def test_seed_same():
"""Verifies that two MNDs initialized with the same
seed produce the same samples """
rng = np.random.RandomState([1,2,3])
#the number in the argument here is the limit on
#seed value
seed = rng.randint(2147462579)
dim = 3
mu = rng.randn(dim)
rank = dim
X = rng.randn(rank,dim)
cov = np.dot(X.T,X)
mnd1 = MND( sigma = cov, mu = mu, seed = seed)
num_samples = 5
rd1 = mnd1.random_design_matrix(num_samples)
rd1 = function([],rd1)()
mnd2 = MND( sigma = cov, mu = mu, seed = seed)
rd2 = mnd2.random_design_matrix(num_samples)
rd2 = function([],rd2)()
assert np.all(rd1 == rd2)
def test_seed_same():
"""Verifies that two MNDs initialized with the same
seed produce the same samples """
rng = np.random.RandomState([1, 2, 3])
#the number in the argument here is the limit on
#seed value
seed = rng.randint(2147462579)
dim = 3
mu = rng.randn(dim)
rank = dim
X = rng.randn(rank, dim)
cov = np.dot(X.T, X)
mnd1 = MND(sigma=cov, mu=mu, seed=seed)
num_samples = 5
rd1 = mnd1.random_design_matrix(num_samples)
rd1 = function([], rd1)()
mnd2 = MND(sigma=cov, mu=mu, seed=seed)
rd2 = mnd2.random_design_matrix(num_samples)
rd2 = function([], rd2)()
assert np.all(rd1 == rd2)
def test_seed_diff():
"""Verifies that two MNDs initialized with different
seeds produce samples that differ at least somewhat
(theoretically the samples could match even under
valid behavior but this is extremely unlikely)"""
skip_if_no_scipy()
rng = np.random.RandomState([1,2,3])
#the number in the argument here is the limit on
#seed value, and we subtract 1 so it will be
#possible to add 1 to it for the second MND
seed = rng.randint(2147462579) -1
dim = 3
mu = rng.randn(dim)
rank = dim
X = rng.randn(rank,dim)
cov = np.dot(X.T,X)
mnd1 = MND( sigma = cov, mu = mu, seed = seed)
num_samples = 5
rd1 = mnd1.random_design_matrix(num_samples)
rd1 = function([],rd1)()
mnd2 = MND( sigma = cov, mu = mu, seed = seed + 1)
rd2 = mnd2.random_design_matrix(num_samples)
rd2 = function([],rd2)()
assert np.any(rd1 != rd2)
def test_seed_diff():
"""Verifies that two MNDs initialized with different
seeds produce samples that differ at least somewhat
(theoretically the samples could match even under
valid behavior but this is extremely unlikely)"""
skip_if_no_scipy()
rng = np.random.RandomState([1, 2, 3])
#the number in the argument here is the limit on
#seed value, and we subtract 1 so it will be
#possible to add 1 to it for the second MND
seed = rng.randint(2147462579) - 1
dim = 3
mu = rng.randn(dim)
rank = dim
X = rng.randn(rank, dim)
cov = np.dot(X.T, X)
mnd1 = MND(sigma=cov, mu=mu, seed=seed)
num_samples = 5
rd1 = mnd1.random_design_matrix(num_samples)
rd1 = function([], rd1)()
mnd2 = MND(sigma=cov, mu=mu, seed=seed + 1)
rd2 = mnd2.random_design_matrix(num_samples)
rd2 = function([], rd2)()
assert np.any(rd1 != rd2)
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)()
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
ml_kls[trial] = ml_kl