = zeros_like(params['slstm'][l][key])
diff_sqrd['slstm'][l][key] = zeros_like(params['slstm'][l][key])
# step counter
t = 1
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1, batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f)
# include bias correction in step width
step_width = learning_rate / (1. - power(decay1, t)) * sqrt(1. - power(decay2, t))
t += 1
# update SLSTM parameters
for l in train_layers:
for key in params['slstm'][l]:
diff_mean['slstm'][l][key] = decay1 * diff_mean['slstm'][l][key] \
+ (1. - decay1) * df['slstm'][l][key]
diff_sqrd['slstm'][l][key] = decay2 * diff_sqrd['slstm'][l][key] \
+ (1. - decay2) * square(df['slstm'][l][key])
params['slstm'][l][key] = params['slstm'][l][key] - \
step_width * diff_mean['slstm'][l][key] / (1e-8 + sqrt(diff_sqrd['slstm'][l][key]))
# update MCGSM parameters
diff_mean['mcgsm'] = decay1 * diff_mean['mcgsm'] + (1. - decay1) * df['mcgsm']
diff_sqrd['mcgsm'] = decay2 * diff_sqrd['mcgsm'] + (1. - decay2) * square(df['mcgsm'])
params['mcgsm'] = params['mcgsm'] - \
step_width * diff_mean['mcgsm'] / (1e-8 + sqrt(diff_sqrd['mcgsm']))
if self.verbosity > 0:
print '{0:>5} {1:>10.4f} {2:>10.4f}'.format(
n, loss[-1], mean(loss[-max([10, 20000 // batch_size]):]))
return loss
else:
raise ValueError('Unknown method \'{0}\'.'.format(method))
def finetune(self, images,
max_iter=1000,
train_means=False,
num_samples_train=500000,
num_samples_valid=100000):
"""
Train MCGSM using L-BFGS while keeping parameters of SLSTM fixed.
@type images: C{ndarray}/C{list}
@param images: an array or a list of images
"""
if images.shape[0] > num_samples_train:
images = images[random_select(num_samples_train, images.shape[0])]
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
print 'Forward...'
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min([hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
print 'Reshape...'
# remove bottom-right pixels (BSDS300)
hiddens = hiddens.reshape(hiddens.shape[0], -1, self.num_hiddens)
outputs = outputs.reshape(outputs.shape[0], -1, self.num_channels)
hiddens = hiddens[:, :-1]
outputs = outputs[:, :-1]
# form inputs to MCGSM
hiddens = hiddens.reshape(-1, self.num_hiddens).T
outputs = outputs.reshape(-1, self.num_channels).T
print 'Finetuning...'
if hiddens.shape[1] > num_samples_train:
num_samples_valid = min([num_samples_valid, hiddens.shape[1] - num_samples_train])
# select subset of data points for finetuning
idx = random_select(num_samples_train + num_samples_valid, hiddens.shape[1])
if num_samples_valid > 0:
# split data into training and validation set
hiddens_train = asarray(hiddens[:, idx[:num_samples_train]], order='F')
outputs_train = asarray(outputs[:, idx[:num_samples_train]], order='F')
hiddens_valid = asarray(hiddens[:, idx[num_samples_train:]], order='F')
outputs_valid = asarray(outputs[:, idx[num_samples_train:]], order='F')
# finetune with early stopping based on validation performance
return self.mcgsm.train(
hiddens_train, outputs_train,
hiddens_valid, outputs_valid,
parameters={
'verbosity': self.verbosity,
'train_means': train_means,
'max_iter': max_iter})
else:
hiddens = asarray(hiddens[:, idx], order='F')
outputs = asarray(outputs[:, idx], order='F')
return self.mcgsm.train(hiddens, outputs, parameters={
'verbosity': self.verbosity,
'train_means': train_means,
'max_iter': max_iter})
def hidden_states(self, images, return_all=False):
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min([hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if return_all:
return inputs, hiddens, outputs
return hiddens
def sample(self, images, min_values=None, max_values=None):
"""
Sample one or several images.
@type images: C{ndarray}
@param images: an array or a list of images to initialize pixels at boundaries
"""
if min_values is not None:
min_values = asarray(min_values).reshape(1, 1, 1, -1)
if max_values is not None:
max_values = asarray(max_values).reshape(1, 1, 1, -1)
# reshape images into four-dimensional arrays
shape = images.shape
if images.ndim == 2:
images = images[None, :, :, None]
elif images.ndim == 3:
if self.num_channels > 1:
images = images[None]
else:
images = images[:, :, :, None]
# create spatial LSTMs for sampling
slstm = []
for l in range(self.num_layers):
slstm.append(SLSTM(
num_rows=1,
num_cols=1,
num_channels=sum(self.input_mask) if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=images.shape[0],
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity))
# container for hidden and memory unit activations
hiddens = []
memory = []
for l in range(self.num_layers):
hiddens.append(defaultdict(lambda: 0.))
memory.append(defaultdict(lambda: 0.))
# locate output pixel
for i_off, j_off in zip(
range(self.output_mask.shape[0]),
range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
# extract patches from images
patches = images[:,
i:i + self.input_mask.shape[0],
j:j + self.input_mask.shape[1]]
# extract causal neighborhoods from patches
inputs = []
for k in range(images.shape[0]):
inputs.append(
generate_data_from_image(
patches[k, :, :], self.input_mask, self.output_mask)[0])
inputs = asarray(inputs)
inputs = inputs.reshape(inputs.shape[0], 1, 1, -1)
if self.preconditioner:
inputs = self._precondition(inputs)
# set hidden unit activations
for l in range(self.num_layers):
slstm[l].net.blobs['h_init_i_jm1'].data[:] = hiddens[l][i, j - 1]
slstm[l].net.blobs['h_init_im1_j'].data[:] = hiddens[l][i - 1, j]
slstm[l].net.blobs['c_init_i_jm1'].data[:] = memory[l][i, j - 1]
slstm[l].net.blobs['c_init_im1_j'].data[:] = memory[l][i - 1, j]
# compute hidden unit activations
activations = inputs
for l in range(self.num_layers):
activations = slstm[l].forward(activations)
# store hidden unit activations
for l in range(self.num_layers):
hiddens[l][i, j] = slstm[l].net.blobs['outputs'].data.copy()
memory[l][i, j] = slstm[l].net.blobs['c_0_0'].data.copy()
for _ in range(10):
# sample MCGSM
outputs = self.mcgsm.sample(
hiddens[-1][i, j].reshape(-1, self.num_hiddens).T)
outputs = outputs.T.reshape(outputs.shape[1], 1, 1, outputs.shape[0])
if not any(isnan(outputs)):
break
print 'Warning: NaNs detected.'
if self.preconditioner:
inputs, outputs = self._precondition_inverse(inputs, outputs)
if max_values is not None:
outputs[outputs > max_values] = max_values[outputs > max_values]
if min_values is not None:
outputs[outputs < min_values] = min_values[outputs < min_values]
# insert sampled pixels into images
images[:, i + i_off, j + j_off][self.output_mask[i_off, j_off]] = outputs
return images.reshape(*shape)
def __setstate__(self, state):
self.__dict__ = state
if not hasattr(self, 'nonlinearity'):
self.nonlinearity = 'TanH'
if not hasattr(self, 'extended'):
self.extended = False
class RIDE(object):
"""
An implementation of the recurrent image density estimator (RIDE).
B{References:}
- Theis, L. and Bethge, M. (2015). I{Generative Image Modeling Using Spatial LSTMs.}
"""
# maximum batch size used by Caffe internally
MAX_BATCH_SIZE = 200
def __init__(
self,
num_channels=1,
num_hiddens=10,
num_components=8,
num_scales=4,
num_features=16,
num_layers=1,
nb_size=5,
nonlinearity="TanH",
verbosity=1,
extended=False,
input_mask=None,
output_mask=None,
):
"""
@type num_channels: C{int}
@param num_channels: dimensionality of each pixel
@type num_hiddens: C{int}
@param num_hiddens: number of LSTM units in each spatial LSTM layer
@type num_components: C{int}
@param num_components: number of mixture components used by the MCGSM
@type num_scales: C{int}
@param num_scales: number of scales used by the MCGSM
@type num_features: C{int}
@param num_features: number of quadratic features used by the MCGSM
@type num_layers: C{int}
@param num_layers: number of layers of spatial LSTM units
@type nb_size: C{int}
@param nb_size: controls the neighborhood of pixels read from an image
@type nonlinearity: C{str}
@param nonlinearity: nonlinearity used by spatial LSTM (e.g., TanH, ReLU)
@type verbosity: C{int}
@param verbosity: controls how much information is printed during training, etc.
@type extended: C{bool}
@param extended: use previous memory states as additional inputs to LSTM (more parameters)
@type input_mask C{ndarray}
@param input_mask: Boolean mask used to define custom input neighborhood of pixels
@type output_mask C{ndarray}
@param output_mask: determines the position of the output pixel relative to the neighborhood
"""
self.verbosity = verbosity
self.num_channels = num_channels
self.num_hiddens = num_hiddens
self.num_layers = num_layers
self.nonlinearity = nonlinearity
self.extended = extended
self.input_mask, self.output_mask = generate_masks([nb_size] * num_channels)
if input_mask is not None:
self.input_mask = input_mask
if output_mask is not None:
self.output_mask = output_mask
self.num_channels = sum(self.output_mask)
self.slstm = [None] * num_layers
self.mcgsm = MCGSM(
dim_in=self.num_hiddens,
dim_out=self.num_channels,
num_components=num_components,
num_scales=num_scales,
num_features=num_features,
)
self.preconditioner = None
def add_layer(self):
"""
Add another spatial LSTM to the network and reinitialize MCGSM.
"""
self.num_layers += 1
# reinitialize MCGSM
self.mcgsm = MCGSM(
dim_in=self.num_hiddens,
dim_out=self.num_channels,
num_components=self.mcgsm.num_components,
num_scales=self.mcgsm.num_scales,
num_features=self.mcgsm.num_features,
)
# add slot for another layer
self.slstm.append(None)
def _precondition(self, inputs, outputs=None):
"""
Remove any correlations within and between inputs and outputs (conditional whitening).
@type inputs: C{ndarray}
@param inputs: pixel neighborhoods stored column-wise
@type outputs: C{ndarray}
@param outputs: output pixels stored column-wise
"""
shape = inputs.shape
if outputs is None:
if self.preconditioner is None:
raise RuntimeError("No preconditioning possible.")
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
# avoids memory issues
MAX_SAMPLES = 500000
if self.preconditioner is None:
if inputs.shape[1] > MAX_SAMPLES:
idx = random_select(MAX_SAMPLES, inputs.shape[1])
self.preconditioner = WhiteningPreconditioner(inputs[:, idx], outputs[:, idx])
else:
self.preconditioner = WhiteningPreconditioner(inputs, outputs)
for b in range(0, inputs.shape[1], MAX_SAMPLES):
inputs[:, b : b + MAX_SAMPLES], outputs[:, b : b + MAX_SAMPLES] = self.preconditioner(
inputs[:, b : b + MAX_SAMPLES], outputs[:, b : b + MAX_SAMPLES]
)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _precondition_inverse(self, inputs, outputs=None):
"""
Reintroduce correlations removed by conditional whitening.
@type inputs: C{ndarray}
@param inputs: pixel neighborhoods stored column-wise
@type outputs: C{ndarray}
@param outputs: output pixels stored column-wise
"""
if self.preconditioner is None:
raise RuntimeError("No preconditioner set.")
shape = inputs.shape
if outputs is None:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner.inverse(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
inputs, outputs = self.preconditioner.inverse(inputs, outputs)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _adjust_gradient(self, inputs, outputs):
"""
Adjust gradients to take into account preconditioning.
@type inputs: C{ndarray}
@param inputs: gradient with respect to conditionally whitened inputs
@type outputs: C{ndarray}
@param outputs: gradient with respect to conditionally whitened outputs
"""
if self.preconditioner is None:
raise RuntimeError("No preconditioner set.")
shape = inputs.shape
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
inputs, outputs = self.preconditioner.adjust_gradient(inputs, outputs)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _preprocess(self, images):
"""
Extract causal neighborhoods from images.
@type images: C{ndarray}/C{list}
@param images: array or list of images to process
@rtype: C{tuple}
@return: one array storing inputs (neighborhoods) and one array storing outputs (pixels)
"""
def process(image):
inputs, outputs = generate_data_from_image(image, self.input_mask, self.output_mask)
inputs = asarray(
inputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1, image.shape[1] - self.input_mask.shape[1] + 1, -1
),
dtype="float32",
)
outputs = asarray(
outputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1, image.shape[1] - self.input_mask.shape[1] + 1, -1
),
dtype="float32",
)
return inputs, outputs
inputs, outputs = zip(*mapp(process, images))
return asarray(inputs), asarray(outputs)
def loglikelihood(self, images):
"""
Returns a log-likelihood for each reachable pixel (in nats).
@type images: C{ndarray}/C{list}
@param images: array or list of images for which to evaluate log-likelihood
@rtype: C{ndarray}
@return: an array of log-likelihoods for each image and predicted pixel
"""
inputs, outputs = self._preprocess(images)
if self.preconditioner is not None:
if self.verbosity > 0:
print "Computing Jacobian..."
logjacobian = self.preconditioner.logjacobian(
inputs.reshape(-1, sum(self.input_mask)).T, outputs.reshape(-1, self.num_channels).T
)
if self.verbosity > 0:
print "Preconditioning..."
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
else:
logjacobian = 0.0
# compute hidden unit activations
hiddens = inputs
batch_size = min([hiddens.shape[0], self.MAX_BATCH_SIZE])
if self.verbosity > 0:
print "Computing hidden states..."
for l in range(self.num_layers):
# create SLSTM
if (
self.slstm[l].num_rows != hiddens.shape[1]
or self.slstm[l].num_cols != hiddens.shape[2]
or self.slstm[l].batch_size != batch_size
):
self.slstm[l] = SLSTM(
num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=batch_size,
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity,
)
hiddens = self.slstm[l].forward(hiddens)
if self.verbosity > 0:
print "Computing likelihood..."
# evaluate log-likelihood
loglik = (
self.mcgsm.loglikelihood(hiddens.reshape(-1, self.num_hiddens).T, outputs.reshape(-1, self.num_channels).T)
+ logjacobian
)
return loglik.reshape(hiddens.shape[0], hiddens.shape[1], hiddens.shape[2])
def evaluate(self, images):
"""
Computes the average negative log-likelihood in bits per pixel.
@type images: C{ndarray}/C{list}
@param images: an array or list of test images
@rtype: C{float}
@return: average negative log-likelihood in bits per pixel
"""
return -mean(self.loglikelihood(images)) / log(2.0) / self.num_channels
def train(
self,
images,
batch_size=50,
num_epochs=20,
method="SGD",
train_means=False,
train_top_layer=False,
momentum=0.9,
learning_rate=1.0,
decay1=0.9,
decay2=0.999,
precondition=True,
):
"""
Train model via stochastic gradient descent (SGD) or sum-of-functions optimizer (SFO).
@type images: C{ndarray}/C{list}
@param images: an array or a list of training images (e.g., Nx32x32x3)
@type batch_size: C{int}
@param batch_size: batch size used by SGD
@type num_epochs: C{int}
@param num_epochs: number of passes through the training set
@type method: C{str}
@param method: either 'SGD', 'SFO', or 'ADAM'
@type train_means: C{bool}
@param train_means: whether or not to optimize the mean parameters of the MCGSM
@type train_top_layer: C{bool}
@param train_top_layer: if true, only the MCGSM and spatial LSTM at the top layer is trained
@type momentum: C{float}
@param momentum: momentum rate used by SGD
@type learning_rate: C{float}
@param learning_rate: learning rate used by SGD
@type decay1: C{float}
@param decay1: hyperparameter used by ADAM
@type decay2: C{float}
@param decay2: hyperparameter used by ADAM
@type precondition: C{bool}
@param precondition: whether or not to perform conditional whitening
@rtype: C{list}
@return: evolution of negative log-likelihood (bits per pixel) over the training
"""
if images.shape[1] < self.input_mask.shape[0] or images.shape[2] < self.input_mask.shape[1]:
raise ValueError("Images too small.")
if self.verbosity > 0:
print "Preprocessing..."
inputs, outputs = self._preprocess(images)
if precondition:
if self.verbosity > 0:
print "Preconditioning..."
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# indicates which layers will be trained
train_layers = [self.num_layers - 1] if train_top_layer else range(self.num_layers)
if self.verbosity > 0:
print "Creating SLSTMs..."
# create SLSTMs
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=inputs.shape[1],
num_cols=inputs.shape[2],
num_channels=inputs.shape[3] if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=min([batch_size, self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity,
)
# compute loss function and its gradient
def f_df(params, idx):
# set model parameters
for l in train_layers:
self.slstm[l].set_parameters(params["slstm"][l])
self.mcgsm._set_parameters(params["mcgsm"], {"train_means": train_means})
# select batch and compute hidden activations
Y = outputs[idx : idx + batch_size]
H = inputs[idx : idx + batch_size]
for l in range(self.num_layers):
H = self.slstm[l].forward(H)
# form inputs to MCGSM
H_flat = H.reshape(-1, self.num_hiddens).T
Y_flat = Y.reshape(-1, self.num_channels).T
norm_const = -H_flat.shape[1]
# compute gradients
df_dh, _, loglik = self.mcgsm._data_gradient(H_flat, Y_flat)
df_dh = df_dh.T.reshape(*H.shape) / norm_const
# average log-likelihood
f = sum(loglik) / norm_const
df_dtheta = {}
df_dtheta["slstm"] = [0.0] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
if l > min(train_layers):
# derivative with respect to inputs of layer l are derivatives
# of hidden states of layer l - 1
df_dtheta["slstm"][l] = self.slstm[l].backward(df_dh, force_backward=True)
df_dh = df_dtheta["slstm"][l]["inputs"]
del df_dtheta["slstm"][l]["inputs"]
else:
# no need to compute derivatives with respect to input units
df_dtheta["slstm"][l] = self.slstm[l].backward(df_dh)
# compute gradient of MCGSM
df_dtheta["mcgsm"] = (
self.mcgsm._parameter_gradient(H_flat, Y_flat, parameters={"train_means": train_means})
* log(2.0)
* self.mcgsm.dim_out
)
return f, df_dtheta
# collect current parameters
params = {}
params["slstm"] = [0.0] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
params["slstm"][l] = self.slstm[l].parameters()
params["mcgsm"] = self.mcgsm._parameters({"train_means": train_means})
# a start index for each batch
start_indices = range(0, inputs.shape[0] - batch_size + 1, batch_size)
if self.verbosity > 0:
print "Training..."
if method.upper() == "SFO":
try:
# optimize using sum-of-functions optimizer
optimizer = SFO(f_df, params, start_indices, display=self.verbosity)
params_opt = optimizer.optimize(num_passes=num_epochs)
# set model parameters
for l in range(self.num_layers):
self.slstm[l].set_parameters(params_opt["slstm"][l])
self.mcgsm._set_parameters(params_opt["mcgsm"], {"train_means": train_means})
except KeyboardInterrupt:
pass
return optimizer.hist_f_flat
elif method.upper() == "SGD":
loss = []
diff = {"slstm": [0.0] * self.num_layers, "mcgsm": zeros_like(params["mcgsm"])}
for l in train_layers:
diff["slstm"][l] = {}
for key in params["slstm"][l]:
diff["slstm"][l][key] = zeros_like(params["slstm"][l][key])
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1, batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f / log(2.0) / self.num_channels)
# update SLSTM parameters
for l in train_layers:
for key in params["slstm"][l]:
diff["slstm"][l][key] = momentum * diff["slstm"][l][key] - df["slstm"][l][key]
params["slstm"][l][key] = params["slstm"][l][key] + learning_rate * diff["slstm"][l][key]
# update MCGSM parameters
diff["mcgsm"] = momentum * diff["mcgsm"] - df["mcgsm"]
params["mcgsm"] = params["mcgsm"] + learning_rate * diff["mcgsm"]
if self.verbosity > 0:
print "{0:>5} {1:>10.4f} {2:>10.4f}".format(
n, loss[-1], mean(loss[-max([10, 20000 // batch_size]) :])
)
return loss
elif method.upper() == "ADAM":
loss = []
diff_mean = {"slstm": [0.0] * self.num_layers, "mcgsm": zeros_like(params["mcgsm"])}
diff_sqrd = {"slstm": [0.0] * self.num_layers, "mcgsm": zeros_like(params["mcgsm"])}
for l in train_layers:
diff_mean["slstm"][l] = {}
diff_sqrd["slstm"][l] = {}
for key in params["slstm"][l]:
diff_mean["slstm"][l][key] = zeros_like(params["slstm"][l][key])
diff_sqrd["slstm"][l][key] = zeros_like(params["slstm"][l][key])
# step counter
t = 1
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1, batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f / log(2.0) / self.num_channels)
# include bias correction in step width
step_width = learning_rate / (1.0 - power(decay1, t)) * sqrt(1.0 - power(decay2, t))
t += 1
# update SLSTM parameters
for l in train_layers:
for key in params["slstm"][l]:
diff_mean["slstm"][l][key] = (
decay1 * diff_mean["slstm"][l][key] + (1.0 - decay1) * df["slstm"][l][key]
)
diff_sqrd["slstm"][l][key] = decay2 * diff_sqrd["slstm"][l][key] + (1.0 - decay2) * square(
df["slstm"][l][key]
)
params["slstm"][l][key] = params["slstm"][l][key] - step_width * diff_mean["slstm"][l][
key
] / (1e-8 + sqrt(diff_sqrd["slstm"][l][key]))
# update MCGSM parameters
diff_mean["mcgsm"] = decay1 * diff_mean["mcgsm"] + (1.0 - decay1) * df["mcgsm"]
diff_sqrd["mcgsm"] = decay2 * diff_sqrd["mcgsm"] + (1.0 - decay2) * square(df["mcgsm"])
params["mcgsm"] = params["mcgsm"] - step_width * diff_mean["mcgsm"] / (
1e-8 + sqrt(diff_sqrd["mcgsm"])
)
if self.verbosity > 0:
print "{0:>5} {1:>10.4f} {2:>10.4f}".format(
n, loss[-1], mean(loss[-max([10, 20000 // batch_size]) :])
)
return loss
else:
raise ValueError("Unknown method '{0}'.".format(method))
def finetune(self, images, max_iter=1000, train_means=False, num_samples_train=500000, num_samples_valid=100000):
"""
Train MCGSM using L-BFGS while keeping parameters of spatial LSTMs fixed.
@type images: C{ndarray}/C{list}
@param images: an array or a list of images
@type max_iter: C{int}
@param max_iter: maximum number of L-BFGS iterations
@type train_means: C{bool}
@param train_means: whether or not to optimize the mean parameters of the MCGSM
@type num_samples_train: C{int}
@param num_samples_train: number of training examples extracted from images
@type num_samples_valid: C{int}
@type num_samples_valid: number of validation examples used for early stopping
@rtype: C{bool}
@return: true if training converged, false otherwise
"""
if images.shape[0] > min([200000, num_samples_train]):
images = images[random_select(min([200000, num_samples_train]), images.shape[0])]
if self.verbosity > 0:
print "Preprocessing..."
inputs, outputs = self._preprocess(images)
if self.preconditioner:
if self.verbosity > 0:
print "Preconditioning..."
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
if self.verbosity > 0:
print "Computing hidden states..."
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min([hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity,
)
hiddens = self.slstm[l].forward(hiddens)
if self.verbosity > 0:
print "Preparing inputs and outputs..."
# form inputs to MCGSM
hiddens = hiddens.reshape(-1, self.num_hiddens).T
outputs = outputs.reshape(-1, self.num_channels).T
if hiddens.shape[1] > num_samples_train:
num_samples_valid = min([num_samples_valid, hiddens.shape[1] - num_samples_train])
# select subset of data points for finetuning
idx = random_select(num_samples_train + num_samples_valid, hiddens.shape[1])
if num_samples_valid > 0:
# split data into training and validation set
hiddens_train = asarray(hiddens[:, idx[:num_samples_train]], order="F")
outputs_train = asarray(outputs[:, idx[:num_samples_train]], order="F")
hiddens_valid = asarray(hiddens[:, idx[num_samples_train:]], order="F")
outputs_valid = asarray(outputs[:, idx[num_samples_train:]], order="F")
# finetune with early stopping based on validation performance
return self.mcgsm.train(
hiddens_train,
outputs_train,
hiddens_valid,
outputs_valid,
parameters={"verbosity": self.verbosity, "train_means": train_means, "max_iter": max_iter},
)
else:
hiddens = asarray(hiddens[:, idx], order="F")
outputs = asarray(outputs[:, idx], order="F")
if self.verbosity > 0:
print "Finetuning..."
return self.mcgsm.train(
hiddens, outputs, parameters={"verbosity": self.verbosity, "train_means": train_means, "max_iter": max_iter}
)
def hidden_states(self, images, return_all=False, layer=None):
"""
Compute hidden states of LSTM units for given images.
By default, the last layer's hidden units are computed.
@type images: C{ndarray}/C{list}
@param images: array or list of images to process
@type return_all: C{bool}
@param return_all: if true, also return preconditioned inputs and outputs
@type layer: C{int}
@param layer: a positive integer controlling which layer's hidden units to compute
@rtype: C{ndarray}/C{tuple}
@return: hidden states or a tuple of inputs, hidden states, and outputs
"""
if self.verbosity > 0:
print "Preprocessing..."
inputs, outputs = self._preprocess(images)
if self.preconditioner is not None:
if self.verbosity > 0:
print "Preconditioning..."
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
batch_size = min([hiddens.shape[0], self.MAX_BATCH_SIZE])
if layer is None or layer < 1:
layer = self.num_layers
for l in range(layer):
if (
self.slstm[l].num_rows != hiddens.shape[1]
or self.slstm[l].num_cols != hiddens.shape[2]
or self.slstm[l].batch_size != batch_size
):
self.slstm[l] = SLSTM(
num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=batch_size,
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity,
)
hiddens = self.slstm[l].forward(hiddens)
if return_all:
return inputs, hiddens, outputs
return hiddens
def gradient(self, images):
"""
Returns the average log-likelihood [nat] and its gradient with respect to pixel values.
@type images: C{ndarray}
@param images: images at which to evaluate the density's gradient
@rtype: C{tuple}
@return: average log-likelihood and gradient with respect to images
"""
if self.verbosity > 0:
print "Preprocessing..."
inputs, outputs = self._preprocess(images)
if self.preconditioner:
if self.verbosity > 0:
print "Preconditioning..."
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
if self.verbosity > 0:
print "Creating SLSTMs..."
# create SLSTMs
batch_size = min([images.shape[0], self.MAX_BATCH_SIZE])
for l in range(self.num_layers):
if (
self.slstm[l] is None
or self.slstm[l].batch_size != batch_size
or self.slstm[l].num_rows != inputs.shape[1]
or self.slstm[l].num_cols != inputs.shape[2]
):
self.slstm[l] = SLSTM(
num_rows=inputs.shape[1],
num_cols=inputs.shape[2],
num_channels=inputs.shape[3] if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=batch_size,
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity,
)
# compute hidden unit activations
hiddens = inputs
for l in range(self.num_layers):
hiddens = self.slstm[l].forward(hiddens)
# form inputs to MCGSM
H_flat = hiddens.reshape(-1, self.num_hiddens).T
Y_flat = outputs.reshape(-1, self.num_channels).T
# compute gradients
df_dh, df_dy, loglik = self.mcgsm._data_gradient(H_flat, Y_flat)
df_dh = df_dh.T.reshape(*hiddens.shape) / H_flat.shape[1]
df_dy = df_dy.T.reshape(*outputs.shape) / H_flat.shape[1]
# average log-likelihood
f = sum(loglik) / H_flat.shape[1]
for l in range(self.num_layers)[::-1]:
df_dh = self.slstm[l].backward(df_dh, force_backward=True)["inputs"]
if self.preconditioner:
df_dh, df_dy = self._adjust_gradient(df_dh, df_dy)
# locate output pixel in output mask
for i_off, j_off in zip(range(self.output_mask.shape[0]), range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
gradient = zeros_like(images)
# make sure mask and gradient have compatible dimensionality
if gradient.ndim == 4 and self.input_mask.ndim == 2:
gradient = gradient[:, :, :, 0]
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
patch = gradient[:, i : i + self.input_mask.shape[0], j : j + self.output_mask.shape[1]]
patch[:, self.input_mask] += df_dh[:, i, j]
patch[:, self.output_mask] += df_dy[:, i, j]
return f, gradient.reshape(*images.shape)
def sample(self, images, min_values=None, max_values=None, mask=None, return_loglik=False):
"""
Sample one or several images.
@type images: C{ndarray}/C{list}
@param images: an array or a list of images to initialize pixels at boundaries
@type min_values: C{ndarray}/C{list}
@param min_values: list of lower bounds for each channel (for increased stability)
@type max_values: C{ndarray}/C{list}
@param max_values: list of upper bounds for each channel (for increased stability)
@type mask: C{ndarray}
@param mask: replace only certain pixels indicated by this Boolean mask
@rtype: C{ndarray}
@return: sampled images of the size of the images given as input
"""
# reshape images into four-dimensional arrays
shape = images.shape
if images.ndim == 2:
images = images[None, :, :, None]
elif images.ndim == 3:
if self.num_channels > 1:
images = images[None]
else:
images = images[:, :, :, None]
# create spatial LSTMs for sampling
for l in range(self.num_layers):
if (
self.slstm[l].num_rows != 1
or self.slstm[l].num_cols != 1
or self.slstm[l].batch_size != images.shape[0]
):
self.slstm[l] = SLSTM(
num_rows=1,
num_cols=1,
num_channels=sum(self.input_mask) if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=images.shape[0],
nonlinearity=self.nonlinearity,
slstm=self.slstm[l],
extended=self.extended,
)
# container for hidden and memory unit activations
hiddens = []
memory = []
for l in range(self.num_layers):
hiddens.append(defaultdict(lambda: 0.0))
memory.append(defaultdict(lambda: 0.0))
# locate output pixel
for i_off, j_off in zip(range(self.output_mask.shape[0]), range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
if min_values is not None:
min_values = asarray(min_values).reshape(1, 1, 1, -1)
if self.output_mask.ndim > 2:
min_values = min_values[:, :, :, self.output_mask[i_off, j_off]]
if max_values is not None:
max_values = asarray(max_values).reshape(1, 1, 1, -1)
if self.output_mask.ndim > 2:
max_values = max_values[:, :, :, self.output_mask[i_off, j_off]]
# unnormalized log-density of generated sample
logq = 0.0
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
# extract patches from images
patches = images[:, i : i + self.input_mask.shape[0], j : j + self.input_mask.shape[1]]
# extract causal neighborhoods from patches
inputs = []
for k in range(images.shape[0]):
inputs.append(generate_data_from_image(patches[k, :, :], self.input_mask, self.output_mask)[0])
inputs = asarray(inputs)
inputs = inputs.reshape(inputs.shape[0], 1, 1, -1)
if self.preconditioner:
inputs = self._precondition(inputs)
# set hidden unit activations
for l in range(self.num_layers):
self.slstm[l].net.blobs["h_init_i_jm1"].data[:] = hiddens[l][i, j - 1]
self.slstm[l].net.blobs["h_init_im1_j"].data[:] = hiddens[l][i - 1, j]
self.slstm[l].net.blobs["c_init_i_jm1"].data[:] = memory[l][i, j - 1]
self.slstm[l].net.blobs["c_init_im1_j"].data[:] = memory[l][i - 1, j]
# compute hidden unit activations
activations = inputs
for l in range(self.num_layers):
activations = self.slstm[l].forward(activations)
# store hidden unit activations
for l in range(self.num_layers):
hiddens[l][i, j] = self.slstm[l].net.blobs["outputs"].data.copy()
memory[l][i, j] = self.slstm[l].net.blobs["c_0_0"].data.copy()
if mask is not None and not mask[i + i_off, j + j_off]:
# skip sampling of this pixel
continue
for _ in range(10):
# sample MCGSM
outputs = self.mcgsm.sample(hiddens[-1][i, j].reshape(-1, self.num_hiddens).T)
if not any(isnan(outputs)):
break
print "Warning: NaNs detected."
if return_loglik:
logq += self.mcgsm.loglikelihood(hiddens[-1][i, j].reshape(-1, self.num_hiddens).T, outputs)
outputs = outputs.T.reshape(outputs.shape[1], 1, 1, outputs.shape[0])
if self.preconditioner:
inputs, outputs = self._precondition_inverse(inputs, outputs)
if max_values is not None:
outputs[outputs > max_values] = max_values[outputs > max_values]
if min_values is not None:
outputs[outputs < min_values] = min_values[outputs < min_values]
# insert sampled pixels into images
if self.output_mask.ndim > 2:
images[:, i + i_off, j + j_off][:, self.output_mask[i_off, j_off]] = outputs
else:
images[:, i + i_off, j + j_off] = outputs
images = images.reshape(*shape)
if return_loglik:
return images, logq
return images
def _logq(self, images, mask):
"""
Computes an unnormalized conditional log-likelihood used by Metropolis-Hastings (e.g., for inpainting).
"""
inputs, hiddens, outputs = self.hidden_states(images, return_all=True)
# locate output pixel
for i_off, j_off in zip(range(self.output_mask.shape[0]), range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
# unnormalized log-density of generated sample
logq = 0.0
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
if not mask[i + i_off, j + j_off]:
# skip evaluation of this pixel
continue
logq += self.mcgsm.loglikelihood(
hiddens[:, i, j, :].reshape(-1, self.num_hiddens).T, outputs[:, i, j, :]
)
return logq
def __setstate__(self, state):
"""
Method used by pickle module, for backwards compatibility reasons.
"""
self.__dict__ = state
if not hasattr(self, "nonlinearity"):
self.nonlinearity = "TanH"
if not hasattr(self, "extended"):
self.extended = False
class RIDE(object):
"""
An implementation of the recurrent image density estimator (RIDE).
B{References:}
- Theis, L. and Bethge, M. (2015). I{Generative Image Modeling Using Spatial LSTMs.}
"""
# maximum batch size used by Caffe internally
MAX_BATCH_SIZE = 200
def __init__(self,
num_channels=1,
num_hiddens=10,
num_components=8,
num_scales=4,
num_features=16,
num_layers=1,
nb_size=5,
nonlinearity='TanH',
verbosity=1,
extended=False,
input_mask=None,
output_mask=None):
"""
@type num_channels: C{int}
@param num_channels: dimensionality of each pixel
@type num_hiddens: C{int}
@param num_hiddens: number of LSTM units in each spatial LSTM layer
@type num_components: C{int}
@param num_components: number of mixture components used by the MCGSM
@type num_scales: C{int}
@param num_scales: number of scales used by the MCGSM
@type num_features: C{int}
@param num_features: number of quadratic features used by the MCGSM
@type num_layers: C{int}
@param num_layers: number of layers of spatial LSTM units
@type nb_size: C{int}
@param nb_size: controls the neighborhood of pixels read from an image
@type nonlinearity: C{str}
@param nonlinearity: nonlinearity used by spatial LSTM (e.g., TanH, ReLU)
@type verbosity: C{int}
@param verbosity: controls how much information is printed during training, etc.
@type extended: C{bool}
@param extended: use previous memory states as additional inputs to LSTM (more parameters)
@type input_mask C{ndarray}
@param input_mask: Boolean mask used to define custom input neighborhood of pixels
@type output_mask C{ndarray}
@param output_mask: determines the position of the output pixel relative to the neighborhood
"""
self.verbosity = verbosity
self.num_channels = num_channels
self.num_hiddens = num_hiddens
self.num_layers = num_layers
self.nonlinearity = nonlinearity
self.extended = extended
self.input_mask, self.output_mask = generate_masks([nb_size] *
num_channels)
if input_mask is not None:
self.input_mask = input_mask
if output_mask is not None:
self.output_mask = output_mask
self.num_channels = sum(self.output_mask)
self.slstm = [None] * num_layers
self.mcgsm = MCGSM(dim_in=self.num_hiddens,
dim_out=self.num_channels,
num_components=num_components,
num_scales=num_scales,
num_features=num_features)
self.preconditioner = None
def add_layer(self):
"""
Add another spatial LSTM to the network and reinitialize MCGSM.
"""
self.num_layers += 1
# reinitialize MCGSM
self.mcgsm = MCGSM(dim_in=self.num_hiddens,
dim_out=self.num_channels,
num_components=self.mcgsm.num_components,
num_scales=self.mcgsm.num_scales,
num_features=self.mcgsm.num_features)
# add slot for another layer
self.slstm.append(None)
def _precondition(self, inputs, outputs=None):
"""
Remove any correlations within and between inputs and outputs (conditional whitening).
@type inputs: C{ndarray}
@param inputs: pixel neighborhoods stored column-wise
@type outputs: C{ndarray}
@param outputs: output pixels stored column-wise
"""
shape = inputs.shape
if outputs is None:
if self.preconditioner is None:
raise RuntimeError('No preconditioning possible.')
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
# avoids memory issues
MAX_SAMPLES = 500000
if self.preconditioner is None:
if inputs.shape[1] > MAX_SAMPLES:
idx = random_select(MAX_SAMPLES, inputs.shape[1])
self.preconditioner = WhiteningPreconditioner(
inputs[:, idx], outputs[:, idx])
else:
self.preconditioner = WhiteningPreconditioner(
inputs, outputs)
for b in range(0, inputs.shape[1], MAX_SAMPLES):
inputs[:, b:b + MAX_SAMPLES], outputs[:, b:b + MAX_SAMPLES] = \
self.preconditioner(inputs[:, b:b + MAX_SAMPLES], outputs[:, b:b + MAX_SAMPLES])
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _precondition_inverse(self, inputs, outputs=None):
"""
Reintroduce correlations removed by conditional whitening.
@type inputs: C{ndarray}
@param inputs: pixel neighborhoods stored column-wise
@type outputs: C{ndarray}
@param outputs: output pixels stored column-wise
"""
if self.preconditioner is None:
raise RuntimeError('No preconditioner set.')
shape = inputs.shape
if outputs is None:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
inputs = self.preconditioner.inverse(inputs)
inputs = inputs.T.reshape(*shape)
return inputs
else:
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
inputs, outputs = self.preconditioner.inverse(inputs, outputs)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _adjust_gradient(self, inputs, outputs):
"""
Adjust gradients to take into account preconditioning.
@type inputs: C{ndarray}
@param inputs: gradient with respect to conditionally whitened inputs
@type outputs: C{ndarray}
@param outputs: gradient with respect to conditionally whitened outputs
"""
if self.preconditioner is None:
raise RuntimeError('No preconditioner set.')
shape = inputs.shape
inputs = inputs.reshape(-1, inputs.shape[-1]).T
outputs = outputs.reshape(-1, outputs.shape[-1]).T
inputs, outputs = self.preconditioner.adjust_gradient(inputs, outputs)
inputs = inputs.T.reshape(*shape)
outputs = outputs.T.reshape(shape[0], shape[1], shape[2], -1)
return inputs, outputs
def _preprocess(self, images):
"""
Extract causal neighborhoods from images.
@type images: C{ndarray}/C{list}
@param images: array or list of images to process
@rtype: C{tuple}
@return: one array storing inputs (neighborhoods) and one array storing outputs (pixels)
"""
def process(image):
inputs, outputs = generate_data_from_image(image, self.input_mask,
self.output_mask)
inputs = asarray(inputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1,
image.shape[1] - self.input_mask.shape[1] + 1, -1),
dtype='float32')
outputs = asarray(outputs.T.reshape(
image.shape[0] - self.input_mask.shape[0] + 1,
image.shape[1] - self.input_mask.shape[1] + 1, -1),
dtype='float32')
return inputs, outputs
inputs, outputs = zip(*mapp(process, images))
return asarray(inputs), asarray(outputs)
def loglikelihood(self, images):
"""
Returns a log-likelihood for each reachable pixel (in nats).
@type images: C{ndarray}/C{list}
@param images: array or list of images for which to evaluate log-likelihood
@rtype: C{ndarray}
@return: an array of log-likelihoods for each image and predicted pixel
"""
inputs, outputs = self._preprocess(images)
if self.preconditioner is not None:
if self.verbosity > 0:
print 'Computing Jacobian...'
logjacobian = self.preconditioner.logjacobian(
inputs.reshape(-1, sum(self.input_mask)).T,
outputs.reshape(-1, self.num_channels).T)
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
else:
logjacobian = 0.
# compute hidden unit activations
hiddens = inputs
batch_size = min([hiddens.shape[0], self.MAX_BATCH_SIZE])
if self.verbosity > 0:
print 'Computing hidden states...'
for l in range(self.num_layers):
# create SLSTM
if self.slstm[l].num_rows != hiddens.shape[1] \
or self.slstm[l].num_cols != hiddens.shape[2] \
or self.slstm[l].batch_size != batch_size:
self.slstm[l] = SLSTM(num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=batch_size,
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if self.verbosity > 0:
print 'Computing likelihood...'
# evaluate log-likelihood
loglik = self.mcgsm.loglikelihood(
hiddens.reshape(-1, self.num_hiddens).T,
outputs.reshape(-1, self.num_channels).T) + logjacobian
return loglik.reshape(hiddens.shape[0], hiddens.shape[1],
hiddens.shape[2])
def evaluate(self, images):
"""
Computes the average negative log-likelihood in bits per pixel.
@type images: C{ndarray}/C{list}
@param images: an array or list of test images
@rtype: C{float}
@return: average negative log-likelihood in bits per pixel
"""
return -mean(self.loglikelihood(images)) / log(2.) / self.num_channels
def train(self,
images,
batch_size=50,
num_epochs=20,
method='SGD',
train_means=False,
train_top_layer=False,
momentum=0.9,
learning_rate=1.,
decay1=0.9,
decay2=0.999,
precondition=True):
"""
Train model via stochastic gradient descent (SGD) or sum-of-functions optimizer (SFO).
@type images: C{ndarray}/C{list}
@param images: an array or a list of training images (e.g., Nx32x32x3)
@type batch_size: C{int}
@param batch_size: batch size used by SGD
@type num_epochs: C{int}
@param num_epochs: number of passes through the training set
@type method: C{str}
@param method: either 'SGD', 'SFO', or 'ADAM'
@type train_means: C{bool}
@param train_means: whether or not to optimize the mean parameters of the MCGSM
@type train_top_layer: C{bool}
@param train_top_layer: if true, only the MCGSM and spatial LSTM at the top layer is trained
@type momentum: C{float}
@param momentum: momentum rate used by SGD
@type learning_rate: C{float}
@param learning_rate: learning rate used by SGD
@type decay1: C{float}
@param decay1: hyperparameter used by ADAM
@type decay2: C{float}
@param decay2: hyperparameter used by ADAM
@type precondition: C{bool}
@param precondition: whether or not to perform conditional whitening
@rtype: C{list}
@return: evolution of negative log-likelihood (bits per pixel) over the training
"""
if images.shape[1] < self.input_mask.shape[0] or images.shape[
2] < self.input_mask.shape[1]:
raise ValueError('Images too small.')
if self.verbosity > 0:
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if precondition:
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# indicates which layers will be trained
train_layers = [self.num_layers -
1] if train_top_layer else range(self.num_layers)
if self.verbosity > 0:
print 'Creating SLSTMs...'
# create SLSTMs
for l in range(self.num_layers):
self.slstm[l] = SLSTM(
num_rows=inputs.shape[1],
num_cols=inputs.shape[2],
num_channels=inputs.shape[3] if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=min([batch_size, self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
# compute loss function and its gradient
def f_df(params, idx):
# set model parameters
for l in train_layers:
self.slstm[l].set_parameters(params['slstm'][l])
self.mcgsm._set_parameters(params['mcgsm'],
{'train_means': train_means})
# select batch and compute hidden activations
Y = outputs[idx:idx + batch_size]
H = inputs[idx:idx + batch_size]
for l in range(self.num_layers):
H = self.slstm[l].forward(H)
# form inputs to MCGSM
H_flat = H.reshape(-1, self.num_hiddens).T
Y_flat = Y.reshape(-1, self.num_channels).T
norm_const = -H_flat.shape[1]
# compute gradients
df_dh, _, loglik = self.mcgsm._data_gradient(H_flat, Y_flat)
df_dh = df_dh.T.reshape(*H.shape) / norm_const
# average log-likelihood
f = sum(loglik) / norm_const
df_dtheta = {}
df_dtheta['slstm'] = [0.] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
if l > min(train_layers):
# derivative with respect to inputs of layer l are derivatives
# of hidden states of layer l - 1
df_dtheta['slstm'][l] = self.slstm[l].backward(
df_dh, force_backward=True)
df_dh = df_dtheta['slstm'][l]['inputs']
del df_dtheta['slstm'][l]['inputs']
else:
# no need to compute derivatives with respect to input units
df_dtheta['slstm'][l] = self.slstm[l].backward(df_dh)
# compute gradient of MCGSM
df_dtheta['mcgsm'] = self.mcgsm._parameter_gradient(
H_flat, Y_flat, parameters={'train_means': train_means
}) * log(2.) * self.mcgsm.dim_out
return f, df_dtheta
# collect current parameters
params = {}
params['slstm'] = [0.] * self.num_layers
for l in range(self.num_layers)[::-1]:
if l not in train_layers:
break
params['slstm'][l] = self.slstm[l].parameters()
params['mcgsm'] = self.mcgsm._parameters({'train_means': train_means})
# a start index for each batch
start_indices = range(0, inputs.shape[0] - batch_size + 1, batch_size)
if self.verbosity > 0:
print 'Training...'
if method.upper() == 'SFO':
try:
# optimize using sum-of-functions optimizer
optimizer = SFO(f_df,
params,
start_indices,
display=self.verbosity)
params_opt = optimizer.optimize(num_passes=num_epochs)
# set model parameters
for l in range(self.num_layers):
self.slstm[l].set_parameters(params_opt['slstm'][l])
self.mcgsm._set_parameters(params_opt['mcgsm'],
{'train_means': train_means})
except KeyboardInterrupt:
pass
return optimizer.hist_f_flat
elif method.upper() == 'SGD':
loss = []
diff = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])
}
for l in train_layers:
diff['slstm'][l] = {}
for key in params['slstm'][l]:
diff['slstm'][l][key] = zeros_like(params['slstm'][l][key])
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1,
batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f / log(2.) / self.num_channels)
# update SLSTM parameters
for l in train_layers:
for key in params['slstm'][l]:
diff['slstm'][l][key] = momentum * diff['slstm'][
l][key] - df['slstm'][l][key]
params['slstm'][l][key] = params['slstm'][l][
key] + learning_rate * diff['slstm'][l][key]
# update MCGSM parameters
diff['mcgsm'] = momentum * diff['mcgsm'] - df['mcgsm']
params['mcgsm'] = params[
'mcgsm'] + learning_rate * diff['mcgsm']
if self.verbosity > 0:
print '{0:>5} {1:>10.4f} {2:>10.4f}'.format(
n, loss[-1],
mean(loss[-max([10, 20000 // batch_size]):]))
return loss
elif method.upper() == 'ADAM':
loss = []
diff_mean = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])
}
diff_sqrd = {
'slstm': [0.] * self.num_layers,
'mcgsm': zeros_like(params['mcgsm'])
}
for l in train_layers:
diff_mean['slstm'][l] = {}
diff_sqrd['slstm'][l] = {}
for key in params['slstm'][l]:
diff_mean['slstm'][l][key] = zeros_like(
params['slstm'][l][key])
diff_sqrd['slstm'][l][key] = zeros_like(
params['slstm'][l][key])
# step counter
t = 1
for n in range(num_epochs):
for b in range(0, inputs.shape[0] - batch_size + 1,
batch_size):
# compute gradients
f, df = f_df(params, b)
loss.append(f / log(2.) / self.num_channels)
# include bias correction in step width
step_width = learning_rate / (
1. - power(decay1, t)) * sqrt(1. - power(decay2, t))
t += 1
# update SLSTM parameters
for l in train_layers:
for key in params['slstm'][l]:
diff_mean['slstm'][l][key] = decay1 * diff_mean['slstm'][l][key] \
+ (1. - decay1) * df['slstm'][l][key]
diff_sqrd['slstm'][l][key] = decay2 * diff_sqrd['slstm'][l][key] \
+ (1. - decay2) * square(df['slstm'][l][key])
params['slstm'][l][key] = params['slstm'][l][key] - \
step_width * diff_mean['slstm'][l][key] / (1e-8 + sqrt(diff_sqrd['slstm'][l][key]))
# update MCGSM parameters
diff_mean['mcgsm'] = decay1 * diff_mean['mcgsm'] + (
1. - decay1) * df['mcgsm']
diff_sqrd['mcgsm'] = decay2 * diff_sqrd['mcgsm'] + (
1. - decay2) * square(df['mcgsm'])
params['mcgsm'] = params['mcgsm'] - \
step_width * diff_mean['mcgsm'] / (1e-8 + sqrt(diff_sqrd['mcgsm']))
if self.verbosity > 0:
print '{0:>5} {1:>10.4f} {2:>10.4f}'.format(
n, loss[-1],
mean(loss[-max([10, 20000 // batch_size]):]))
return loss
else:
raise ValueError('Unknown method \'{0}\'.'.format(method))
def finetune(self,
images,
max_iter=1000,
train_means=False,
num_samples_train=500000,
num_samples_valid=100000):
"""
Train MCGSM using L-BFGS while keeping parameters of spatial LSTMs fixed.
@type images: C{ndarray}/C{list}
@param images: an array or a list of images
@type max_iter: C{int}
@param max_iter: maximum number of L-BFGS iterations
@type train_means: C{bool}
@param train_means: whether or not to optimize the mean parameters of the MCGSM
@type num_samples_train: C{int}
@param num_samples_train: number of training examples extracted from images
@type num_samples_valid: C{int}
@type num_samples_valid: number of validation examples used for early stopping
@rtype: C{bool}
@return: true if training converged, false otherwise
"""
if images.shape[0] > min([200000, num_samples_train]):
images = images[random_select(min([200000, num_samples_train]),
images.shape[0])]
if self.verbosity > 0:
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner:
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
if self.verbosity > 0:
print 'Computing hidden states...'
for l in range(self.num_layers):
self.slstm[l] = SLSTM(num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=min(
[hiddens.shape[0], self.MAX_BATCH_SIZE]),
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if self.verbosity > 0:
print 'Preparing inputs and outputs...'
# form inputs to MCGSM
hiddens = hiddens.reshape(-1, self.num_hiddens).T
outputs = outputs.reshape(-1, self.num_channels).T
if hiddens.shape[1] > num_samples_train:
num_samples_valid = min(
[num_samples_valid, hiddens.shape[1] - num_samples_train])
# select subset of data points for finetuning
idx = random_select(num_samples_train + num_samples_valid,
hiddens.shape[1])
if num_samples_valid > 0:
# split data into training and validation set
hiddens_train = asarray(hiddens[:, idx[:num_samples_train]],
order='F')
outputs_train = asarray(outputs[:, idx[:num_samples_train]],
order='F')
hiddens_valid = asarray(hiddens[:, idx[num_samples_train:]],
order='F')
outputs_valid = asarray(outputs[:, idx[num_samples_train:]],
order='F')
# finetune with early stopping based on validation performance
return self.mcgsm.train(hiddens_train,
outputs_train,
hiddens_valid,
outputs_valid,
parameters={
'verbosity': self.verbosity,
'train_means': train_means,
'max_iter': max_iter
})
else:
hiddens = asarray(hiddens[:, idx], order='F')
outputs = asarray(outputs[:, idx], order='F')
if self.verbosity > 0:
print 'Finetuning...'
return self.mcgsm.train(hiddens,
outputs,
parameters={
'verbosity': self.verbosity,
'train_means': train_means,
'max_iter': max_iter
})
def hidden_states(self, images, return_all=False, layer=None):
"""
Compute hidden states of LSTM units for given images.
By default, the last layer's hidden units are computed.
@type images: C{ndarray}/C{list}
@param images: array or list of images to process
@type return_all: C{bool}
@param return_all: if true, also return preconditioned inputs and outputs
@type layer: C{int}
@param layer: a positive integer controlling which layer's hidden units to compute
@rtype: C{ndarray}/C{tuple}
@return: hidden states or a tuple of inputs, hidden states, and outputs
"""
if self.verbosity > 0:
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner is not None:
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
# compute hidden unit activations
hiddens = inputs
batch_size = min([hiddens.shape[0], self.MAX_BATCH_SIZE])
if layer is None or layer < 1:
layer = self.num_layers
for l in range(layer):
if self.slstm[l].num_rows != hiddens.shape[1] \
or self.slstm[l].num_cols != hiddens.shape[2] \
or self.slstm[l].batch_size != batch_size:
self.slstm[l] = SLSTM(num_rows=hiddens.shape[1],
num_cols=hiddens.shape[2],
num_channels=hiddens.shape[3],
num_hiddens=self.num_hiddens,
batch_size=batch_size,
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
hiddens = self.slstm[l].forward(hiddens)
if return_all:
return inputs, hiddens, outputs
return hiddens
def gradient(self, images):
"""
Returns the average log-likelihood [nat] and its gradient with respect to pixel values.
@type images: C{ndarray}
@param images: images at which to evaluate the density's gradient
@rtype: C{tuple}
@return: average log-likelihood and gradient with respect to images
"""
if self.verbosity > 0:
print 'Preprocessing...'
inputs, outputs = self._preprocess(images)
if self.preconditioner:
if self.verbosity > 0:
print 'Preconditioning...'
# remove correlations
inputs, outputs = self._precondition(inputs, outputs)
if self.verbosity > 0:
print 'Creating SLSTMs...'
# create SLSTMs
batch_size = min([images.shape[0], self.MAX_BATCH_SIZE])
for l in range(self.num_layers):
if self.slstm[l] is None or \
self.slstm[l].batch_size != batch_size or \
self.slstm[l].num_rows != inputs.shape[1] or \
self.slstm[l].num_cols != inputs.shape[2]:
self.slstm[l] = SLSTM(num_rows=inputs.shape[1],
num_cols=inputs.shape[2],
num_channels=inputs.shape[3]
if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=batch_size,
nonlinearity=self.nonlinearity,
extended=self.extended,
slstm=self.slstm[l],
verbosity=self.verbosity)
# compute hidden unit activations
hiddens = inputs
for l in range(self.num_layers):
hiddens = self.slstm[l].forward(hiddens)
# form inputs to MCGSM
H_flat = hiddens.reshape(-1, self.num_hiddens).T
Y_flat = outputs.reshape(-1, self.num_channels).T
# compute gradients
df_dh, df_dy, loglik = self.mcgsm._data_gradient(H_flat, Y_flat)
df_dh = df_dh.T.reshape(*hiddens.shape) / H_flat.shape[1]
df_dy = df_dy.T.reshape(*outputs.shape) / H_flat.shape[1]
# average log-likelihood
f = sum(loglik) / H_flat.shape[1]
for l in range(self.num_layers)[::-1]:
df_dh = self.slstm[l].backward(df_dh,
force_backward=True)['inputs']
if self.preconditioner:
df_dh, df_dy = self._adjust_gradient(df_dh, df_dy)
# locate output pixel in output mask
for i_off, j_off in zip(range(self.output_mask.shape[0]),
range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
gradient = zeros_like(images)
# make sure mask and gradient have compatible dimensionality
if gradient.ndim == 4 and self.input_mask.ndim == 2:
gradient = gradient[:, :, :, 0]
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
patch = gradient[:, i:i + self.input_mask.shape[0],
j:j + self.output_mask.shape[1]]
patch[:, self.input_mask] += df_dh[:, i, j]
patch[:, self.output_mask] += df_dy[:, i, j]
return f, gradient.reshape(*images.shape)
def sample(self,
images,
min_values=None,
max_values=None,
mask=None,
return_loglik=False):
"""
Sample one or several images.
@type images: C{ndarray}/C{list}
@param images: an array or a list of images to initialize pixels at boundaries
@type min_values: C{ndarray}/C{list}
@param min_values: list of lower bounds for each channel (for increased stability)
@type max_values: C{ndarray}/C{list}
@param max_values: list of upper bounds for each channel (for increased stability)
@type mask: C{ndarray}
@param mask: replace only certain pixels indicated by this Boolean mask
@rtype: C{ndarray}
@return: sampled images of the size of the images given as input
"""
# reshape images into four-dimensional arrays
shape = images.shape
if images.ndim == 2:
images = images[None, :, :, None]
elif images.ndim == 3:
if self.num_channels > 1:
images = images[None]
else:
images = images[:, :, :, None]
# create spatial LSTMs for sampling
for l in range(self.num_layers):
if self.slstm[l].num_rows != 1 \
or self.slstm[l].num_cols != 1 \
or self.slstm[l].batch_size != images.shape[0]:
self.slstm[l] = SLSTM(num_rows=1,
num_cols=1,
num_channels=sum(self.input_mask)
if l < 1 else self.num_hiddens,
num_hiddens=self.num_hiddens,
batch_size=images.shape[0],
nonlinearity=self.nonlinearity,
slstm=self.slstm[l],
extended=self.extended)
# container for hidden and memory unit activations
hiddens = []
memory = []
for l in range(self.num_layers):
hiddens.append(defaultdict(lambda: 0.))
memory.append(defaultdict(lambda: 0.))
# locate output pixel
for i_off, j_off in zip(range(self.output_mask.shape[0]),
range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
if min_values is not None:
min_values = asarray(min_values).reshape(1, 1, 1, -1)
if self.output_mask.ndim > 2:
min_values = min_values[:, :, :, self.output_mask[i_off,
j_off]]
if max_values is not None:
max_values = asarray(max_values).reshape(1, 1, 1, -1)
if self.output_mask.ndim > 2:
max_values = max_values[:, :, :, self.output_mask[i_off,
j_off]]
# unnormalized log-density of generated sample
logq = 0.
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
# extract patches from images
patches = images[:, i:i + self.input_mask.shape[0],
j:j + self.input_mask.shape[1]]
# extract causal neighborhoods from patches
inputs = []
for k in range(images.shape[0]):
inputs.append(
generate_data_from_image(patches[k, :, :],
self.input_mask,
self.output_mask)[0])
inputs = asarray(inputs)
inputs = inputs.reshape(inputs.shape[0], 1, 1, -1)
if self.preconditioner:
inputs = self._precondition(inputs)
# set hidden unit activations
for l in range(self.num_layers):
self.slstm[l].net.blobs['h_init_i_jm1'].data[:] = hiddens[
l][i, j - 1]
self.slstm[l].net.blobs['h_init_im1_j'].data[:] = hiddens[
l][i - 1, j]
self.slstm[l].net.blobs['c_init_i_jm1'].data[:] = memory[
l][i, j - 1]
self.slstm[l].net.blobs['c_init_im1_j'].data[:] = memory[
l][i - 1, j]
# compute hidden unit activations
activations = inputs
for l in range(self.num_layers):
activations = self.slstm[l].forward(activations)
# store hidden unit activations
for l in range(self.num_layers):
hiddens[l][
i, j] = self.slstm[l].net.blobs['outputs'].data.copy()
memory[l][
i, j] = self.slstm[l].net.blobs['c_0_0'].data.copy()
if mask is not None and not mask[i + i_off, j + j_off]:
# skip sampling of this pixel
continue
for _ in range(10):
# sample MCGSM
outputs = self.mcgsm.sample(hiddens[-1][i, j].reshape(
-1, self.num_hiddens).T)
if not any(isnan(outputs)):
break
print 'Warning: NaNs detected.'
if return_loglik:
logq += self.mcgsm.loglikelihood(
hiddens[-1][i, j].reshape(-1, self.num_hiddens).T,
outputs)
outputs = outputs.T.reshape(outputs.shape[1], 1, 1,
outputs.shape[0])
if self.preconditioner:
inputs, outputs = self._precondition_inverse(
inputs, outputs)
if max_values is not None:
outputs[outputs > max_values] = max_values[
outputs > max_values]
if min_values is not None:
outputs[outputs < min_values] = min_values[
outputs < min_values]
# insert sampled pixels into images
if self.output_mask.ndim > 2:
images[:, i + i_off,
j + j_off][:, self.output_mask[i_off,
j_off]] = outputs
else:
images[:, i + i_off, j + j_off] = outputs
images = images.reshape(*shape)
if return_loglik:
return images, logq
return images
def _logq(self, images, mask):
"""
Computes an unnormalized conditional log-likelihood used by Metropolis-Hastings (e.g., for inpainting).
"""
inputs, hiddens, outputs = self.hidden_states(images, return_all=True)
# locate output pixel
for i_off, j_off in zip(range(self.output_mask.shape[0]),
range(self.output_mask.shape[1])):
if any(self.output_mask[i_off, j_off]):
break
# unnormalized log-density of generated sample
logq = 0.
for i in range(images.shape[1] - self.input_mask.shape[0] + 1):
for j in range(images.shape[2] - self.input_mask.shape[1] + 1):
if not mask[i + i_off, j + j_off]:
# skip evaluation of this pixel
continue
logq += self.mcgsm.loglikelihood(
hiddens[:, i, j, :].reshape(-1, self.num_hiddens).T,
outputs[:, i, j, :])
return logq
def __setstate__(self, state):
"""
Method used by pickle module, for backwards compatibility reasons.
"""
self.__dict__ = state
if not hasattr(self, 'nonlinearity'):
self.nonlinearity = 'TanH'
if not hasattr(self, 'extended'):
self.extended = False