def __init__(self, get_optimizer, theano_warning='raise'):
v = self.v
w = self.w
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
x, z = ndict.ordereddicts(self.variables())
self.var_x, self.var_z, = x, z
# Helper variables
A = T.fmatrix('A')
self.var_A = A
# Get gradient symbols
allvars = list(x.values()) + list(
z.values()) + [A] # note: '+' concatenates lists
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler than this)
self.dist_qz = {}
self.dist_px = {}
self.dist_pz = {}
logpx, logpz, logqz = self.factors(x, z, A)
if get_optimizer == None:
def get_optimizer(w, g):
from collections import OrderedDict
updates = OrderedDict()
for i in w:
updates[w[i]] = w[i]
return updates
# Log-likelihood lower bound
self.f_L = theanofunction(allvars, [logpx, logpz, logqz])
L = (logpx + logpz - logqz).sum()
g = T.grad(L, list(v.values()) + list(w.values()))
gv, gw = dict(list(zip(list(v.keys()), g[0:len(v)]))), dict(
list(zip(list(w.keys()), g[len(v):len(v) + len(w)])))
updates = get_optimizer(v, gv)
updates.update(get_optimizer(w, gw))
#self.profmode = theano.ProfileMode(optimizer='fast_run', linker=theano.gof.OpWiseCLinker())
#self.f_evalAndUpdate = theano.function(allvars, [logpx + logpz - logqz], updates=updates_w, mode=self.profmode)
#theano.printing.debugprint(self.f_evalAndUpdate)
self.f_eval = theanofunction(allvars, [logpx + logpz - logqz])
self.f_evalAndUpdate = theanofunction(allvars, [logpx + logpz - logqz],
updates=updates)
def __init__(self, get_optimizer, theano_warning="raise"):
v = self.v
w = self.w
theanofunction = lazytheanofunc("warn", mode="FAST_RUN")
theanofunction_silent = lazytheanofunc("ignore", mode="FAST_RUN")
# Create theano expressions
x, z = ndict.ordereddicts(self.variables())
self.var_x, self.var_z, = x, z
# Helper variables
A = T.fmatrix("A")
self.var_A = A
# Get gradient symbols
allvars = x.values() + z.values() + [A] # note: '+' concatenates lists
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler than this)
self.dist_qz = {}
self.dist_px = {}
self.dist_pz = {}
logpx, logpz, logqz = self.factors(x, z, A)
if get_optimizer == None:
def get_optimizer(w, g):
from collections import OrderedDict
updates = OrderedDict()
for i in w:
updates[w[i]] = w[i]
return updates
# Log-likelihood lower bound
self.f_L = theanofunction(allvars, [logpx, logpz, logqz])
L = (logpx + logpz - logqz).sum()
g = T.grad(L, v.values() + w.values())
gv, gw = dict(zip(v.keys(), g[0 : len(v)])), dict(zip(w.keys(), g[len(v) : len(v) + len(w)]))
updates = get_optimizer(v, gv)
updates.update(get_optimizer(w, gw))
# self.profmode = theano.ProfileMode(optimizer='fast_run', linker=theano.gof.OpWiseCLinker())
# self.f_evalAndUpdate = theano.function(allvars, [logpx + logpz - logqz], updates=updates_w, mode=self.profmode)
# theano.printing.debugprint(self.f_evalAndUpdate)
self.f_eval = theanofunction(allvars, [logpx + logpz - logqz])
self.f_evalAndUpdate = theanofunction(allvars, [logpx + logpz - logqz], updates=updates)
def __init__(self, theano_warning='raise'):
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
v, w, x, z = ndict.ordereddicts(self.variables())
self.var_v, self.var_w, self.var_x, self.var_z, = v, w, x, z
# Helper variables
A = T.dmatrix('A')
self.var_A = A
# Get gradient symbols
allvars = list(v.values()) + list(w.values()) + list(
x.values()) + list(z.values()) + [A
] # note: '+' concatenates lists
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler than this)
self.dist_qz = {}
self.dist_px = {}
self.dist_pz = {}
logpv, logpw, logpx, logpz, logqz = self.factors(v, w, x, z, A)
# Log-likelihood lower bound
self.f_L = theanofunction(allvars, [logpx, logpz, logqz])
L = (logpx + logpz - logqz).sum()
dL_dw = T.grad(L, list(v.values()) + list(w.values()))
self.f_dL_dw = theanofunction(allvars, [logpx, logpz, logqz] + dL_dw)
weights = T.dmatrix()
dL_weighted_dw = T.grad((weights * (logpx + logpz - logqz)).sum(),
list(v.values()) + list(w.values()))
self.f_dL_weighted_dw = theanofunction(
allvars + [weights],
[logpx + logpz - logqz, weights *
(logpx + logpz - logqz)] + dL_weighted_dw)
# prior
dlogpw_dw = T.grad(logpv + logpw,
list(v.values()) + list(w.values()),
disconnected_inputs='ignore')
self.f_logpw = theanofunction(
list(v.values()) + list(w.values()), [logpv, logpw])
self.f_dlogpw_dw = theanofunction(
list(v.values()) + list(w.values()), [logpv, logpw] + dlogpw_dw)
def factors(self, w, x, z, A):
# Define logp(w)
logpw = 0
for i in range(len(self.n_units)-1):
logpw += ap.logpdfs.normal(w['w'+str(i)], 0, self.prior_sd).sum()
logpw += ap.logpdfs.normal(w['b'+str(i)], 0, self.prior_sd).sum()
if self.nonlinearity == 'tanh':
f = T.tanh
elif self.nonlinearity == 'sigmoid':
f = T.nnet.sigmoid
elif self.nonlinearity == 'softplus':
f = T.nnet.softplus
else:
raise Exception("Unknown nonlinarity "+self.nonlinearity)
# Define logp(x)
hiddens = [T.dot(w['w0'], x['x']) + T.dot(w['b0'], A)]
for i in range(1, len(self.n_units)-1):
hiddens.append(T.dot(w['w'+str(i)], f(hiddens[-1])) + T.dot(w['b'+str(i)], A))
self.p = T.nnet.softmax(hiddens[-1].T).T
self.entropy = T.nnet.categorical_crossentropy(self.p.T, self.p.T).T
logpx = (- T.nnet.categorical_crossentropy(self.p.T, x['y'].T).T).reshape((1,-1))
# function for distribution q(z|x)
theanofunc = lazytheanofunc('ignore', mode='FAST_RUN')
self.dist_px['y'] = theanofunc([x['x']] + w.values() + [A], self.p)
logpz = 0 * A
return logpw, logpx, logpz
def factors(self, w, x, z, A):
# Define logp(w)
logpw = 0
for i in range(len(self.n_units)-1):
logpw += ap.logpdfs.normal(w['w'+str(i)], 0, self.prior_sd).sum()
logpw += ap.logpdfs.normal(w['b'+str(i)], 0, self.prior_sd).sum()
if self.nonlinearity == 'tanh':
f = T.tanh
elif self.nonlinearity == 'sigmoid':
f = T.nnet.sigmoid
elif self.nonlinearity == 'softplus':
f = T.nnet.softplus
else:
raise Exception("Unknown nonlinarity "+self.nonlinearity)
# Define logp(x)
hiddens = [T.dot(w['w0'], x['x']) + T.dot(w['b0'], A)]
for i in range(1, len(self.n_units)-1):
hiddens.append(T.dot(w['w'+str(i)], f(hiddens[-1])) + T.dot(w['b'+str(i)], A))
self.p = T.nnet.softmax(hiddens[-1].T).T
self.entropy = T.nnet.categorical_crossentropy(self.p.T, self.p.T).T
logpx = (- T.nnet.categorical_crossentropy(self.p.T, x['y'].T).T).reshape((1,-1))
# function for distribution q(z|x)
theanofunc = lazytheanofunc('ignore', mode='FAST_RUN')
self.dist_px['y'] = theanofunc([x['x']] + list(w.values()) + [A], self.p)
logpz = 0 * A
return logpw, logpx, logpz
def __init__(self, theano_warning='raise'):
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
v, w, x, z = ndict.ordereddicts(self.variables())
self.var_v, self.var_w, self.var_x, self.var_z, = v, w, x, z
# Helper variables
A = T.dmatrix('A')
self.var_A = A
# Get gradient symbols
allvars = v.values() + w.values() + x.values() + z.values() + [A] # note: '+' concatenates lists
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler than this)
self.dist_qz = {}
self.dist_px = {}
self.dist_pz = {}
logpv, logpw, logpx, logpz, logqz = self.factors(v, w, x, z, A)
# Log-likelihood lower bound
self.f_L = theanofunction(allvars, [logpx, logpz, logqz])
L = (logpx + logpz - logqz).sum()
dL_dw = T.grad(L, v.values() + w.values())
self.f_dL_dw = theanofunction(allvars, [logpx, logpz, logqz] + dL_dw)
weights = T.dmatrix()
dL_weighted_dw = T.grad((weights * (logpx + logpz - logqz)).sum(), v.values() + w.values())
self.f_dL_weighted_dw = theanofunction(allvars + [weights], [logpx + logpz - logqz, weights*(logpx + logpz - logqz)] + dL_weighted_dw)
# prior
dlogpw_dw = T.grad(logpv + logpw, v.values() + w.values(), disconnected_inputs='ignore')
self.f_logpw = theanofunction(v.values() + w.values(), [logpv, logpw])
self.f_dlogpw_dw = theanofunction(v.values() + w.values(), [logpv, logpw] + dlogpw_dw)
def factors(self, v, w, x, z, A):
'''
z['eps'] are the independent epsilons (Gaussian with unit variance)
x['x'] is the data
x['y'] is categorial data (1-of-K coded)
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(y) + log p(x|y,z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x,y): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
def f_softplus(x): return T.log(T.exp(x) + 1)# - np.log(2)
def f_rectlin(x): return x*(x>0)
def f_rectlin2(x): return x*(x>0) + 0.01 * x
nonlinear = {'tanh': T.tanh, 'sigmoid': T.nnet.sigmoid, 'softplus': f_softplus, 'rectlin': f_rectlin, 'rectlin2': f_rectlin2}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
# Compute q(z|x)
hidden_q = [nonlinear_q(T.dot(v['w0'], x['x']) + T.dot(v['b0'], A))]
for i in range(1, len(self.n_hidden_q)):
hidden_q.append(nonlinear_q(T.dot(v['w'+str(i)], hidden_q[-1]) + T.dot(v['b'+str(i)], A)))
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(v['logvar_b'], A)
else: raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('ignore', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x']] + v.values() + [A], [q_mean, q_logvar])
# Compute virtual sample
_z = q_mean + T.exp(0.5 * q_logvar) * z['eps']
# Compute log p(x|z)
hidden_p = [nonlinear_p(T.dot(w['w0'], _z) + T.dot(w['b0'], A))]
for i in range(1, len(self.n_hidden_p)):
hidden_p.append(nonlinear_p(T.dot(w['w'+str(i)], hidden_p[-1]) + T.dot(w['b'+str(i)], A)))
if self.type_px == 'bernoulli':
px = T.nnet.sigmoid(T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = - T.nnet.binary_crossentropy(px, x['x'])
self.dist_px['x'] = theanofunc([_z] + w.values() + [A], px)
elif self.type_px == 'gaussian'or self.type_px == 'sigmoidgaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
if self.type_px == 'sigmoidgaussian':
x_mean = T.nnet.sigmoid(x_mean)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([_z] + w.values() + [A], [x_mean, x_logvar])
else: raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(np.ones((1, self.n_x)), _logpx) # logpx = logp(x|z,w) + logp(y|x,w)
# log p(y|x)
_logpy = T.dot(w['out_w_y'], hidden_q[-1]) + T.dot(w['out_b_y'], A)
py = T.nnet.softmax(_logpy.T).T
logpy = (- T.nnet.categorical_crossentropy(py.T, x['y'].T).T).reshape((1,-1))
self.dist_px['y'] = theanofunc([x['x']] + v.values() + w.values() + [A], py)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
logpz = -0.5 * (np.log(2 * np.pi) + (q_mean**2 + T.exp(q_logvar))).sum(axis=0, keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']), A)).sum(axis=0, keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = - 0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0, keepdims=True)
else: raise Exception()
# Note: logpv and logpw are a scalars
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
logpv = 0
logpv += f_prior(v['w0'])
for i in range(1, len(self.n_hidden_q)):
logpv += f_prior(v['w'+str(i)])
logpv += f_prior(v['mean_w'])
if self.type_qz in ['gaussian','gaussianmarg']:
logpv += f_prior(v['logvar_w'])
logpw = 0
logpw += f_prior(w['w0'])
for i in range(1, len(self.n_hidden_p)):
logpw += f_prior(w['w'+str(i)])
logpw += f_prior(w['out_w'])
logpw += f_prior(w['out_w_y'])
if self.type_px in ['sigmoidgaussian', 'gaussian']:
logpw += f_prior(w['out_logvar_w'])
if self.type_pz == 'studentt':
logpw += f_prior(w['logv'])
# Custom grad, for when only 'x' is given (and not 'y')
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
dL2_dw = T.grad((logpx + logpz - logqz).sum(), v.values() + w.values(), disconnected_inputs = 'ignore')
allvars = self.var_v.values() + self.var_w.values() + [x['x']] + z.values() + [A]
self.f_dL2_dw = theanofunction(allvars, [logpx, logpz, logqz] + dL2_dw)
return logpv, logpw, logpx+logpy, logpz, logqz
def factors(self, x, z, A):
v = self.v
w = self.w
'''
z is unused
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
def f_softplus(x): return T.log(T.exp(x) + 1)# - np.log(2)
def f_rectlin(x): return x*(x>0)
def f_rectlin2(x): return x*(x>0) + 0.01 * x
nonlinear = {'tanh': T.tanh, 'sigmoid': T.nnet.sigmoid, 'softplus': f_softplus, 'rectlin': f_rectlin, 'rectlin2': f_rectlin2}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
#rng = rng_curand.CURAND_RandomStreams(0)
import theano.tensor.shared_randomstreams
rng = theano.tensor.shared_randomstreams.RandomStreams(0)
# Compute q(z|x,y)
hidden_q = [nonlinear_q(T.dot(v['w0x'], x['x']) + T.dot(v['w0y'], x['y']) + T.dot(v['b0'], A))]
for i in range(1, len(self.n_hidden_q)):
hidden_q.append(nonlinear_q(T.dot(v['w'+str(i)], hidden_q[-1]) + T.dot(v['b'+str(i)], A)))
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(v['logvar_b'], A)
else: raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x'], x['y']] + [A], [q_mean, q_logvar])
# Compute virtual sample
eps = rng.normal(size=q_mean.shape, dtype='float32')
_z = q_mean + T.exp(0.5 * q_logvar) * eps
# Compute log p(x|z)
hidden_p = [nonlinear_p(T.dot(w['w0y'], x['y']) + T.dot(w['w0z'], _z) + T.dot(w['b0'], A))]
for i in range(1, len(self.n_hidden_p)):
hidden_p.append(nonlinear_p(T.dot(w['w'+str(i)], hidden_p[-1]) + T.dot(w['b'+str(i)], A)))
if self.dropout:
hidden_p[-1] *= 2. * (rng.uniform(size=hidden_p[-1].shape, dtype='float32') > .5)
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = - T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([x['y'], _z] + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([x['y'], _z] + [A], [x_mean, x_logvar])
elif self.type_px == 'laplace':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.laplace(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([x['y'], _z] + [A], [x_mean, x_logvar])
else: raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(shared32(np.ones((1, self.n_x))), _logpx) # logpx = log p(x|z,w)
# log p(y) (prior of y)
#_logpy = w['logpy']
#if self.uniform_y: _logpy *= 0
#py_model = T.nnet.softmax(T.dot(_logpy, A).T).T
#logpy = (- T.nnet.categorical_crossentropy(py_model.T, x['y'].T).T).reshape((1,-1))
#logpx += logpy
#self.dist_px['y'] = theanofunc([A], py_model)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
logpz = -0.5 * (np.log(2 * np.pi) + (q_mean**2 + T.exp(q_logvar))).sum(axis=0, keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'mog':
pz = 0
for i in range(self.n_mixture):
pz += T.exp(ap.logpdfs.normal2(_z, T.dot(w['mog_mean'+str(i)], A), T.dot(w['mog_logvar'+str(i)], A)))
logpz = T.log(pz).sum(axis=0, keepdims=True) - self.n_z * np.log(float(self.n_mixture))
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']), A)).sum(axis=0, keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = - 0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0, keepdims=True)
else: raise Exception()
# Note: logpv and logpw are a scalars
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
logpv = 0
logpv += f_prior(v['w0x'])
logpv += f_prior(v['w0y'])
for i in range(1, len(self.n_hidden_q)):
logpv += f_prior(v['w'+str(i)])
logpv += f_prior(v['mean_w'])
if self.type_qz in ['gaussian','gaussianmarg']:
logpv += f_prior(v['logvar_w'])
logpw = 0
logpw += f_prior(w['w0y'])
logpw += f_prior(w['w0z'])
for i in range(1, len(self.n_hidden_p)):
logpw += f_prior(w['w'+str(i)])
logpw += f_prior(w['out_w'])
if self.type_px in ['sigmoidgaussian', 'gaussian','laplace']:
logpw += f_prior(w['out_logvar_w'])
if self.type_pz == 'studentt':
logpw += f_prior(w['logv'])
#return logpv, logpw, logpx, logpz, logqz
return logpx, logpz, logqz
def __init__(self, theano_warning='raise', hessian=True):
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
w, x, z = ndict.ordereddicts(self.variables())
self.var_w, self.var_x, self.var_z, = w, x, z
# Helper variables
A = T.dmatrix('A')
self.var_A = A
# Get gradient symbols
self.allvars = list(w.values()) + list(x.values()) + list(
z.values()) + [A] # note: '+' concatenates lists
self.allvars_keys = list(w.keys()) + list(x.keys()) + list(
z.keys()) + ['A']
if False:
# Put test values
# needs fully implemented gen_xz(), which is not always the case
# Also, the FD has no test values
theano.config.compute_test_value = 'raise'
_w = self.init_w()
for i in _w:
w[i].tag.test_value = _w[i]
_x, _z, _ = self.gen_xz(_w, {}, {}, 10)
_x, _z = self.xz_to_theano(_x, _z)
for i in _x:
x[i].tag.test_value = _x[i]
for i in _z:
z[i].tag.test_value = _z[i]
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler then this)
self.dist_px = {}
self.dist_pz = {}
logpw, logpx, logpz = self.factors(w, x, z, A)
self.var_logpw, self.var_logpx, self.var_logpz = logpw, logpx, logpz
# Complete-data likelihood estimate
logpxz = logpx.sum() + logpz.sum()
self.f_logpxz = theanofunction(self.allvars, [logpx, logpz])
dlogpxz_dwz = T.grad(logpxz, list(w.values()) + list(z.values()))
self.f_dlogpxz_dwz = theanofunction(self.allvars,
[logpx, logpz] + dlogpxz_dwz)
#self.f_dlogpxz_dw = theanofunction(allvars, [logpxz] + dlogpxz_dw)
#self.f_dlogpxz_dz = theanofunction(allvars, [logpxz] + dlogpxz_dz)
# prior
dlogpw_dw = T.grad(logpw,
list(w.values()),
disconnected_inputs='ignore')
self.f_logpw = theanofunction(list(w.values()), logpw)
self.f_dlogpw_dw = theanofunction(list(w.values()),
[logpw] + dlogpw_dw)
if False:
# MC-LIKELIHOOD
logpx_max = logpx.max()
logpxmc = T.log(T.exp(logpx - logpx_max).mean()) + logpx_max
self.f_logpxmc = theanofunction(self.allvars, logpxmc)
dlogpxmc_dw = T.grad(logpxmc,
list(w.values()),
disconnected_inputs=theano_warning)
self.f_dlogpxmc_dw = theanofunction(self.allvars,
[logpxmc] + dlogpxmc_dw)
if True and len(z) > 0:
# Fisher divergence (FD)
gz = T.grad(logpxz, list(z.values()))
gz2 = [T.dmatrix() for _ in gz]
fd = 0
for i in range(len(gz)):
fd += T.sum((gz[i] - gz2[i])**2)
dfd_dw = T.grad(fd, list(w.values()))
self.f_dfd_dw = theanofunction(self.allvars + gz2,
[logpx, logpz, fd] + dfd_dw)
if False and hessian:
# Hessian of logpxz wrt z (works best with n_batch=1)
hessian_z = theano.gradient.hessian(logpxz, z_concat)
self.f_hessian_z = theanofunction(self.allvars, hessian_z)
def __init__(self, theano_warning='raise', hessian=True):
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
w, x, z = ndict.ordereddicts(self.variables())
self.var_w, self.var_x, self.var_z, = w, x, z
# Helper variables
A = T.dmatrix('A')
self.var_A = A
# Get gradient symbols
self.allvars = w.values() + x.values() + z.values() + [A] # note: '+' concatenates lists
self.allvars_keys = w.keys() + x.keys() + z.keys() + ['A']
if False:
# Put test values
# needs fully implemented gen_xz(), which is not always the case
# Also, the FD has no test values
theano.config.compute_test_value = 'raise'
_w = self.init_w()
for i in _w: w[i].tag.test_value = _w[i]
_x, _z, _ = self.gen_xz(_w, {}, {}, 10)
_x, _z = self.xz_to_theano(_x, _z)
for i in _x: x[i].tag.test_value = _x[i]
for i in _z: z[i].tag.test_value = _z[i]
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler then this)
self.dist_px = {}
self.dist_pz = {}
logpw, logpx, logpz = self.factors(w, x, z, A)
self.var_logpw, self.var_logpx, self.var_logpz = logpw, logpx, logpz
# Complete-data likelihood estimate
logpxz = logpx.sum() + logpz.sum()
self.f_logpxz = theanofunction(self.allvars, [logpx, logpz])
dlogpxz_dwz = T.grad(logpxz, w.values() + z.values())
self.f_dlogpxz_dwz = theanofunction(self.allvars, [logpx, logpz] + dlogpxz_dwz)
#self.f_dlogpxz_dw = theanofunction(allvars, [logpxz] + dlogpxz_dw)
#self.f_dlogpxz_dz = theanofunction(allvars, [logpxz] + dlogpxz_dz)
# prior
dlogpw_dw = T.grad(logpw, w.values(), disconnected_inputs='ignore')
self.f_logpw = theanofunction(w.values(), logpw)
self.f_dlogpw_dw = theanofunction(w.values(), [logpw] + dlogpw_dw)
if False:
# MC-LIKELIHOOD
logpx_max = logpx.max()
logpxmc = T.log(T.exp(logpx - logpx_max).mean()) + logpx_max
self.f_logpxmc = theanofunction(self.allvars, logpxmc)
dlogpxmc_dw = T.grad(logpxmc, w.values(), disconnected_inputs=theano_warning)
self.f_dlogpxmc_dw = theanofunction(self.allvars, [logpxmc] + dlogpxmc_dw)
if True and len(z) > 0:
# Fisher divergence (FD)
gz = T.grad(logpxz, z.values())
gz2 = [T.dmatrix() for _ in gz]
fd = 0
for i in range(len(gz)):
fd += T.sum((gz[i]-gz2[i])**2)
dfd_dw = T.grad(fd, w.values())
self.f_dfd_dw = theanofunction(self.allvars + gz2, [logpx, logpz, fd] + dfd_dw)
if False and hessian:
# Hessian of logpxz wrt z (works best with n_batch=1)
hessian_z = theano.gradient.hessian(logpxz, z_concat)
self.f_hessian_z = theanofunction(self.allvars, hessian_z)
def factors(self, x, z, A):
v = self.v
w = self.w
'''
z is unused
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
# Compute q(z|x)
hidden_q = [x['x']]
def f_softplus(x): return T.log(T.exp(x) + 1)# - np.log(2)
def f_rectlin(x): return x*(x>0)
def f_rectlin2(x): return x*(x>0) + 0.01 * x
nonlinear = {'tanh': T.tanh, 'sigmoid': T.nnet.sigmoid, 'softplus': f_softplus, 'rectlin': f_rectlin, 'rectlin2': f_rectlin2}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
#rng = rng_curand.CURAND_RandomStreams(0)
import theano.tensor.shared_randomstreams
rng = theano.tensor.shared_randomstreams.RandomStreams(0)
# TOTAL HACK
#hidden_q.append(nonlinear_q(T.dot(v['scale0'], A) * T.dot(w['out_w'].T, hidden_q[-1]) + T.dot(v['b0'], A)))
#hidden_q.append(nonlinear_q(T.dot(v['scale1'], A) * T.dot(w['w1'].T, hidden_q[-1]) + T.dot(v['b1'], A)))
for i in range(len(self.n_hidden_q)):
hidden_q.append(nonlinear_q(T.dot(v['w'+str(i)], hidden_q[-1]) + T.dot(v['b'+str(i)], A)))
if self.dropout:
hidden_q[-1] *= 2. * (rng.uniform(size=hidden_q[-1].shape, dtype='float32') > .5)
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(v['logvar_b'], A)
else: raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x']] + [A], [q_mean, q_logvar])
# Compute virtual sample
eps = rng.normal(size=q_mean.shape, dtype='float32')
_z = q_mean + T.exp(0.5 * q_logvar) * eps
# Compute log p(x|z)
hidden_p = [_z]
for i in range(len(self.n_hidden_p)):
hidden_p.append(nonlinear_p(T.dot(w['w'+str(i)], hidden_p[-1]) + T.dot(w['b'+str(i)], A)))
if self.dropout:
hidden_p[-1] *= 2. * (rng.uniform(size=hidden_p[-1].shape, dtype='float32') > .5)
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = - T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([_z] + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
elif self.type_px == 'bounded01':
x_mean = T.nnet.sigmoid(T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
x_logvar = T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
# Make it a mixture between uniform and Gaussian
w_unif = T.nnet.sigmoid(T.dot(w['out_unif'], A))
_logpx = T.log(w_unif + (1-w_unif) * T.exp(_logpx))
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
else: raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(shared32(np.ones((1, self.n_x))), _logpx) # logpx = log p(x|z,w)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
logpz = -0.5 * (np.log(2 * np.pi) + (q_mean**2 + T.exp(q_logvar))).sum(axis=0, keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'mog':
pz = 0
for i in range(self.n_mixture):
pz += T.exp(ap.logpdfs.normal2(_z, T.dot(w['mog_mean'+str(i)], A), T.dot(w['mog_logvar'+str(i)], A)))
logpz = T.log(pz).sum(axis=0, keepdims=True) - self.n_z * np.log(float(self.n_mixture))
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']), A)).sum(axis=0, keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = - 0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0, keepdims=True)
else: raise Exception()
# [new part] Fisher divergence of latent variables
if self.var_smoothing > 0:
dlogq_dz = T.grad(logqz.sum(), _z) # gives error when using gaussianmarg instead of gaussian
dlogp_dz = T.grad((logpx + logpz).sum(), _z)
FD = 0.5 * ((dlogq_dz - dlogp_dz)**2).sum(axis=0, keepdims=True)
# [end new part]
logqz -= self.var_smoothing * FD
# Note: logpv and logpw are a scalars
if True:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
else:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.standard_laplace(_w / prior_sd).sum()
return logpx, logpz, logqz
def __init__(self, get_optimizer, theano_warning='raise'):
v = self.v
w = self.w
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
x, z = ndict.ordereddicts(self.variables())
self.var_x, self.var_z, = x, z
# Helper variables
A = T.fmatrix('A')
self.var_A = A
'''
# Get gradient symbols
print 'model, x'
for (d, xx) in x.items():
print d
print xx.shape
print x.values()
'''
allvars = x.values() + z.values() + [A] # note: '+' concatenates lists
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler than this)
self.dist_qz = {}
self.dist_px = {}
self.dist_pz = {}
factors = self.factors(x, z, A)
if len(factors) == 3:
(logpx, logpz, logqz) = factors
cost = 0
sparsity_penalty = 0
else:
(logpx, logpz, logqz, cost, sparsity_penalty) = factors
if get_optimizer == None:
def get_optimizer(w, g):
from collections import OrderedDict
updates = OrderedDict()
for i in w:
updates[w[i]] = w[i]
return updates
# Log-likelihood lower bound
self.f_L = theanofunction(
allvars, [logpx, logpz, logqz, cost, sparsity_penalty])
L = (logpx + logpz - logqz).sum() - cost - sparsity_penalty
g = T.grad(L, v.values() + w.values())
gv, gw = dict(zip(v.keys(), g[0:len(v)])), dict(
zip(w.keys(), g[len(v):len(v) + len(w)]))
updates = get_optimizer(v, gv)
updates.update(get_optimizer(w, gw))
#self.profmode = theano.ProfileMode(optimizer='fast_run', linker=theano.gof.OpWiseCLinker())
#self.f_evalAndUpdate = theano.function(allvars, [logpx + logpz - logqz], updates=updates_w, mode=self.profmode)
#theano.printing.debugprint(self.f_evalAndUpdate)
self.f_eval_test = theanofunction(
allvars, [logpx + logpz - logqz, logpx, logpz, -logqz])
self.f_eval = theanofunction(allvars, [logpx + logpz - logqz])
self.f_evalAndUpdate = theanofunction(allvars, [logpx + logpz - logqz],
updates=updates)
self.f_eval_for_classcondition_prior = theanofunction(
allvars, [logpx - logqz])
def factors(self, x, z, A):
v = self.v # parameters of recognition model.
w = self.w # parameters of generative model.
'''
z is unused
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
# Compute q(z|x)
hidden_q = [x['x']]
hidden_q_s = [x['x']]
def f_softplus(x): return T.log(T.exp(x) + 1)# - np.log(2)
def f_rectlin(x): return x*(x>0)
def f_rectlin2(x): return x*(x>0) + 0.01 * x
nonlinear = {'tanh': T.tanh, 'sigmoid': T.nnet.sigmoid, 'softplus': f_softplus, 'rectlin': f_rectlin, 'rectlin2': f_rectlin2}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
#rng = rng_curand.CURAND_RandomStreams(0)
import theano.tensor.shared_randomstreams
rng = theano.tensor.shared_randomstreams.RandomStreams(0)
# TOTAL HACK
#hidden_q.append(nonlinear_q(T.dot(v['scale0'], A) * T.dot(w['out_w'].T, hidden_q[-1]) + T.dot(v['b0'], A)))
#hidden_q.append(nonlinear_q(T.dot(v['scale1'], A) * T.dot(w['w1'].T, hidden_q[-1]) + T.dot(v['b1'], A)))
for i in range(len(self.n_hidden_q)):
hidden_q.append(nonlinear_q(T.dot(v['w'+str(i)], hidden_q[-1]) + T.dot(v['b'+str(i)], A)))
hidden_q_s.append(T.nnet.sigmoid(T.dot(v['w'+str(i)], hidden_q_s[-1]) + T.dot(v['b'+str(i)], A)))
if self.dropout:
hidden_q[-1] *= 2. * (rng.uniform(size=hidden_q[-1].shape, dtype='float32') > .5)
hidden_q_s[-1] *= 2. * (rng.uniform(size=hidden_q_s[-1].shape, dtype='float32') > .5)
'''
print 'mm_model'
for (d, xx) in x.items():
print d
'''
#print 'x', x['mean_prior'].type
#print 'T', (T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)).type
if not self.train_residual:
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
else:
q_mean = x['mean_prior'] + T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
#q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(v['logvar_b'], A)
else: raise Exception()
ell = cast32(self.ell)
self.param_c = shared32(0)
sv = self.sv
a_a = cast32(self.average_activation)
s_w = cast32(self.sparsity_weight)
def activate():
res = 0
if self.super_to_mean:
lenw = len(v['W'].get_value())
res += T.dot(v['W'][:-1,:].T, q_mean)
res += T.dot(v['W'][lenw-1:lenw,:].T, A)
else:
lenw = len(v['W'].get_value())
for (hi, hidden) in enumerate(hidden_q[1+sv:]):
res += T.dot(v['W'][sum(self.n_hidden_q[sv:sv+hi]):sum(self.n_hidden_q[sv:sv+hi+1]),:].T, hidden)
res += T.dot(v['W'][lenw-1:lenw,:].T, A)
return res
predy = T.argmax(activate(), axis=0)
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x'], x['mean_prior']] + [A], [q_mean, q_logvar])
self.dist_qz['hidden'] = theanofunc([x['x'], x['mean_prior']] + [A], hidden_q[1:])
self.dist_qz['predy'] = theanofunc([x['x'], x['mean_prior']] + [A], predy)
# compute cost (posterior regularization).
true_resp = (activate() * x['y']).sum(axis=0, keepdims=True)
T.addbroadcast(true_resp, 0)
cost = self.param_c * (ell * (1-x['y']) + activate() - true_resp).max(axis=0).sum() \
+ self.Lambda * (v['W'] * v['W']).sum()
# compute the sparsity penalty
sparsity_penalty = 0
for i in range(1, len(hidden_q_s)):
sparsity_penalty += (a_a*T.log(a_a/(hidden_q_s[i].mean(axis=1))) + (1-a_a)*T.log((1-a_a)/(1-(hidden_q_s[i].mean(axis=1))))).sum(axis=0)
sparsity_penalty *= s_w
# Compute virtual sample
eps = rng.normal(size=q_mean.shape, dtype='float32')
_z = q_mean + T.exp(0.5 * q_logvar) * eps
# Compute log p(x|z)
hidden_p = [_z]
for i in range(len(self.n_hidden_p)):
hidden_p.append(nonlinear_p(T.dot(w['w'+str(i)], hidden_p[-1]) + T.dot(w['b'+str(i)], A)))
if self.dropout:
hidden_p[-1] *= 2. * (rng.uniform(size=hidden_p[-1].shape, dtype='float32') > .5)
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = - T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([_z] + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
elif self.type_px == 'bounded01':
x_mean = T.nnet.sigmoid(T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
x_logvar = T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
# Make it a mixture between uniform and Gaussian
w_unif = T.nnet.sigmoid(T.dot(w['out_unif'], A))
_logpx = T.log(w_unif + (1-w_unif) * T.exp(_logpx))
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
else: raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(shared32(np.ones((1, self.n_x))), _logpx) # logpx = log p(x|z,w)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
if not self.train_residual:
logpz = -0.5 * (np.log(2 * np.pi * self.sigma_square) + ((q_mean-x['mean_prior'])**2 + T.exp(q_logvar))/self.sigma_square).sum(axis=0, keepdims=True)
else:
logpz = -0.5 * (np.log(2 * np.pi * self.sigma_square) + (q_mean**2 + T.exp(q_logvar))/self.sigma_square).sum(axis=0, keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'mog':
pz = 0
for i in range(self.n_mixture):
pz += T.exp(ap.logpdfs.normal2(_z, T.dot(w['mog_mean'+str(i)], A), T.dot(w['mog_logvar'+str(i)], A)))
logpz = T.log(pz).sum(axis=0, keepdims=True) - self.n_z * np.log(float(self.n_mixture))
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']), A)).sum(axis=0, keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = - 0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0, keepdims=True)
else: raise Exception()
# [new part] Fisher divergence of latent variables
if self.var_smoothing > 0:
dlogq_dz = T.grad(logqz.sum(), _z) # gives error when using gaussianmarg instead of gaussian
dlogp_dz = T.grad((logpx + logpz).sum(), _z)
FD = 0.5 * ((dlogq_dz - dlogp_dz)**2).sum(axis=0, keepdims=True)
# [end new part]
logqz -= self.var_smoothing * FD
# Note: logpv and logpw are a scalars
if True:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
else:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.standard_laplace(_w / prior_sd).sum()
return logpx, logpz, logqz, cost, sparsity_penalty
def factors(self, v, w, x, z, A):
'''
z['eps'] is the independent epsilons (Gaussian with unit variance)
x['x'] is the data
x['y'] is categorial data (1-of-K coded)
The names of list z[...] may be confusing here: the latent variable z is not included in the list z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(y) + log p(x|y,z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x,y): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
def f_softplus(x):
return T.log(T.exp(x) + 1) # - np.log(2)
def f_rectlin(x):
return x * (x > 0)
def f_rectlin2(x):
return x * (x > 0) + 0.01 * x
nonlinear = {
'tanh': T.tanh,
'sigmoid': T.nnet.sigmoid,
'softplus': f_softplus,
'rectlin': f_rectlin,
'rectlin2': f_rectlin2
}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
# Compute q(z|x,y)
hidden_q = [
nonlinear_q(
T.dot(v['w0x'], x['x']) + T.dot(v['w0y'], x['y']) +
T.dot(v['b0'], A))
]
for i in range(1, len(self.n_hidden_q)):
hidden_q.append(
nonlinear_q(
T.dot(v['w' + str(i)], hidden_q[-1]) +
T.dot(v['b' + str(i)], A)))
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(
v['logvar_b'], A)
else:
raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('ignore', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x'], x['y']] + list(v.values()) +
[A], [q_mean, q_logvar])
# Compute virtual sample
_z = q_mean + T.exp(0.5 * q_logvar) * z['eps']
# Compute log p(x|y,z)
hidden_p = [
nonlinear_p(
T.dot(w['w0y'], x['y']) + T.dot(w['w0z'], _z) +
T.dot(w['b0'], A))
]
for i in range(1, len(self.n_hidden_p)):
hidden_p.append(
nonlinear_p(
T.dot(w['w' + str(i)], hidden_p[-1]) +
T.dot(w['b' + str(i)], A)))
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = -T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([x['y'], _z] + list(w.values()) +
[A], p)
elif self.type_px == 'gaussian' or self.type_px == 'sigmoidgaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
if self.type_px == 'sigmoidgaussian':
x_mean = T.nnet.sigmoid(x_mean)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([x['y'], _z] + list(w.values()) +
[A], [x_mean, x_logvar])
else:
raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(np.ones((1, self.n_x)),
_logpx) # logpx = logp(y|w) + logp(x|z,w)
# log p(y) (prior of y)
_logpy = w['logpy']
if self.uniform_y: _logpy *= 0
py_model = T.nnet.softmax(T.dot(_logpy, A).T).T
logpy = (
-T.nnet.categorical_crossentropy(py_model.T, x['y'].T).T).reshape(
(1, -1))
logpx += logpy
self.dist_px['y'] = theanofunc(list(w.values()) + [A], py_model)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
logpz = -0.5 * (np.log(2 * np.pi) +
(q_mean**2 + T.exp(q_logvar))).sum(axis=0,
keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']),
A)).sum(axis=0,
keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = -0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(
axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0,
keepdims=True)
else:
raise Exception()
# Note: logpv and logpw are a scalars
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
logpv = 0
logpv += f_prior(v['w0x'])
logpv += f_prior(v['w0y'])
for i in range(1, len(self.n_hidden_q)):
logpv += f_prior(v['w' + str(i)])
logpv += f_prior(v['mean_w'])
if self.type_qz in ['gaussian', 'gaussianmarg']:
logpv += f_prior(v['logvar_w'])
logpw = 0
logpw += f_prior(w['w0y'])
logpw += f_prior(w['w0z'])
for i in range(1, len(self.n_hidden_p)):
logpw += f_prior(w['w' + str(i)])
logpw += f_prior(w['out_w'])
if self.type_px in ['sigmoidgaussian', 'gaussian']:
logpw += f_prior(w['out_logvar_w'])
if self.type_pz == 'studentt':
logpw += f_prior(w['logv'])
return logpv, logpw, logpx, logpz, logqz
def factors(self, x, z, A):
v = self.v
w = self.w
'''
z is unused
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
def f_softplus(x):
return T.log(T.exp(x) + 1) # - np.log(2)
def f_rectlin(x):
return x * (x > 0)
def f_rectlin2(x):
return x * (x > 0) + 0.01 * x
nonlinear = {
'tanh': T.tanh,
'sigmoid': T.nnet.sigmoid,
'softplus': f_softplus,
'rectlin': f_rectlin,
'rectlin2': f_rectlin2
}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
#rng = rng_curand.CURAND_RandomStreams(0)
import theano.tensor.shared_randomstreams
rng = theano.tensor.shared_randomstreams.RandomStreams(0)
# Compute q(z|x,y)
hidden_q = [
nonlinear_q(
T.dot(v['w0x'], x['x']) + T.dot(v['w0y'], x['y']) +
T.dot(v['b0'], A))
]
for i in range(1, len(self.n_hidden_q)):
hidden_q.append(
nonlinear_q(
T.dot(v['w' + str(i)], hidden_q[-1]) +
T.dot(v['b' + str(i)], A)))
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(
v['logvar_b'], A)
else:
raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x'], x['y']] + [A],
[q_mean, q_logvar])
# Compute virtual sample
eps = rng.normal(size=q_mean.shape, dtype='float32')
_z = q_mean + T.exp(0.5 * q_logvar) * eps
# Compute log p(x|z)
hidden_p = [
nonlinear_p(
T.dot(w['w0y'], x['y']) + T.dot(w['w0z'], _z) +
T.dot(w['b0'], A))
]
for i in range(1, len(self.n_hidden_p)):
hidden_p.append(
nonlinear_p(
T.dot(w['w' + str(i)], hidden_p[-1]) +
T.dot(w['b' + str(i)], A)))
if self.dropout:
hidden_p[-1] *= 2. * (rng.uniform(size=hidden_p[-1].shape,
dtype='float32') > .5)
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = -T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([x['y'], _z] + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([x['y'], _z] + [A],
[x_mean, x_logvar])
elif self.type_px == 'laplace':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
_logpx = ap.logpdfs.laplace(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([x['y'], _z] + [A],
[x_mean, x_logvar])
else:
raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(shared32(np.ones((1, self.n_x))),
_logpx) # logpx = log p(x|z,w)
# log p(y) (prior of y)
#_logpy = w['logpy']
#if self.uniform_y: _logpy *= 0
#py_model = T.nnet.softmax(T.dot(_logpy, A).T).T
#logpy = (- T.nnet.categorical_crossentropy(py_model.T, x['y'].T).T).reshape((1,-1))
#logpx += logpy
#self.dist_px['y'] = theanofunc([A], py_model)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
logpz = -0.5 * (np.log(2 * np.pi) +
(q_mean**2 + T.exp(q_logvar))).sum(axis=0,
keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'mog':
pz = 0
for i in range(self.n_mixture):
pz += T.exp(
ap.logpdfs.normal2(_z, T.dot(w['mog_mean' + str(i)], A),
T.dot(w['mog_logvar' + str(i)], A)))
logpz = T.log(pz).sum(axis=0, keepdims=True) - self.n_z * np.log(
float(self.n_mixture))
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']),
A)).sum(axis=0,
keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = -0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(
axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0,
keepdims=True)
else:
raise Exception()
# Note: logpv and logpw are a scalars
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
logpv = 0
logpv += f_prior(v['w0x'])
logpv += f_prior(v['w0y'])
for i in range(1, len(self.n_hidden_q)):
logpv += f_prior(v['w' + str(i)])
logpv += f_prior(v['mean_w'])
if self.type_qz in ['gaussian', 'gaussianmarg']:
logpv += f_prior(v['logvar_w'])
logpw = 0
logpw += f_prior(w['w0y'])
logpw += f_prior(w['w0z'])
for i in range(1, len(self.n_hidden_p)):
logpw += f_prior(w['w' + str(i)])
logpw += f_prior(w['out_w'])
if self.type_px in ['sigmoidgaussian', 'gaussian', 'laplace']:
logpw += f_prior(w['out_logvar_w'])
if self.type_pz == 'studentt':
logpw += f_prior(w['logv'])
#return logpv, logpw, logpx, logpz, logqz
return logpx, logpz, logqz
def factors(self, v, w, x, z, A):
'''
z['eps'] is the independent epsilons (Gaussian with unit variance)
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
# Compute q(z|x)
hidden_q = [x['x']]
def f_softplus(x):
return T.log(T.exp(x) + 1) # - np.log(2)
def f_rectlin(x):
return x * (x > 0)
def f_rectlin2(x):
return x * (x > 0) + 0.01 * x
nonlinear = {
'tanh': T.tanh,
'sigmoid': T.nnet.sigmoid,
'softplus': f_softplus,
'rectlin': f_rectlin,
'rectlin2': f_rectlin2
}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
for i in range(len(self.n_hidden_q)):
hidden_q.append(
nonlinear_q(
T.dot(v['w' + str(i)], hidden_q[-1]) +
T.dot(v['b' + str(i)], A)))
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(
v['logvar_b'], A)
else:
raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x']] + v.values() + [A],
[q_mean, q_logvar])
# Compute virtual sample
_z = q_mean + T.exp(0.5 * q_logvar) * z['eps']
# Compute log p(x|z)
hidden_p = [_z]
for i in range(len(self.n_hidden_p)):
hidden_p.append(
nonlinear_p(
T.dot(w['w' + str(i)], hidden_p[-1]) +
T.dot(w['b' + str(i)], A)))
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = -T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([_z] + w.values() + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([_z] + w.values() + [A],
[x_mean, x_logvar])
elif self.type_px == 'bounded01':
x_mean = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
x_logvar = T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
# Make it a mixture between uniform and Gaussian
w_unif = T.nnet.sigmoid(T.dot(w['out_unif'], A))
_logpx = T.log(w_unif + (1 - w_unif) * T.exp(_logpx))
self.dist_px['x'] = theanofunc([_z] + w.values() + [A],
[x_mean, x_logvar])
else:
raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(np.ones((1, self.n_x)), _logpx) # logpx = log p(x|z,w)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
logpz = -0.5 * (np.log(2 * np.pi) +
(q_mean**2 + T.exp(q_logvar))).sum(axis=0,
keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']),
A)).sum(axis=0,
keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = -0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(
axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0,
keepdims=True)
else:
raise Exception()
# [new part] Fisher divergence of latent variables
if self.var_smoothing > 0:
dlogq_dz = T.grad(
logqz.sum(),
_z) # gives error when using gaussianmarg instead of gaussian
dlogp_dz = T.grad((logpx + logpz).sum(), _z)
FD = 0.5 * ((dlogq_dz - dlogp_dz)**2).sum(axis=0, keepdims=True)
# [end new part]
logqz -= self.var_smoothing * FD
# Note: logpv and logpw are a scalars
if True:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
else:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.standard_laplace(_w / prior_sd).sum()
logpv = 0
for i in range(len(self.n_hidden_q)):
logpv += f_prior(v['w' + str(i)])
logpv += f_prior(v['mean_w'])
if self.type_qz in ['gaussian', 'gaussianmarg']:
logpv += f_prior(v['logvar_w'])
logpw = 0
for i in range(len(self.n_hidden_p)):
logpw += f_prior(w['w' + str(i)])
logpw += f_prior(w['out_w'])
if self.type_px == 'gaussian':
logpw += f_prior(w['out_logvar_w'])
if self.type_pz == 'studentt':
logpw += f_prior(w['logv'])
return logpv, logpw, logpx, logpz, logqz
def factors(self, x, z, A):
v = self.v # parameters of recognition model.
w = self.w # parameters of generative model.
'''
z is unused
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
# Compute q(z|x)
hidden_q = [x['x']]
hidden_q_s = [x['x']]
def f_softplus(x):
return T.log(T.exp(x) + 1) # - np.log(2)
def f_rectlin(x):
return x * (x > 0)
def f_rectlin2(x):
return x * (x > 0) + 0.01 * x
nonlinear = {
'tanh': T.tanh,
'sigmoid': T.nnet.sigmoid,
'softplus': f_softplus,
'rectlin': f_rectlin,
'rectlin2': f_rectlin2
}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
#rng = rng_curand.CURAND_RandomStreams(0)
import theano.tensor.shared_randomstreams
rng = theano.tensor.shared_randomstreams.RandomStreams(0)
# TOTAL HACK
#hidden_q.append(nonlinear_q(T.dot(v['scale0'], A) * T.dot(w['out_w'].T, hidden_q[-1]) + T.dot(v['b0'], A)))
#hidden_q.append(nonlinear_q(T.dot(v['scale1'], A) * T.dot(w['w1'].T, hidden_q[-1]) + T.dot(v['b1'], A)))
for i in range(len(self.n_hidden_q)):
hidden_q.append(
nonlinear_q(
T.dot(v['w' + str(i)], hidden_q[-1]) +
T.dot(v['b' + str(i)], A)))
hidden_q_s.append(
T.nnet.sigmoid(
T.dot(v['w' + str(i)], hidden_q_s[-1]) +
T.dot(v['b' + str(i)], A)))
if self.dropout:
hidden_q[-1] *= 2. * (rng.uniform(size=hidden_q[-1].shape,
dtype='float32') > .5)
hidden_q_s[-1] *= 2. * (rng.uniform(size=hidden_q_s[-1].shape,
dtype='float32') > .5)
'''
print 'mm_model'
for (d, xx) in x.items():
print d
'''
#print 'x', x['mean_prior'].type
#print 'T', (T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)).type
if not self.train_residual:
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
else:
q_mean = x['mean_prior'] + T.dot(
v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
#q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(
v['logvar_b'], A)
else:
raise Exception()
ell = cast32(self.ell)
self.param_c = shared32(0)
sv = self.sv
a_a = cast32(self.average_activation)
s_w = cast32(self.sparsity_weight)
def activate():
res = 0
if self.super_to_mean:
lenw = len(v['W'].get_value())
res += T.dot(v['W'][:-1, :].T, q_mean)
res += T.dot(v['W'][lenw - 1:lenw, :].T, A)
else:
lenw = len(v['W'].get_value())
for (hi, hidden) in enumerate(hidden_q[1 + sv:]):
res += T.dot(
v['W'][sum(self.n_hidden_q[sv:sv + hi]
):sum(self.n_hidden_q[sv:sv + hi +
1]), :].T, hidden)
res += T.dot(v['W'][lenw - 1:lenw, :].T, A)
return res
predy = T.argmax(activate(), axis=0)
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x'], x['mean_prior']] + [A],
[q_mean, q_logvar])
self.dist_qz['hidden'] = theanofunc([x['x'], x['mean_prior']] + [A],
hidden_q[1:])
self.dist_qz['predy'] = theanofunc([x['x'], x['mean_prior']] + [A],
predy)
# compute cost (posterior regularization).
true_resp = (activate() * x['y']).sum(axis=0, keepdims=True)
T.addbroadcast(true_resp, 0)
cost = self.param_c * (ell * (1-x['y']) + activate() - true_resp).max(axis=0).sum() \
+ self.Lambda * (v['W'] * v['W']).sum()
# compute the sparsity penalty
sparsity_penalty = 0
for i in range(1, len(hidden_q_s)):
sparsity_penalty += (a_a * T.log(a_a /
(hidden_q_s[i].mean(axis=1))) +
(1 - a_a) * T.log(
(1 - a_a) /
(1 - (hidden_q_s[i].mean(axis=1))))).sum(
axis=0)
sparsity_penalty *= s_w
# Compute virtual sample
eps = rng.normal(size=q_mean.shape, dtype='float32')
_z = q_mean + T.exp(0.5 * q_logvar) * eps
# Compute log p(x|z)
hidden_p = [_z]
for i in range(len(self.n_hidden_p)):
hidden_p.append(
nonlinear_p(
T.dot(w['w' + str(i)], hidden_p[-1]) +
T.dot(w['b' + str(i)], A)))
if self.dropout:
hidden_p[-1] *= 2. * (rng.uniform(size=hidden_p[-1].shape,
dtype='float32') > .5)
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = -T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([_z] + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
elif self.type_px == 'bounded01':
x_mean = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
x_logvar = T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
# Make it a mixture between uniform and Gaussian
w_unif = T.nnet.sigmoid(T.dot(w['out_unif'], A))
_logpx = T.log(w_unif + (1 - w_unif) * T.exp(_logpx))
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
else:
raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(shared32(np.ones((1, self.n_x))),
_logpx) # logpx = log p(x|z,w)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
if not self.train_residual:
logpz = -0.5 * (np.log(2 * np.pi * self.sigma_square) + (
(q_mean - x['mean_prior'])**2 + T.exp(q_logvar)) /
self.sigma_square).sum(axis=0, keepdims=True)
else:
logpz = -0.5 * (np.log(2 * np.pi * self.sigma_square) +
(q_mean**2 + T.exp(q_logvar)) /
self.sigma_square).sum(axis=0, keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'mog':
pz = 0
for i in range(self.n_mixture):
pz += T.exp(
ap.logpdfs.normal2(_z, T.dot(w['mog_mean' + str(i)], A),
T.dot(w['mog_logvar' + str(i)], A)))
logpz = T.log(pz).sum(axis=0, keepdims=True) - self.n_z * np.log(
float(self.n_mixture))
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']),
A)).sum(axis=0,
keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = -0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(
axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0,
keepdims=True)
else:
raise Exception()
# [new part] Fisher divergence of latent variables
if self.var_smoothing > 0:
dlogq_dz = T.grad(
logqz.sum(),
_z) # gives error when using gaussianmarg instead of gaussian
dlogp_dz = T.grad((logpx + logpz).sum(), _z)
FD = 0.5 * ((dlogq_dz - dlogp_dz)**2).sum(axis=0, keepdims=True)
# [end new part]
logqz -= self.var_smoothing * FD
# Note: logpv and logpw are a scalars
if True:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
else:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.standard_laplace(_w / prior_sd).sum()
return logpx, logpz, logqz, cost, sparsity_penalty
def factors(self, x, z, A):
v = self.v
w = self.w
'''
z is unused
x['x'] is the data
The names of dict z[...] may be confusing here: the latent variable z is not included in the dict z[...],
but implicitely computed from epsilon and parameters in w.
z is computed with g(.) from eps and variational parameters
let logpx be the generative model density: log p(x|z) where z=g(.)
let logpz be the prior of Z plus the entropy of q(z|x): logp(z) + H_q(z|x)
So the lower bound L(x) = logpx + logpz
let logpv and logpw be the (prior) density of the parameters
'''
# Compute q(z|x)
hidden_q = [x['x']]
def f_softplus(x):
return T.log(T.exp(x) + 1) # - np.log(2)
def f_rectlin(x):
return x * (x > 0)
def f_rectlin2(x):
return x * (x > 0) + 0.01 * x
nonlinear = {
'tanh': T.tanh,
'sigmoid': T.nnet.sigmoid,
'softplus': f_softplus,
'rectlin': f_rectlin,
'rectlin2': f_rectlin2
}
nonlinear_q = nonlinear[self.nonlinear_q]
nonlinear_p = nonlinear[self.nonlinear_p]
#rng = rng_curand.CURAND_RandomStreams(0)
import theano.tensor.shared_randomstreams
rng = theano.tensor.shared_randomstreams.RandomStreams(0)
# TOTAL HACK
#hidden_q.append(nonlinear_q(T.dot(v['scale0'], A) * T.dot(w['out_w'].T, hidden_q[-1]) + T.dot(v['b0'], A)))
#hidden_q.append(nonlinear_q(T.dot(v['scale1'], A) * T.dot(w['w1'].T, hidden_q[-1]) + T.dot(v['b1'], A)))
for i in range(len(self.n_hidden_q)):
hidden_q.append(
nonlinear_q(
T.dot(v['w' + str(i)], hidden_q[-1]) +
T.dot(v['b' + str(i)], A)))
if self.dropout:
hidden_q[-1] *= 2. * (rng.uniform(size=hidden_q[-1].shape,
dtype='float32') > .5)
if not self.train_residual:
q_mean = T.dot(v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
else:
q_mean = x['mean_prior'] + T.dot(
v['mean_w'], hidden_q[-1]) + T.dot(v['mean_b'], A)
if self.type_qz == 'gaussian' or self.type_qz == 'gaussianmarg':
q_logvar = T.dot(v['logvar_w'], hidden_q[-1]) + T.dot(
v['logvar_b'], A)
else:
raise Exception()
# function for distribution q(z|x)
theanofunc = lazytheanofunc('warn', mode='FAST_RUN')
self.dist_qz['z'] = theanofunc([x['x'], x['mean_prior']] + [A],
[q_mean, q_logvar])
self.dist_qz['hidden'] = theanofunc([x['x'], x['mean_prior']] + [A],
hidden_q[1:])
# Compute virtual sample
eps = rng.normal(size=q_mean.shape, dtype='float32')
_z = q_mean + T.exp(0.5 * q_logvar) * eps
# Compute log p(x|z)
hidden_p = [_z]
for i in range(len(self.n_hidden_p)):
hidden_p.append(
nonlinear_p(
T.dot(w['w' + str(i)], hidden_p[-1]) +
T.dot(w['b' + str(i)], A)))
if self.dropout:
hidden_p[-1] *= 2. * (rng.uniform(size=hidden_p[-1].shape,
dtype='float32') > .5)
if self.type_px == 'bernoulli':
p = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
_logpx = -T.nnet.binary_crossentropy(p, x['x'])
self.dist_px['x'] = theanofunc([_z] + [A], p)
elif self.type_px == 'gaussian':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
elif self.type_px == 'bounded01':
x_mean = T.nnet.sigmoid(
T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A))
x_logvar = T.dot(w['out_logvar_b'], A)
_logpx = ap.logpdfs.normal2(x['x'], x_mean, x_logvar)
# Make it a mixture between uniform and Gaussian
w_unif = T.nnet.sigmoid(T.dot(w['out_unif'], A))
_logpx = T.log(w_unif + (1 - w_unif) * T.exp(_logpx))
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
elif self.type_px == 'exponential':
log_x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
_logpx = ap.logpdfs.exp(x['x'], log_x_mean)
self.dist_px['x'] = theanofunc([_z] + [A], [log_x_mean])
elif self.type_px == 'mixture':
x_mean = T.dot(w['out_w'], hidden_p[-1]) + T.dot(w['out_b'], A)
x_logvar = T.dot(w['out_logvar_w'], hidden_p[-1]) + T.dot(
w['out_logvar_b'], A)
normal_list = np.asarray([1, 6, 10, 14, 18])
exponential_list = np.asarray(
[0, 3, 5, 9, 13, 17, 21, 22, 23, 24, 25, 26, 27])
uniform_list = np.asarray([2, 4, 7, 11, 15, 19])
threemodal_list = np.asarray([8, 12, 16, 20])
#print type(x['x'])
_logpx_normal = ap.logpdfs.normal2(x['x'][normal_list, :],
x_mean[normal_list, :],
x_logvar[normal_list, :])
#print type(x_mean)
_logpx_exponential = ap.logpdfs.exp(x['x'][exponential_list, :],
x_mean[exponential_list, :])
_logpx = _logpx_normal + _logpx_exponential
self.dist_px['x'] = theanofunc([_z] + [A], [x_mean, x_logvar])
else:
raise Exception("")
# Note: logpx is a row vector (one element per sample)
logpx = T.dot(shared32(np.ones((1, self.n_x))),
_logpx) # logpx = log p(x|z,w)
# log p(z) (prior of z)
if self.type_pz == 'gaussianmarg':
if not self.train_residual:
logpz = -0.5 * (np.log(2 * np.pi * self.sigma_square) + (
(q_mean - x['mean_prior'])**2 + T.exp(q_logvar)) /
self.sigma_square).sum(axis=0, keepdims=True)
else:
logpz = -0.5 * (np.log(2 * np.pi * self.sigma_square) +
(q_mean**2 + T.exp(q_logvar)) /
self.sigma_square).sum(axis=0, keepdims=True)
elif self.type_pz == 'gaussian':
logpz = ap.logpdfs.standard_normal(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'mog':
pz = 0
for i in range(self.n_mixture):
pz += T.exp(
ap.logpdfs.normal2(_z, T.dot(w['mog_mean' + str(i)], A),
T.dot(w['mog_logvar' + str(i)], A)))
logpz = T.log(pz).sum(axis=0, keepdims=True) - self.n_z * np.log(
float(self.n_mixture))
elif self.type_pz == 'laplace':
logpz = ap.logpdfs.standard_laplace(_z).sum(axis=0, keepdims=True)
elif self.type_pz == 'studentt':
logpz = ap.logpdfs.studentt(_z, T.dot(T.exp(w['logv']),
A)).sum(axis=0,
keepdims=True)
else:
raise Exception("Unknown type_pz")
# loq q(z|x) (entropy of z)
if self.type_qz == 'gaussianmarg':
logqz = -0.5 * (np.log(2 * np.pi) + 1 + q_logvar).sum(
axis=0, keepdims=True)
elif self.type_qz == 'gaussian':
logqz = ap.logpdfs.normal2(_z, q_mean, q_logvar).sum(axis=0,
keepdims=True)
else:
raise Exception()
# [new part] Fisher divergence of latent variables
if self.var_smoothing > 0:
dlogq_dz = T.grad(
logqz.sum(),
_z) # gives error when using gaussianmarg instead of gaussian
dlogp_dz = T.grad((logpx + logpz).sum(), _z)
FD = 0.5 * ((dlogq_dz - dlogp_dz)**2).sum(axis=0, keepdims=True)
# [end new part]
logqz -= self.var_smoothing * FD
# Note: logpv and logpw are a scalars
if True:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.normal(_w, 0, prior_sd).sum()
else:
def f_prior(_w, prior_sd=self.prior_sd):
return ap.logpdfs.standard_laplace(_w / prior_sd).sum()
return logpx, logpz, logqz
def __init__(self, get_optimizer, theano_warning='raise'):
v = self.v
w = self.w
theanofunction = lazytheanofunc('warn', mode='FAST_RUN')
theanofunction_silent = lazytheanofunc('ignore', mode='FAST_RUN')
# Create theano expressions
x, z = ndict.ordereddicts(self.variables())
self.var_x, self.var_z, = x, z
# Helper variables
A = T.fmatrix('A')
self.var_A = A
'''
# Get gradient symbols
print 'model, x'
for (d, xx) in x.items():
print d
print xx.shape
print x.values()
'''
allvars = x.values() + z.values() + [A] # note: '+' concatenates lists
# TODO: more beautiful/standardized way of setting distributions
# (should be even simpler than this)
self.dist_qz = {}
self.dist_px = {}
self.dist_pz = {}
factors = self.factors(x, z, A)
if len(factors) == 3:
(logpx, logpz, logqz) = factors
cost = 0
sparsity_penalty = 0
else:
(logpx, logpz, logqz, cost, sparsity_penalty) = factors
if get_optimizer == None:
def get_optimizer(w, g):
from collections import OrderedDict
updates = OrderedDict()
for i in w: updates[w[i]] = w[i]
return updates
# Log-likelihood lower bound
self.f_L = theanofunction(allvars, [logpx, logpz, logqz, cost, sparsity_penalty])
L = (logpx + logpz - logqz).sum() - cost - sparsity_penalty
g = T.grad(L, v.values() + w.values())
gv, gw = dict(zip(v.keys(), g[0:len(v)])), dict(zip(w.keys(), g[len(v):len(v)+len(w)]))
updates = get_optimizer(v, gv)
updates.update(get_optimizer(w, gw))
#self.profmode = theano.ProfileMode(optimizer='fast_run', linker=theano.gof.OpWiseCLinker())
#self.f_evalAndUpdate = theano.function(allvars, [logpx + logpz - logqz], updates=updates_w, mode=self.profmode)
#theano.printing.debugprint(self.f_evalAndUpdate)
self.f_eval_test = theanofunction(allvars, [logpx + logpz - logqz, logpx, logpz, -logqz])
self.f_eval = theanofunction(allvars, [logpx + logpz - logqz])
self.f_evalAndUpdate = theanofunction(allvars, [logpx + logpz - logqz], updates=updates)
self.f_eval_for_classcondition_prior = theanofunction(allvars, [logpx - logqz])
