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)
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)
])
import copy
from sklearn.utils import shuffle
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 import scipy as sc from scipy import stats from mimo.distributions import TruncatedStickBreaking alpha = 10 K = 100 sb = TruncatedStickBreaking(K, np.ones(K), np.ones(K) * alpha) weights = np.vstack([sb.rvs() for _ in range(10000)]) weights = np.mean(weights, axis=0) import matplotlib.pyplot as plt plt.axis([0, K + 1, 0, np.max(weights)]) plt.bar(range(1, K + 1), weights) plt.show() h = sc.stats.norm omega = h.rvs(size=(10, K)) x = np.linspace(-3, 3, 200) sample_cdfs = (weights[..., np.newaxis] * np.less.outer(omega, x)).sum(axis=1) fig, ax = plt.subplots(figsize=(8, 6)) ax.plot(x, sample_cdfs[1:].T, c='gray', alpha=0.75)