def init_params(y, N_data, K_clusters, D_data, tol,
max_iter): #initialize parameters for FI-NPL by picking MLE
R_restarts = 10
pi_bb = np.zeros((R_restarts, K_clusters)) #mixing weights
mu_bb = np.zeros((R_restarts, K_clusters, D_data)) #means
sigma_bb = np.zeros((R_restarts, K_clusters, D_data)) #covariances
ll_bb = np.zeros(R_restarts)
#Initialize parameters randomly
pi_init = np.random.dirichlet(np.ones(K_clusters), R_restarts)
mu_init = 8 * np.random.rand(R_restarts, K_clusters, D_data) - 2
sigma_init = invgamma.rvs(1, size=(R_restarts, K_clusters, D_data))
for i in range(R_restarts):
model = skgm.GaussianMixture(K_clusters,
covariance_type='diag',
means_init=mu_init[i],
weights_init=pi_init[i],
precisions_init=1 / sigma_init[i],
tol=tol,
max_iter=max_iter)
model.fit(y, np.ones(N_data))
pi_bb[i] = model.weights_
mu_bb[i] = model.means_
sigma_bb[i] = np.sqrt(model.covariances_)
ll_bb[i] = model.score(y, np.ones(N_data)) * N_data
ind = np.argmax(ll_bb)
return pi_bb[ind], mu_bb[ind], sigma_bb[ind]
def maximise_mle(y, weights, pi_init, mu_init, sigma_init, K_clusters, tol,
max_iter, N_data): #maximization for FI-NPL
model = skgm.GaussianMixture(K_clusters,
covariance_type='diag',
means_init=mu_init,
weights_init=pi_init,
precisions_init=1 / sigma_init,
tol=tol,
max_iter=max_iter)
model.fit(y, N_data * weights)
pi_bb = model.weights_
mu_bb = model.means_
sigma_bb = np.sqrt(model.covariances_)
return pi_bb, mu_bb, sigma_bb
def lppd(y, pi, mu, sigma, K): #calculate posterior predictive of test
model = skgm.GaussianMixture(K, covariance_type='diag')
B = np.shape(mu)[0]
N_test = np.shape(y)[0]
ll_test = np.zeros((B, N_test))
model.fit(y, np.ones(N_test))
for i in range(B):
model.means_ = mu[i, :]
model.covariances_ = sigma[i, :]**2
model.precisions_ = 1 / (sigma[i, :]**2)
model.weights_ = pi[i, :]
model.precisions_cholesky_ = _compute_precision_cholesky(
model.covariances_, model.covariance_type)
ll_test[i] = model.score_lppd(y)
lppd_test = np.sum(sp.special.logsumexp(ll_test, axis=0) - np.log(B))
return lppd_test
def IS_lppd(y, pi, mu, sigma, K,
logweights_is): #calculate posterior predictive of test
model = skgm.GaussianMixture(K, covariance_type='diag')
B = np.shape(mu)[0]
N_test = np.shape(y)[0]
ll_test = np.zeros(N_test)
model.fit(y, np.ones(N_test))
for i in tqdm(range(B)):
model.means_ = mu[i, :, :]
model.covariances_ = sigma[i, :]**2
model.precisions_ = 1 / (sigma[i, :]**2)
model.weights_ = pi[i, :]
model.precisions_cholesky_ = _compute_precision_cholesky(
model.covariances_, model.covariance_type)
if i == 0:
ll_test = model.score_lppd(y) + logweights_is[i]
else:
ll_test = np.logaddexp(ll_test,
model.score_lppd(y) + logweights_is[i])
lppd_test = np.sum(ll_test)
return lppd_test
def maximise(y,
y_prior,
weights,
pi_init,
mu_init,
sigma_init,
alph_conc,
T_trunc,
K_clusters,
tol,
max_iter,
R_restarts,
N_data,
D_data,
postsamples=None): #maximization for RR-NPL
if alph_conc != 0:
y_tot = np.concatenate((y, y_prior))
else:
y_tot = y
pi_bb = np.zeros((R_restarts, K_clusters)) #mixing weights
mu_bb = np.zeros((R_restarts, K_clusters, D_data)) #means
sigma_bb = np.zeros((R_restarts, K_clusters, D_data)) #covariances
ll_bb = np.zeros(R_restarts)
n_tot = np.shape(y_tot)[0]
for i in range(R_restarts):
model = skgm.GaussianMixture(K_clusters,
covariance_type='diag',
means_init=mu_init[i],
weights_init=pi_init[i],
precisions_init=1 / sigma_init[i],
tol=tol,
max_iter=max_iter)
model.fit(y_tot, n_tot * weights)
pi_bb[i] = model.weights_
mu_bb[i] = model.means_
sigma_bb[i] = np.sqrt(model.covariances_)
ll_bb[i] = model.score(y_tot, weights) * n_tot
ind = np.argmax(ll_bb)
return pi_bb[ind], mu_bb[ind], sigma_bb[ind]