x = i * step - 6.
data[i, 0] = x + npr.normal(0, 0.1)
data[i, 1] = 3. * (np.sin(x) + npr.normal(0, .1))
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)
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 = []
# initialize Normal
psi_nw = 1e0
kappa = 1e-2
# initialize Matrix-Normal
psi_mnw = 1e0
K = 1e-3
for n in range(args.nb_models):
basis_hypparams = dict(mu=np.zeros((input_dim, )),
psi=np.eye(input_dim) * psi_nw,
kappa=kappa,
nu=input_dim + 1)
aux = NormalWishart(**basis_hypparams)
basis_prior.append(aux)
models_hypparams = dict(M=np.zeros((target_dim, nb_params)),
K=K * np.eye(nb_params),
nu=target_dim + 1,
psi=np.eye(target_dim) * psi_mnw)
aux = MatrixNormalWishart(**models_hypparams)
models_prior.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=[
GaussianWithNormalWishart(basis_prior[i])
for i in range(args.nb_models)
],
models=[
LinearGaussianWithMatrixNormalWishart(models_prior[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=[
GaussianWithNormalWishart(basis_prior[i])
for i in range(args.nb_models)
],
models=[
LinearGaussianWithMatrixNormalWishart(models_prior[i],
affine=args.affine)
for i in range(args.nb_models)
])
ilr.add_data(target, input, whiten=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 GaussianWithCovariance
from mimo.distributions import GaussianWithPrecision
from mimo.distributions import NormalWishart
from mimo.distributions import GaussianWithNormalWishart
npr.seed(1337)
dim, nb_samples, nb_datasets = 3, 500, 5
dist = GaussianWithCovariance(mu=npr.randn(dim),
sigma=1. * np.diag(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 = GaussianWithPrecision(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, )), kappa=0.01, psi=np.eye(dim), nu=dim + 1)
prior = NormalWishart(**hypparams)
model = GaussianWithNormalWishart(prior=prior)
model.max_aposteriori(data)
print("MAP mean" + "\n", model.likelihood.mu.T, "\n" + "MAP sigma" + "\n",
model.likelihood.sigma)
nb_params = input_dim
if args.affine:
nb_params += 1
basis_prior, models_prior = [], []
psi_nw, kappa = 1e0, 1e-2
psi_mnw, K = 1e0, 1e-2
for n in range(args.nb_models):
basis_hypparams = dict(mu=np.zeros((input_dim, )),
psi=np.eye(input_dim) * psi_nw,
kappa=kappa,
nu=input_dim + 1)
aux = NormalWishart(**basis_hypparams)
basis_prior.append(aux)
models_hypparams = dict(M=np.zeros((target_dim, nb_params)),
K=K * np.eye(nb_params),
nu=target_dim + 1,
psi=np.eye(target_dim) * psi_mnw)
aux = MatrixNormalWishart(**models_hypparams)
models_prior.append(aux)
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)