def main():
import random
from niw import NIW
logging.basicConfig(level=logging.INFO)
random.seed(1)
np.random.seed(1)
# Data parameters
D = 2 # dimensions
N = 20 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.
K = 3 # initial number of components
n_iter = 20
# Generate data
mu_scale = 4.0
covar_scale = 0.7
z_true = np.random.randint(0, K_true, N)
mu = np.random.randn(D, K_true)*mu_scale
X = mu[:, z_true] + np.random.randn(D, N)*covar_scale
X = X.T
# Intialize prior
m_0 = np.zeros(D)
k_0 = covar_scale**2/mu_scale**2
v_0 = D + 3
S_0 = covar_scale**2*v_0*np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
# Setup IGMM
igmm = IGMM(X, prior, alpha, assignments="rand", K=K)
# igmm = IGMM(X, prior, alpha, assignments="each-in-own")
# igmm = IGMM(X, prior, alpha, assignments="one-by-one", K=K)
# Perform Gibbs sampling
logger.info("Initial log marginal prob: " + str(igmm.log_marg()))
record = igmm.gibbs_sample(n_iter)
logger.info("Assignments: " + str(igmm.components.assignments))
def main():
from niw import NIW
# LOG POSTERIOR EXAMPLE
prior = NIW(m_0=np.array([0.5, -0.1, 0.1]), k_0=2.0, v_0=5.0, S_0=5.0*np.eye(3))
gmm = GaussianComponents(np.array([
[1.2, 0.9, 0.2],
[-0.1, 0.8, -0.2],
[0.5, 0.4, 0.3]
]), prior)
gmm.add_item(0, 0)
gmm.add_item(1, 0)
print "Log prior of [0.5, 0.4, 0.3]:", gmm.log_prior(2)
print "Log posterior of [0.5, 0.4, 0.3]:", gmm.log_post_pred_k(2, 0)
print
# ADDING AND REMOVING DATA VECTORS EXAMPLE
prior = NIW(m_0=np.array([0.0, 0.0]), k_0=2.0, v_0=5.0, S_0=5.0*np.eye(2))
gmm = GaussianComponents(np.array([
[1.2, 0.9],
[-0.1, 0.8],
[0.5, 0.4]
]), prior)
print "Log prior of [1.2, 0.9]:", gmm.log_prior(0)
gmm.add_item(0, 0)
gmm.add_item(1, 0)
print "Log posterior of [0.5, 0.4]:", gmm.log_post_pred_k(2, 0)
gmm.add_item(2, 0)
print "Log posterior of [0.5, 0.4] after adding:", gmm.log_post_pred_k(2, 0)
gmm.del_item(2)
print "Log posterior of [0.5, 0.4] after removing:", gmm.log_post_pred_k(2, 0)
print
# LOG MARGINAL EXAMPLE
# Data
X = np.array([
[-0.3406, -0.3593, -0.0686],
[-0.3381, 0.2993, 0.925],
[-0.5, -0.101, 0.75]
])
N, D = X.shape
# Setup densities
m_0 = np.zeros(D)
k_0 = 0.05
v_0 = D + 3
S_0 = 0.5*np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior, [0, 0, 0])
# Calculate log marginal of data
log_marg = gmm.log_marg_k(0)
print "Log marginal:", gmm.log_marg_k(0)
print
# HIGHER DIMENSIONAL EXAMPLE
# Data generated with np.random.seed(2); np.random.rand(11, 4)
X = np.array([
[ 0.4359949 , 0.02592623, 0.54966248, 0.43532239],
[ 0.4203678 , 0.33033482, 0.20464863, 0.61927097],
[ 0.29965467, 0.26682728, 0.62113383, 0.52914209],
[ 0.13457995, 0.51357812, 0.18443987, 0.78533515],
[ 0.85397529, 0.49423684, 0.84656149, 0.07964548],
[ 0.50524609, 0.0652865 , 0.42812233, 0.09653092],
[ 0.12715997, 0.59674531, 0.226012 , 0.10694568],
[ 0.22030621, 0.34982629, 0.46778748, 0.20174323],
[ 0.64040673, 0.48306984, 0.50523672, 0.38689265],
[ 0.79363745, 0.58000418, 0.1622986 , 0.70075235],
[ 0.96455108, 0.50000836, 0.88952006, 0.34161365]
])
N, D = X.shape
# Setup densities
m_0 = X.mean(axis=0)
k_0 = 0.05
v_0 = D + 10
S_0 = 0.5*np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior, [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1])
print "Consider vector:", X[10]
print "Log post predictive:", log_post_pred_unvectorized(gmm, 10)
print "Log post predictive:", gmm.log_post_pred(10)
print "Log marginal for component 0:", gmm.log_marg_k(0)
def main():
from niw import NIW
# logging.basicConfig(level=logging.DEBUG)
# LOG POSTERIOR EXAMPLE
# Prior
D = 3
m_0 = np.array([0.5, -0.1, 0.1])
k_0 = 2.0
S_0 = 5.0 * np.ones(D)
v_0 = 5
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Data
X = np.array([[0.5, 0.4, 0.3], [1.2, 0.9, 0.2], [-0.1, 0.8, -0.2],
[0.0, 0.5, -1.0]])
x = X[0]
# Setup single-component model
gmm = GaussianComponentsDiag(X, prior)
N, _ = X.shape
for i in range(N):
gmm.add_item(i, 0)
# Calculate posterior by hand
k_N = k_0 + N
v_N = v_0 + N
m_N = (k_0 * m_0 + N * X[:N].mean(axis=0)) / k_N
S_N = S_0 + np.square(
X[:N]).sum(axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
print("Log posterior of " + str(x) + ":", gmm.log_post_pred_k(0, 0))
print("Log posterior of " + str(x) + ": " + str(
np.sum([
students_t(x[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
for i in range(len(x))
])))
print()
# MULTIPLE COMPONENT EXAMPLE
# Data generated with np.random.seed(2); np.random.rand(11, 4)
X = np.array([[0.4359949, 0.02592623, 0.54966248, 0.43532239],
[0.4203678, 0.33033482, 0.20464863, 0.61927097],
[0.29965467, 0.26682728, 0.62113383, 0.52914209],
[0.13457995, 0.51357812, 0.18443987, 0.78533515],
[0.85397529, 0.49423684, 0.84656149, 0.07964548],
[0.50524609, 0.0652865, 0.42812233, 0.09653092],
[0.12715997, 0.59674531, 0.226012, 0.10694568],
[0.22030621, 0.34982629, 0.46778748, 0.20174323],
[0.64040673, 0.48306984, 0.50523672, 0.38689265],
[0.79363745, 0.58000418, 0.1622986, 0.70075235],
[0.96455108, 0.50000836, 0.88952006, 0.34161365]])
N, D = X.shape
# Setup densities
m_0 = X.mean(axis=0)
k_0 = 0.05
v_0 = D + 10
S_0 = 0.5 * np.ones(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponentsDiag(X, prior, [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1])
print("Consider vector:", X[10])
print("Log post predictive:", log_post_pred_unvectorized(gmm, 10))
print("Log post predictive:", gmm.log_post_pred(10))
print("Log marginal for component 0:", gmm.log_marg_k(0))