def main():
# Load data
X = pickle.load(open(data_fn, "rb"))
N, D = X.shape
# Model parameters
alpha = 1.
K = 4 # number of components
mu_scale = 3.0
covar_scale = 1.0
# Sampling parameters
n_runs = 2
n_iter = 12
# 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)
# Initialize component assignment: this is not random for testing purposes
z = np.array([i * np.ones(N / K) for i in range(K)],
dtype=np.int).flatten()
# Setup FBGMM
fbgmm = FBGMM(X, prior, alpha, K, assignments=z)
print("Initial log marginal prob:", fbgmm.log_marg())
# Perform several Gibbs sampling runs and average the log marginals
log_margs = np.zeros(n_iter)
for j in range(n_runs):
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
log_margs += record["log_marg"]
log_margs /= n_runs
# Plot results
fig = plt.figure()
ax = fig.add_subplot(111)
plot_mixture_model(ax, fbgmm)
for k in range(fbgmm.components.K):
mu, sigma = fbgmm.components.rand_k(k)
plot_ellipse(ax, mu, sigma)
# Plot log probability
plt.figure()
plt.plot(list(range(n_iter)), log_margs)
plt.xlabel("Iterations")
plt.ylabel("Log prob")
plt.show()
def main():
# Load data
X = pickle.load(open(data_fn, "rb"))
N, D = X.shape
# Model parameters
alpha = 1.
K = 4 # number of components
mu_scale = 3.0
covar_scale = 1.0
# Sampling parameters
n_runs = 2
n_iter = 12
# 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)
# Initialize component assignment: this is not random for testing purposes
z = np.array([i*np.ones(N/K) for i in range(K)], dtype=np.int).flatten()
# Setup FBGMM
fbgmm = FBGMM(X, prior, alpha, K, assignments=z)
print("Initial log marginal prob:", fbgmm.log_marg())
# Perform several Gibbs sampling runs and average the log marginals
log_margs = np.zeros(n_iter)
for j in range(n_runs):
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
log_margs += record["log_marg"]
log_margs /= n_runs
# Plot results
fig = plt.figure()
ax = fig.add_subplot(111)
plot_mixture_model(ax, fbgmm)
for k in range(fbgmm.components.K):
mu, sigma = fbgmm.components.rand_k(k)
plot_ellipse(ax, mu, sigma)
# Plot log probability
plt.figure()
plt.plot(list(range(n_iter)), log_margs)
plt.xlabel("Iterations")
plt.ylabel("Log prob")
plt.show()
def gmm(X,
K=4,
n_iter=100,
alpha=1.0,
mu_scale=4.0,
var_scale=0.5,
covar_scale=0.7,
posterior_predictive_check=False):
N, D = X.shape
# Initialize 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.ones(D)
prior = NIW(m_0, k_0, v_0, S_0)
# Setup FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
K = fbgmm.components.K
mus = np.zeros(shape=(K, D))
covars = [np.zeros((D, D)) for i in range(0, K)]
for k in range(fbgmm.components.K):
mu, var = fbgmm.components.rand_k(k)
mus[k, :] = mu
covars[k] = np.diag(var)
# Generate new points for posterior predictive check
# Generate the same number of points as N
if posterior_predictive_check:
np.random.seed(1)
rstate = 1
alphas = (alpha / K) + fbgmm.components.counts
pis = dirichlet.rvs(alphas, random_state=rstate)[0]
Z = np.zeros(N, dtype=np.uint32)
X = np.zeros((N, D))
for n in range(N):
Z[n] = np.floor(np.argmax(multinomial(1, pis)))
X[n] = multivariate_normal.rvs(mean=mus[Z[n]], cov=covars[Z[n]])
return fbgmm.components.assignments, mus, (X, Z)
return fbgmm.components.assignments, mus
def test_sampling_2d_assignments():
random.seed(1)
np.random.seed(1)
# Data parameters
D = 2 # dimensions
N = 100 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.
K = 3 # number of components
n_iter = 10
# 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 FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
assignments_expected = np.array([
0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0,
2, 0, 1, 0, 2, 1, 1, 0, 2, 2, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2,
0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 1, 2, 2, 1, 0, 0, 1, 0, 2, 2, 1,
2, 0, 0, 2
])
assignments = fbgmm.components.assignments
npt.assert_array_equal(assignments, assignments_expected)
def main():
# Data parameters
D = 2 # dimensions
N = 100 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.
K = 4 # 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
var_scale = 0.5 # if you make this really small, you basically get k-means
mu_0 = np.zeros(D)
k_0 = covar_scale**2/mu_scale**2
var = covar_scale**2*np.ones(D)*var_scale
var_0 = var/k_0
prior = FixedVarPrior(var, mu_0, var_0)
# Setup FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand", covariance_type="fixed")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
# Plot results
fig = plt.figure()
ax = fig.add_subplot(111)
plot_mixture_model(ax, fbgmm)
for k in range(fbgmm.components.K):
mu = fbgmm.components.rand_k(k)
sigma = np.diag(var)
plot_ellipse(ax, mu, sigma)
plt.show()
def main():
# Data parameters
D = 2 # dimensions
N = 100 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.
K = 4 # 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
var_scale = 0.5 # if you make this really small, you basically get k-means
mu_0 = np.zeros(D)
k_0 = covar_scale**2 / mu_scale**2
var = covar_scale**2 * np.ones(D) * var_scale
var_0 = var / k_0
prior = FixedVarPrior(var, mu_0, var_0)
# Setup FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand", covariance_type="fixed")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
# Plot results
fig = plt.figure()
ax = fig.add_subplot(111)
plot_mixture_model(ax, fbgmm)
for k in range(fbgmm.components.K):
mu = fbgmm.components.rand_k(k)
sigma = np.diag(var)
plot_ellipse(ax, mu, sigma)
plt.show()
def test_sampling_2d_log_marg_deleted_components():
random.seed(1)
np.random.seed(1)
# Data parameters
D = 2 # dimensions
N = 10 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.
K = 6 # number of components
n_iter = 1
# 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 FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
expected_log_marg = -60.1448630929
log_marg = fbgmm.log_marg()
print(fbgmm.components.assignments)
npt.assert_almost_equal(log_marg, expected_log_marg)
def main():
# Data parameters
D = 2 # dimensions
N = 100 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.
K = 4 # 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 FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
# Plot results
fig = plt.figure()
ax = fig.add_subplot(111)
plot_mixture_model(ax, fbgmm)
for k in range(fbgmm.components.K):
# mu, sigma = fbgmm.components.map(k)
mu, sigma = fbgmm.components.rand_k(k)
plot_ellipse(ax, mu, sigma)
plt.show()
def main():
# Data parameters
D = 2 # dimensions
N = 100 # number of points to generate
K_true = 4 # the true number of components
# Model parameters
alpha = 1.0
K = 4 # 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.ones(D)
prior = NIW(m_0, k_0, v_0, S_0)
# Setup FBGMM
fbgmm = FBGMM(X, prior, alpha, K, "rand", covariance_type="diag")
# Perform Gibbs sampling
record = fbgmm.gibbs_sample(n_iter)
# Plot results
fig = plt.figure()
ax = fig.add_subplot(111)
plot_mixture_model(ax, fbgmm)
for k in range(fbgmm.components.K):
mu, sigma = fbgmm.components.rand_k(k)
plot_ellipse(ax, mu, np.diag(sigma))
plt.show()
