plt.figure()
plt.plot(data[:, 0], data[:, 1], 'kx')
plt.title('data')
nb_models = 25
gating_hypparams = dict(K=nb_models, alphas=np.ones((nb_models, )))
gating_prior = Dirichlet(**gating_hypparams)
components_hypparams = dict(mu=np.zeros((2, )), kappa=0.01,
psi=np.eye(2), nu=3)
components_prior = NormalWishart(**components_hypparams)
gmm = BayesianMixtureOfGaussians(gating=CategoricalWithDirichlet(gating_prior),
components=[GaussianWithNormalWishart(components_prior)
for _ in range(nb_models)])
gmm.add_data(data, labels_from_prior=True)
allscores = []
allmodels = []
for superitr in range(5):
# Gibbs sampling to wander around the posterior
gmm.resample(maxiter=25)
# mean field to lock onto a mode
scores = gmm.meanfield_coordinate_descent(maxiter=100)
allscores.append(scores)
allmodels.append(copy.deepcopy(gmm))
gating = Categorical(K=2)
components = [GaussianWithDiagonalCovariance(mu=np.array([1., 1.]), sigmas=np.array([0.25, 0.5])),
GaussianWithDiagonalCovariance(mu=np.array([-1., -1.]), sigmas=np.array([0.5, 0.25]))]
gmm = MixtureOfGaussians(gating=gating, components=components)
obs, z = gmm.rvs(500)
gmm.plot(obs)
gating_hypparams = dict(K=2, alphas=np.ones((2, )))
gating_prior = Dirichlet(**gating_hypparams)
components_hypparams = dict(mu=np.zeros((2, )),
kappas=1e-2 * np.ones((2, )),
alphas=1. * np.ones((2, )),
betas=1. / (2. * 1e4) * np.ones((2, )))
components_prior = NormalGamma(**components_hypparams)
model = BayesianMixtureOfGaussians(gating=CategoricalWithDirichlet(gating_prior),
components=[GaussianWithNormalGamma(components_prior)
for _ in range(2)])
model.add_data(obs)
model.max_aposteriori(maxiter=1000)
plt.figure()
model.plot(obs)
gating = Categorical(K=2)
components = [GaussianWithCovariance(mu=np.array([1., 1.]), sigma=0.25 * np.eye(2)),
GaussianWithCovariance(mu=np.array([-1., -1.]), sigma=0.5 * np.eye(2))]
gmm = MixtureOfGaussians(gating=gating, components=components)
obs, z = gmm.rvs(500)
gmm.plot(obs)
gating_hypparams = dict(K=2, alphas=np.ones((2, )))
gating_prior = Dirichlet(**gating_hypparams)
components_hypparams = dict(mu=np.zeros((2, )),
kappas=1e-2 * np.ones((2, )),
alphas=1. * np.ones((2, )),
betas=1. / (2. * 1e4) * np.ones((2, )))
components_prior = NormalGamma(**components_hypparams)
model = BayesianMixtureOfGaussians(gating=CategoricalWithDirichlet(gating_prior),
components=[GaussianWithNormalGamma(components_prior)
for _ in range(2)])
model.add_data(obs)
model.resample()
model.meanfield_coordinate_descent(maxiter=2500)
plt.figure()
model.plot(obs)
plt.figure()
plt.plot(data[:, 0], data[:, 1], 'kx')
plt.title('data')
nb_models = 25
gating_hypparams = dict(K=nb_models, alphas=np.ones((nb_models, )))
gating_prior = Dirichlet(**gating_hypparams)
components_hypparams = dict(mu=np.zeros((2, )),
kappa=0.01,
psi=np.eye(2),
nu=3)
components_prior = NormalWishart(**components_hypparams)
gmm = BayesianMixtureOfGaussians(
gating=CategoricalWithDirichlet(gating_prior),
components=[
GaussianWithNormalWishart(components_prior) for _ in range(nb_models)
])
gmm.add_data(data, labels_from_prior=True)
gmm.resample(maxiter=2500)
plt.figure()
plt.title('posterior')
gmm.plot()
plt.show()
plt.figure()
plt.plot(data[:, 0], data[:, 1], 'kx')
plt.title('data')
nb_models = 25
gating_hypparams = dict(K=nb_models, alphas=np.ones((nb_models, )))
gating_prior = Dirichlet(**gating_hypparams)
components_hypparams = dict(mu=np.zeros((2, )), kappa=0.01,
psi=np.eye(2), nu=3)
components_prior = NormalWishart(**components_hypparams)
gmm = BayesianMixtureOfGaussians(gating=CategoricalWithDirichlet(gating_prior),
components=[GaussianWithNormalWishart(components_prior)
for _ in range(nb_models)])
gmm.add_data(data, labels_from_prior=True)
allscores = []
allmodels = []
for superitr in range(5):
# Gibbs sampling to wander around the posterior
gmm.resample(maxiter=25)
# Stochastic Meanfield VI
gmm.meanfield_stochastic_descent(stepsize=1e-2, maxiter=100, batchsize=128)
allscores.append(gmm.meanfield_update())
allmodels.append(copy.deepcopy(gmm))