def _job(kwargs):
args = kwargs.pop('arguments')
seed = kwargs.pop('seed')
input = kwargs.pop('train_input')
target = kwargs.pop('train_target')
input_dim = input.shape[-1]
target_dim = target.shape[-1]
# set random seed
np.random.seed(seed)
nb_params = input_dim
if args.affine:
nb_params += 1
basis_prior = []
models_prior = []
models_hypprior = []
# initialize Normal
alpha_ng = 1.
beta_ng = 1. / (2. * 1e2)
kappas = 1e-2
# initialize Matrix-Normal
psi_mnw = 1e0
K = 1e0
# initialize ard-Gamma
alphas_ard = 1.
betas_ard = 1. / (2. * 1e2)
for n in range(args.nb_models):
basis_hypparams = dict(mu=np.zeros((input_dim, )),
alphas=np.ones(input_dim) * alpha_ng,
betas=np.ones(input_dim) * beta_ng,
kappas=np.ones(input_dim) * kappas)
aux = NormalGamma(**basis_hypparams)
basis_prior.append(aux)
models_hypparams = dict(M=np.zeros((target_dim, nb_params)),
K=np.eye(nb_params) * K,
nu=target_dim + 1,
psi=np.eye(target_dim) * psi_mnw)
aux = MatrixNormalWishart(**models_hypparams)
models_prior.append(aux)
models_hyphypparams = dict(alphas=alphas_ard * np.ones(nb_params),
betas=betas_ard * np.ones(nb_params))
aux = Gamma(**models_hyphypparams)
models_hypprior.append(aux)
# define gating
if args.prior == 'stick-breaking':
gating_hypparams = dict(K=args.nb_models,
gammas=np.ones((args.nb_models, )),
deltas=np.ones(
(args.nb_models, )) * args.alpha)
gating_prior = TruncatedStickBreaking(**gating_hypparams)
ilr = BayesianMixtureOfLinearGaussians(
gating=CategoricalWithStickBreaking(gating_prior),
basis=[
GaussianWithNormalGamma(basis_prior[i])
for i in range(args.nb_models)
],
models=[
LinearGaussianWithMatrixNormalWishartAndAutomaticRelevance(
models_prior[i], models_hypprior[i], affine=args.affine)
for i in range(args.nb_models)
])
else:
gating_hypparams = dict(K=args.nb_models,
alphas=np.ones(
(args.nb_models, )) * args.alpha)
gating_prior = Dirichlet(**gating_hypparams)
ilr = BayesianMixtureOfLinearGaussians(
gating=CategoricalWithDirichlet(gating_prior),
basis=[
GaussianWithNormalGamma(basis_prior[i])
for i in range(args.nb_models)
],
models=[
LinearGaussianWithMatrixNormalWishartAndAutomaticRelevance(
models_prior[i], models_hypprior[i], affine=args.affine)
for i in range(args.nb_models)
])
ilr.add_data(target, input, whiten=False, labels_from_prior=True)
# Gibbs sampling
ilr.resample(maxiter=args.gibbs_iters, progprint=args.verbose)
for _ in range(args.super_iters):
if args.stochastic:
# Stochastic meanfield VI
ilr.meanfield_stochastic_descent(maxiter=args.svi_iters,
stepsize=args.svi_stepsize,
batchsize=args.svi_batchsize)
if args.deterministic:
# Meanfield VI
ilr.meanfield_coordinate_descent(tol=args.earlystop,
maxiter=args.meanfield_iters,
progprint=args.verbose)
ilr.gating.prior = ilr.gating.posterior
for i in range(ilr.likelihood.size):
ilr.basis[i].prior = ilr.basis[i].posterior
ilr.models[i].prior = ilr.models[i].posterior
return ilr
import numpy as np
import numpy.random as npr
from mimo.distributions import GaussianWithDiagonalCovariance
from mimo.distributions import NormalGamma
from mimo.distributions import GaussianWithNormalGamma
npr.seed(1337)
dim, nb_samples, nb_datasets = 3, 500, 5
dist = GaussianWithDiagonalCovariance(mu=npr.randn(dim),
sigmas=1. * npr.rand(dim))
data = [dist.rvs(size=nb_samples) for _ in range(nb_datasets)]
print("True mean" + "\n", dist.mu.T, "\n" + "True sigma" + "\n", dist.sigma)
hypparams = dict(mu=np.zeros((dim, )),
kappas=1e-2 * np.ones((dim, )),
alphas=1. * np.ones((dim, )),
betas=1. / 2. * np.ones((dim, )))
prior = NormalGamma(**hypparams)
model = GaussianWithNormalGamma(prior=prior)
model.meanfield_update(data)
print("Meanfield mean" + "\n", model.likelihood.mu.T,
"\n" + "Meanfield sigma" + "\n", model.likelihood.sigma)
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)
import numpy as np
import numpy.random as npr
from mimo.distributions import GaussianWithDiagonalCovariance
from mimo.distributions import NormalGamma
from mimo.distributions import GaussianWithNormalGamma
npr.seed(1337)
dim, nb_samples, nb_datasets = 3, 500, 5
dist = GaussianWithDiagonalCovariance(mu=npr.randn(dim),
sigmas=1. * npr.rand(dim))
data = [dist.rvs(size=nb_samples) for _ in range(nb_datasets)]
print("True mean" + "\n", dist.mu.T, "\n" + "True sigma" + "\n", dist.sigma)
model = GaussianWithDiagonalCovariance(mu=np.zeros((dim, )))
model.max_likelihood(data)
print("ML mean" + "\n", model.mu.T, "\n" + "ML sigma" + "\n", model.sigma)
hypparams = dict(mu=np.zeros((dim, )),
kappas=1e-2 * np.ones((dim, )),
alphas=1. * np.ones((dim, )),
betas=1. / 2. * np.ones((dim, )))
prior = NormalGamma(**hypparams)
model = GaussianWithNormalGamma(prior=prior)
model.max_aposteriori(data)
print("MAP mean" + "\n", model.likelihood.mu.T, "\n" + "MAP sigma" + "\n",
model.likelihood.sigma)
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(1000)
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(maxiter=500)
plt.figure()
model.plot(obs)
import numpy as np
import numpy.random as npr
from mimo.distributions import GaussianWithDiagonalCovariance
from mimo.distributions import NormalGamma
from mimo.distributions import GaussianWithNormalGamma
npr.seed(1337)
dim, nb_samples, nb_datasets = 3, 500, 5
dist = GaussianWithDiagonalCovariance(mu=npr.randn(dim),
sigmas=1. * npr.rand(dim))
data = [dist.rvs(size=nb_samples) for _ in range(nb_datasets)]
print("True mean" + "\n", dist.mu.T, "\n" + "True sigma" + "\n", dist.sigma)
#
hypparams = dict(mu=np.zeros((dim, )),
kappas=1e-2 * np.ones((dim, )),
alphas=1. * np.ones((dim, )),
betas=1. / 2. * np.ones((dim, )))
prior = NormalGamma(**hypparams)
model = GaussianWithNormalGamma(prior=prior)
model.resample(data)
print("Gibbs mean" + "\n", model.likelihood.mu.T, "\n" + "Gibbs sigma" + "\n",
model.likelihood.sigma)