def __init__(self):
dim = 3
self.dim = dim
self.p = DiagonalMND( nvis = dim,
init_beta = 1.,
init_mu = 0.,
min_beta = 1e-6,
max_beta = 1e6)
self.q = DiagonalMND( nvis = dim,
init_beta = 1.,
init_mu = 0.,
min_beta = 1e-6,
max_beta = 1e6)
def test_log_partition_function():
""" tests that the log partition function is right in the simple 1D case"""
sigma = 2.3
model = DiagonalMND(nvis=1, init_beta=1 / np.square(sigma), min_beta=1e-6, max_beta=1e6, init_mu=17.0)
log_Z = model.log_partition_function()
log_Z = function([], log_Z)()
ground = np.log(sigma * np.sqrt(2.0 * np.pi))
print ground
print log_Z
assert np.allclose(ground, log_Z)
def test_log_partition_function():
""" tests that the log partition function is right in the simple 1D case"""
sigma = 2.3
model = DiagonalMND(nvis=1,init_beta=1/np.square(sigma),
min_beta = 1e-6, max_beta = 1e6, init_mu = 17.)
log_Z = model.log_partition_function()
log_Z = function([],log_Z)()
ground = np.log( sigma * np.sqrt(2.*np.pi))
print ground
print log_Z
assert np.allclose(ground, log_Z)
idxs = np.arange(num_beta)
pos = idxs / float(num_beta - 1)
scaled_shifted = pos * (max_exp - min_exp) + min_exp
betas = 10**scaled_shifted
kls = np.zeros((trials, num_beta))
ml_kls = np.zeros((trials, ))
for trial in xrange(trials):
#generate the data
data_distribution = MND(sigma=np.identity(dim) / true_beta,
mu=np.zeros((dim, )),
seed=17 * (trial + 1))
true = DiagonalMND(nvis=dim,
init_beta=true_beta,
init_mu=0.,
min_beta=.1,
max_beta=10.)
X = sharedX(function([], data_distribution.random_design_matrix(m))())
Xv = X.get_value()
mu = Xv.mean(axis=0)
print 'maximum likelihood mu: ', mu
diff = Xv - mu
var = np.square(diff).mean(axis=0)
mlbeta = 1. / var
print 'maximum likelihood beta: ', mlbeta
ml_model = DiagonalMND(nvis=dim,
init_mu=mu,
init_beta=mlbeta,
min_beta=0.0,
assert ml_kl >= 0.0
ml_kls[trial] = ml_kl
print 'maximum likelihood kl divergence:',ml_kl
best_mse = None
#Try each noise beta
for idx1 in xrange(num_beta):
beta = betas[idx1]
print 'Running experiment for ',beta
#Allocate a fresh model
model = DiagonalMND(
nvis = dim,
init_mu = 0.,
init_beta = .1,
min_beta = .001,
max_beta = 1e30)
#Make the noise distribution
noise_distribution = AdditiveDiagonalMND(
init_beta = beta,
nvis = dim
)
#generate the noise samples
noise_func = function([], noise_distribution.random_design_matrix(X))
Y = []
for i in xrange(noise_per_clean):
Y.append(sharedX(noise_func()))
#Generate the values of beta to consider
idxs = np.arange(num_beta)
pos = idxs / float(num_beta-1)
scaled_shifted = pos * (max_exp-min_exp) + min_exp
betas = 10 ** scaled_shifted
kls = np.zeros((trials,num_beta))
ml_kls = np.zeros((trials,))
for trial in xrange(trials):
#generate the data
data_distribution = MND( sigma = np.identity(dim) / true_beta,
mu = np.zeros((dim,)), seed = 17 * (trial+1) )
true = DiagonalMND( nvis = dim, init_beta = true_beta, init_mu = 0.,
min_beta = .1, max_beta = 10.)
X = sharedX(function([],data_distribution.random_design_matrix(m))())
Xv = X.get_value()
mu = Xv.mean(axis=0)
print 'maximum likelihood mu: ',mu
diff = Xv - mu
var = np.square(diff).mean(axis=0)
mlbeta = 1./var
print 'maximum likelihood beta: ',mlbeta
ml_model = DiagonalMND( nvis = dim, init_mu = mu, init_beta = mlbeta,
min_beta = 0.0,
max_beta = 1e6)
ml_kl = kl_divergence( true, ml_model)
ml_kl = function([],ml_kl)()
assert ml_kl >= 0.0
print 'maximum likelihood beta: ', mlbeta
ml_mse[trial] = np.abs(mlbeta - true_beta).mean()
ml_betas[trial] = mlbeta
best_mse = None
#Try each noise beta
for idx1 in xrange(num_beta):
beta = betas[idx1]
print 'Running experiment for ', beta
#Allocate a fresh model
model = DiagonalMND(nvis=dim,
init_mu=0.,
init_beta=.1,
min_beta=.001,
max_beta=1e30)
#Make the noise distribution
noise_distribution = AdditiveDiagonalMND(init_beta=beta, nvis=dim)
#generate the noise samples
noise_func = function([], noise_distribution.random_design_matrix(X))
Y = []
for i in xrange(noise_per_clean):
Y.append(sharedX(noise_func()))
#Get the objective function
nce = DNCE(noise_distribution)
J = nce(model, X, Y)