def gibbs_init_step(self,
nb_days,
nb_particles,
sigma2_s_param=None,
sigma2_g_param=None):
""" Initialize all the variables required for the bootstrap filter init using gibbs sampling
And perform the gibbs initialization step """
#Gibbs step 0
if sigma2_s_param is None:
self.sigma_s_star_2[0, 0] = invgamma.rvs(a=10**(-2),
scale=10**(2),
size=1)[0]
else:
self.sigma_s_star_2[0, 0] = sigma2_s_param
if sigma2_g_param is None:
self.sigma_g_star_2[0, 0] = invgamma.rvs(a=10**(-2),
scale=10**(2),
size=1)[0]
else:
self.sigma_g_star_2[0, 0] = sigma2_g_param
self.s[0, 0] = self.truncated_norm(0, inf, 0, 10**8)
self.g_heat[0, 0] = self.truncated_norm(-inf, 0, 0, 10**8)
for i in range(1, nb_days):
self.s[i, 0] = self.s[i - 1, 0] + self.truncated_norm(
-self.s[i - 1, 0], inf, 0, self.sigma_s_star_2[0, 0])
self.g_heat[i, 0] = self.g_heat[i - 1, 0] + self.truncated_norm(
-inf, -self.g_heat[i - 1, 0], 0, self.sigma_g_star_2[0, 0])
def calculate_difference((hh, Xs)):
# step3の階差の計算--------------------------------------
# step3の階差計算の和の計算で使用する変数の初期化
dift = 0.
difw = 0.
difbeta = np.array([np.float(0)] * nz)
#
dift = sum((Xs[hh, 0, 1:TIMES] - Xs[hh, 0, 0:TIMES - 1])**2)
difw = sum((Xs[hh, k, 1:TIMES] +
sum(Xs[hh, k:(k - 1) + SEASONALYTY - 1, 0:TIMES - 1]))**2)
for d in xrange(nz):
difbeta[d] = sum((Xs[hh, (k - 1) + SEASONALYTY + d, 1:TIMES] -
Xs[hh, (k - 1) + SEASONALYTY + d, 0:TIMES - 1])**2)
# step3--------------------------------------
Sita_sys[hh, 0, 0] = invgamma.rvs((nu0 + TIMES) / 2,
scale=(s0 + dift) / 2,
size=1)[0]
Sita_sys[hh, 1, 1] = invgamma.rvs((nu0 + TIMES) / 2,
scale=(s0 + difw) / 2,
size=1)[0]
for d in xrange(nz):
Sita_sys[hh, 2 + d, 2 + d] = invgamma.rvs((nu0 + TIMES) / 2,
scale=(s0 + difbeta[d]) / 2,
size=1)[0]
return Sita_sys[hh, :, :]
def sample_g(c_value, V):
n = len(V)
V = np.array(V)
#print(n)
index = V**2 < 0
para = c_value/2
sho = 0
while(sho<20 and np.sum(index)<n):
V_new = invgamma.rvs(a = 1, loc=0, scale=para).reshape(-1)
u = np.random.rand(n)
index_up = (u< V_new/(1+V_new)).reshape(-1)
#print(index_up)
V[index_up] = V_new[index_up]
index = (index+index_up)>0
sho = sho + 1
left = np.where(index == False)[0]
for those in left:
V_new = invgamma.rvs(a = 1, loc = 0, scale = para[those], size = 100)
u = np.random.rand(100)
index_up = (u<V_new/(1+V_new)).reshape(-1)
#print("judge done")
if np.sum(index_up) != 0:
V[those] = V_new[index_up][0]
index[those] = True
if n!=sum(index):
print(n, sum(index))
return V
def sv_parameter_generator(s=None,phi_mode=0.97,phi_a_shape=300,sqrt_sigma_mode=0.20,sigma_shape=2,sqrt_beta_mode=0.20,beta_shape=2,saveOpt=False,displayOpt=True,filename='sv_parameters.csv'):
if s is None:
pass
else:
seed(s)
phi_b_shape=2+(phi_a_shape-1)/float(phi_mode)-phi_a_shape
phi=beta(1+phi_a_shape,1+phi_b_shape,1)[0]
sigma_mode=sqrt_sigma_mode**2
sigma_scale=sigma_mode*(sigma_shape+1)
sigma=sqrt(invgamma.rvs(sigma_shape,scale=sigma_mode))
beta_mode=sqrt_beta_mode**2
beta_scale=beta_mode*(beta_shape+1)
beta_=sqrt(invgamma.rvs(beta_shape,scale=beta_mode))
if saveOpt:
np.savetxt(filename,np.array([phi,sigma,beta_]),fmt='%.17f')
if displayOpt:
print 'Generated parameters:'
print ' phi = ', phi
print ' sigma = ',sigma
print ' beta = ', beta_
if saveOpt:
print 'Saved to ',filename
return phi,sigma,beta_
def updatePriorVals(self,weights,biases):
new_sW = np.zeros(self.sW.shape)
new_mean = np.zeros(self.mean.shape)
weights_cpu = weights.get()
n_w = np.float32(weights_cpu.shape[1])
shape_new = self.shape + n_w/2.0
for i in range(0,len(weights_cpu)):
scale_new = self.scale + ((weights_cpu[i])**2).sum()/2.0
new_val = invgamma.rvs(shape_new,scale=scale_new,size=1)
new_sW[0,i] = np.float32(new_val)
new_mean[0,i] = np.float32(scale_new/(shape_new-1.0))
#print 'New shape for feature ' + str(i+1) + ': ' + str(shape_new)
#print 'New scale for feature ' + str(i+1) + ': ' + str(1.0/rate_new)
#print 'New standard deviation for feature ' + str(i+1) + ': ' + str(new_val)
self.sW = gpuarray.to_gpu(new_sW.astype(self.precision))
self.mean = gpuarray.to_gpu(new_mean.astype(self.precision))
## Biases have common variance
biases_cpu = biases.get()
n_b = np.float32(biases.shape[1])
shape_new = self.shape + n_b/2.0
scale_new = self.scale + ((biases_cpu)**2).sum()/2.0
new_val = invgamma.rvs(shape_new,scale=scale_new,size=1)
new_sB = np.float32(new_val)
self.sB = gpuarray.to_gpu(new_sB)
def calculate_difference_m(Xs): # 人間すべてに対応
# step3の階差の計算--------------------------------------
# step3の階差計算の和の計算で使用する変数の初期化
dift = np.zeros(nhh, dtype=np.float)
difw = np.zeros(nhh, dtype=np.float)
difbeta = np.zeros((nhh, nz), dtype=np.float)
#
dift = np.sum((Xs[:, 0, 1:TIMES] - Xs[:, 0, 0:TIMES - 1])**2, axis=1)
difw = np.sum(
(Xs[:, k, 1:TIMES] +
np.sum(Xs[:, k:(k - 1) + SEASONALYTY - 1, 0:TIMES - 1], axis=1))**2,
axis=1)
for d in xrange(nz):
difbeta[:, d] = np.sum((Xs[:, (k - 1) + SEASONALYTY + d, 1:TIMES] -
Xs[:,
(k - 1) + SEASONALYTY + d, 0:TIMES - 1])**2,
axis=1)
# step3--------------------------------------
Sita_sys[:, 0, 0] = invgamma.rvs((nu0 + TIMES) / 2,
scale=(s0 + dift) / 2,
size=nhh)
Sita_sys[:, 1, 1] = invgamma.rvs((nu0 + TIMES) / 2,
scale=(s0 + difw) / 2,
size=nhh)
for d in xrange(nz):
Sita_sys[:, 2 + d, 2 + d] = invgamma.rvs(
(nu0 + TIMES) / 2, scale=(s0 + difbeta[:, d]) / 2, size=nhh)
return Sita_sys[:, :, :]
def __init__(self,shape,scale,layer,precision=np.float32):
self.precision = precision
self.shape = shape
self.scale = scale
init_var = invgamma.rvs(1.0,scale=1.0,size=(1,layer.weights.shape[1])).astype(precision)
self.sW = gpuarray.to_gpu(init_var)
init_var = invgamma.rvs(1.0,scale=1.0,size=(1,1)).astype(precision)
self.sB = gpuarray.to_gpu(init_var)
kernels = SourceModule(open(path+'/kernels.cu', "r").read())
self.add_prior_w_kernel = kernels.get_function("add_gaussian_unit_grad")
self.add_prior_b_kernel = kernels.get_function("add_bias_grad")
self.scale_momentum_kernel = kernels.get_function("scale_momentum_normal_unit")
def draw_expected_value(self, x, num_samples=1):
# draw a sample from normal innvgamma posterior which is
# same as expected reward given this model.
# TODO: check if it is actually the same with sampling from a student's t distribution
if num_samples > 1:
mu_tile = self.mu * np.ones(num_samples)
sigma_sqr_tile = []
for i in range(num_samples):
sigma_sqr_tile[i] = invgamma.rvs(self.alpha, scale=self.beta)
return np.random.normal(mu_tile, sigma_sqr_tile)
# first sample sigma^2 with inverse gamma
sigma_sqr = invgamma.rvs(self.alpha, scale=self.beta)
# then sample x from normal with self.mean and sigma^2/nu
return np.random.normal(self.mu, sigma_sqr / self.v)
def __init__(self, path=None, image_size=128, K_potts=10, beta_potts=1, mu_mean=1, mu_std=1, alpha=1, beta=10):
"""
:param path: Path of the image we want to compress. If no path is selected, a random gray scale image is
generated
:param image_size: the passed image will be resized to this size
:param K_potts: number of values possible for each component of the Potts model
:param beta_potts: The Beta parameter of the Potts model
:param mu_mean: parameter to compute the initial means of the mu vector
:param mu_std: parameter to compute the initial std of the mu vector
:param alpha: initial alpha parameter for the InvGamma law
:param beta: initial beta parameter for the InvGamma law
:var self.mu : initial value of the mu vector
:var self.sigma: initial value of the sigma vector
:var self.potts_values: initial value of each pixel in the Potts model
"""
if path is None:
self.image = np.random.randint(0, 256, size=(image_size, image_size))
else:
image = Image.open(path)
image.thumbnail((image_size, image_size), Image.ANTIALIAS)
gray_image = ImageOps.grayscale(image)
self.image = np.array(gray_image)
self.rows, self.columns = self.image.shape
self.k_potts = K_potts
self.beta_potts = beta_potts
self.mu_mean = np.arange(0, 255, 255 * mu_mean / self.k_potts)
self.mu_std = [mu_std] * self.k_potts
self.alpha = np.array([alpha] * self.k_potts)
self.beta = np.array([beta] * self.k_potts)
self.mu = np.random.normal(self.mu_mean, self.mu_std, self.k_potts)
self.sigma = invgamma.rvs(self.alpha, scale=self.beta, size=self.k_potts)
self.potts_values = np.zeros((self.rows, self.columns))
def linear(seq_length=30, num_samples=28*5*100, a0=10, b0=0.01, k=2, **kwargs):
"""
Generate data from linear trend from probabilistic model.
The invgamma function in scipy corresponds to wiki defn. of inverse gamma:
scipy a = wiki alpha = a0
scipy scale = wiki beta = b0
k is the number of regression coefficients (just 2 here, slope and intercept)
"""
T = np.zeros(shape=(seq_length, 2))
T[:, 0] = np.arange(seq_length)
T[:, 1] = 1 # equivalent to X
lambda0 = 0.01*np.eye(k) # diagonal covariance for beta
y = np.zeros(shape=(num_samples, seq_length, 1))
sigmasq = invgamma.rvs(a=a0, scale=b0, size=num_samples)
increasing = np.random.choice([-1, 1], num_samples) # flip slope
for n in range(num_samples):
sigmasq_n = sigmasq[n]
offset = np.random.uniform(low=-0.5, high=0.5) # todo limits
mu0 = np.array([increasing[n]*(1.0-offset)/seq_length, offset])
beta = multivariate_normal.rvs(mean=mu0, cov=sigmasq_n*lambda0)
epsilon = np.random.normal(loc=0, scale=np.sqrt(sigmasq_n), size=seq_length)
y[n, :, :] = (np.dot(T, beta) + epsilon).reshape(seq_length, 1)
marginal = partial(linear_marginal_likelihood, X=T, a0=a0, b0=b0, mu0=mu0, lambda0=lambda0)
samples = y
pdf = marginal
return samples, pdf
def update_sigma2(alpha, beta, gamma, b, G, n_i, uni_diet, id_g, uni_id, N_g, p, W, X, Z, y):
temp1 = (np.sum(N_g.values()) + np.sum(gamma))/2.0
temp3 = 0.0
for g_index in xrange(G):
g = uni_diet[g_index]
temp2 = 0.0
if np.all(gamma[g_index] == 0): #check if all gamma's are 0
for i in id_g[g]:
i_index = np.where(uni_id == i)[0][0]
temp2 += (y[i] - np.dot(W[i],alpha) - np.dot(Z[i], b[i_index].reshape(p, 1))).T.dot(y[i] - np.dot(W[i],alpha) - np.dot(Z[i], b[i_index].reshape(p, 1)))
temp3 += temp2
else: #if not all gamma's are 0
temp6 = XXsum(g_index, uni_diet, id_g, gamma, X)
temp5 = np.zeros([np.sum(gamma[g_index]),1])
for i in id_g[g]:
i_index = np.where(uni_id == i)[0][0]
temp2 += (y[i] - np.dot(W[i],alpha) - np.dot(X[i][:,gamma[g_index]!=0], beta[g_index][gamma[g_index]!=0].reshape(np.sum(gamma[g_index]),1)) - np.dot(Z[i], b[i_index].reshape(p, 1))).T.dot(y[i] - np.dot(W[i],alpha) - np.dot(X[i][:,gamma[g_index]!=0], beta[g_index][gamma[g_index]!=0].reshape(np.sum(gamma[g_index]),1)) - np.dot(Z[i], b[i_index].reshape(p, 1)))
temp5 += np.dot(X[i][:,gamma[g_index]!=0].T, y[i] - np.dot(W[i], alpha) - np.dot(Z[i], b[i_index].reshape(p, 1)))
temp4 = np.dot((beta[g_index][gamma[g_index]!=0].reshape(np.sum(gamma[g_index]),1) - pinv(temp6).dot(temp5)).T, temp6).dot(beta[g_index][gamma[g_index]!=0].reshape(np.sum(gamma[g_index]),1) - pinv(temp6).dot(temp5))
temp3 += temp2 + temp4/N_g[g]
temp3 = temp3/2.0
#update
sigma2_new = invgamma.rvs(temp1, scale = temp3, size = 1)
return sigma2_new
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 _sample_posterior_predictive(self, x_t, n_samples=1):
# p(sigma^2)
sigma_sq_t_list = [
invgamma.rvs(self._a_list[j], scale=self._b_list[j])
for j in range(self._n_actions)
]
try:
# p(w|sigma^2) = N(mu, sigam^2 * cov)
W_t = [
np.random.multivariate_normal(
self._mu_list[j], sigma_sq_t_list[j] * self._cov_list[j])
for j in range(self._n_actions)
]
except np.linalg.LinAlgError as e:
print("Error in {}".format(type(self).__name__))
print('Errors: {}.'.format(e.args[0]))
W_t = [
np.random.multivariate_normal(np.zeros(self._d),
np.eye(self._d))
for i in range(self._n_actions)
]
# p(r_new | params)
mean_t_predictive = np.dot(W_t, x_t)
cov_t_predictive = sigma_sq_t_list * np.eye(self._n_actions)
r_t_estimates = np.random.multivariate_normal(mean_t_predictive,
cov=cov_t_predictive,
size=1)
r_t_estimates = r_t_estimates.squeeze()
assert r_t_estimates.shape[0] == self._n_actions
return r_t_estimates
def mixture_model(self):
self.assignmentIteration = 0
self.parameterIteration = 0
if self.Util.alpha_initial_sample:
# concentration parameter prior: inverse gamma function with scale parameter: 1
self.alpha = invgamma.rvs(a=1, size=1)
else:
self.alpha = self.Util.alpha_initial
self.n = 1
self.K = 1
self.z.append(0)
# draw a new pattern for the first frame
wx, wy, pwx, pwy = self.Util.draw_w()
frame_first = []
frame_first.append(self.frames[0])
ux, uy, sigmax, sigmay, sigman = self.cov_mean(frame_first)
pattern_0 = MotionPattern(ux, uy, sigmax, sigmay, sigman, wx, wy)
pattern_0.update_para(self.frames[0])
self.b.append(pattern_0)
# update partition
self.partition = self.z2partition(self.z, self.K)
# from the second frame, do update assignment
for i in range(1, len(self.frames)):
self.n = i + 1
# first assign unseen frame to cluster 0
self.z.append(0)
# update assignment of frame i
self.update_assignment(i)
print('Initializing Frame: ', i, 'total frames: ',
len(self.frames))
def simulate(copula, n):
"""
Generates random variables with selected copula's structure.
Parameters
----------
copula : Copula
The Copula to sample.
n : integer
The size of the sample.
"""
d = copula.getDimension()
X = []
if type(copula).__name__ == "GaussianCopula":
# We get correlation matrix from covariance matrix
Sigma = copula.getCovariance()
D = sqrtm(np.diag(np.diag(Sigma)))
Dinv = inv(D)
P = np.dot(np.dot(Dinv, Sigma), Dinv)
A = cholesky(P)
for i in range(n):
Z = np.random.normal(size=d)
V = np.dot(A, Z)
U = stats.norm.cdf(V)
X.append(U)
elif type(copula).__name__ == "ArchimedeanCopula":
U = np.random.rand(n, d)
# LaplaceâStieltjes invert transform
LSinv = {
'clayton':
lambda theta: np.random.gamma(shape=1. / theta),
'gumbel':
lambda theta: stats.levy_stable.rvs(
1. / theta, 1., 0,
math.cos(math.pi / (2 * theta))**theta),
'frank':
lambda theta: stats.logser.rvs(1. - math.exp(-theta)),
'amh':
lambda theta: stats.geom.rvs(theta)
}
for i in range(n):
V = LSinv[copula.getFamily()](copula.getParameter())
X_i = [copula.inverseGenerator(-np.log(u) / V) for u in U[i, :]]
X.append(X_i)
elif type(copula).__name__ == "StudentCopula":
nu = copula.getFreedomDegrees()
Sigma = copula.getCovariance()
for i in range(n):
Z = multivariate_normal.rvs(size=1, cov=Sigma)
W = invgamma.rvs(nu / 2., size=1)
U = np.sqrt(W) * Z
X_i = [student.cdf(u, nu) for u in U]
X.append(X_i)
return X
def _sample_posterior_predictive(self, x_t, n_samples=1):
# 1. p(sigma^2)
sigma_sq_t = invgamma.rvs(self._a, scale=self._b)
try:
# p(w|sigma^2) = N(mu, sigam^2 * cov)
w_t = np.random.multivariate_normal(self._mu,
sigma_sq_t * self._cov)
except np.linalg.LinAlgError as e:
logger.debug("Error in {}".format(type(self).__name__))
logger.debug('Errors: {}.'.format(e.args[0]))
w_t = np.random.multivariate_normal(np.zeros(self._d),
np.eye(self._d))
# modify context
u_t, S_t = x_t
n_actions = S_t.shape[0]
x_ta = [
np.concatenate((u_t, S_t[j, :], [1])) for j in range(n_actions)
]
assert len(x_ta[0]) == self._d
# 2. p(r_new | params)
mean_t_predictive = [np.dot(w_t, x_ta[j]) for j in range(n_actions)]
cov_t_predictive = sigma_sq_t * np.eye(n_actions)
r_t_estimates = np.random.multivariate_normal(mean_t_predictive,
cov=cov_t_predictive,
size=1)
r_t_estimates = r_t_estimates.squeeze()
assert r_t_estimates.shape[0] == n_actions
return r_t_estimates
def sweep(sigma2, mu_0, sigma2_0, alpha, beta, data):
posterior_mean, posterior_variance = mean_posterior(
data, mu_0, sigma2_0, sigma2)
mu = norm.rvs(posterior_mean, scale=np.sqrt(posterior_variance))
posterior_alpha, posterior_beta = variance_posterior(data, alpha, beta, mu)
sigma2 = invgamma.rvs(posterior_alpha, scale=posterior_beta)
return mu, sigma2
def gibbs_sampler(selective_posterior,
nsample=2000,
nburnin=100,
proposal_scale=None,
step=1.):
state = selective_posterior.initial_estimate
stepsize = 1. / (step * selective_posterior.ntarget)
if proposal_scale is None:
proposal_scale = selective_posterior.inverse_info
sampler = langevin(state, selective_posterior.log_posterior,
proposal_scale, stepsize,
np.sqrt(selective_posterior.dispersion))
samples = np.zeros((nsample, selective_posterior.ntarget))
scale_samples = np.zeros(nsample)
scale_update = np.sqrt(selective_posterior.dispersion)
for i in range(nsample):
sample = sampler.__next__()
samples[i, :] = sample
scale_update_sq = invgamma.rvs(
a=(0.1 + selective_posterior.ntarget +
selective_posterior.ntarget / 2),
scale=0.1 - ((scale_update**2) * sampler.posterior_[0]),
size=1)
scale_samples[i] = np.sqrt(scale_update_sq)
sampler.scaling = np.sqrt(scale_update_sq)
return samples[nburnin:, :], scale_samples[nburnin:]
def action(self):
"""Samples beta's from posterior, and chooses best action accordingly.
Returns:
action: Selected action for the context.
"""
if len(self.data.positive_actions) == 0:
# Return fake positive action if run out of positives
return -1, np.zeros(self.data.actions_dim), self.data.positive_reward, self.data.positive_reward
# Sample sigma2, and beta conditional on sigma2
sigma2_s = self.b * invgamma.rvs(self.a)
try:
beta_s = np.random.multivariate_normal(self.mu, sigma2_s * self.cov)
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling from {}.'.format(self.hparams.name))
print('Details: {} | {}.'.format(str(e), e.args))
d = self.hparams.actions_dim + 1
beta_s = np.random.multivariate_normal(np.zeros(d), np.eye(d))
# Compute sampled expected rewards, intercept is last component of beta
pred_rs = [
np.dot(beta_s[:-1], action.T) + beta_s[-1]
for action in self.data.actions
]
action_i = np.argmax(pred_rs)
return action_i, self.data.actions[action_i], pred_rs[action_i], self.data.rewards[action_i]
def updates(self, particleNum, maxStage, xdata, ydata, dimNum,
hyper_sigma_1, hyper_sigma_2):
total_mu_mat = np.zeros((self.mTree, len(ydata)))
for mi in range(self.mTree):
total_mu_mat[mi] = self.add_dts[mi].assign_to_data(
len(self.add_dts[mi].z_label) - 1)
for mi in range(self.mTree):
add_dts_other_mu = np.sum(total_mu_mat, axis=0) - total_mu_mat[mi]
dts_mi = copy.deepcopy(self.add_dts[mi])
dts_mi.dts_update(particleNum, dts_mi, maxStage, xdata, ydata,
add_dts_other_mu)
total_mu_mat[mi] = dts_mi.assign_to_data(len(dts_mi.z_label) - 1)
self.add_dts[mi] = dts_mi
# update the hyper-parameters of the variance
posterior_hyper_sigma_1 = hyper_sigma_1 + len(
xdata) / 2 # the number refers to the number of terminal nodes
square_of_errors = np.sum((np.sum(total_mu_mat, axis=0) - ydata)**2)
posterior_hyper_sigma_2 = hyper_sigma_2 + square_of_errors / 2
self.true_var = invgamma.rvs(a=posterior_hyper_sigma_1,
loc=0,
scale=posterior_hyper_sigma_2)
# pass the self.true_var to each tree of the addtree
for add_dts_i in self.add_dts:
add_dts_i.true_var = self.true_var
def _sample(self, context, parallelize=False, n_threads=-1):
"""
Samples beta's from posterior, and samples from expected values.
Args:
context: Context for which the action need to be chosen.
Returns:
action: sampled reward vector."""
# Sample sigma2, and beta conditional on sigma2
context = context.reshape(-1, self.hparams['context_dim'])
n_rows = len(context)
a_projected = np.repeat(np.array(self.a)[np.newaxis, :],
n_rows,
axis=0)
sigma2_s = self.b * invgamma.rvs(a_projected)
if n_rows == 1:
sigma2_s = sigma2_s.reshape(1, -1)
beta_s = []
try:
for i in range(self.hparams['num_actions']):
global mus
global covs
mus = np.repeat(self.mu[i][np.newaxis, :], n_rows, axis=0)
s2s = sigma2_s[:, i]
rep = np.repeat(s2s[:, np.newaxis],
self.hparams['context_dim'] + 1,
axis=1)
rep = np.repeat(rep[:, :, np.newaxis],
self.hparams['context_dim'] + 1,
axis=2)
covs = np.repeat(self.cov[i][np.newaxis, :, :], n_rows, axis=0)
covs = rep * covs
if parallelize:
multivariates = parallelize_multivar(mus,
covs,
n_threads=n_threads)
else:
multivariates = [
np.random.multivariate_normal(mus[j], covs[j])
for j in range(n_rows)
]
beta_s.append(multivariates)
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
# Todo: Fix This
print('Exception when sampling from {}.'.format(self.name))
print('Details: {} | {}.'.format(e.message, e.args))
d = self.hparams['context_dim'] + 1
for i in range(self.hparams['num_actions']):
multivariates = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for j in range(n_rows)
]
beta_s.append(multivariates)
beta_s = np.array(beta_s)
# Compute sampled expected values, intercept is last component of beta
vals = [(beta_s[i, :, :-1] * context).sum(axis=-1) + beta_s[i, :, -1]
for i in range(self.hparams['num_actions'])]
return np.array(vals)
def draw_mus_and_sigmas(data, m0, k0, s_sq0, v0,n_samples=10000):
# number of samples
N = size(data)
# find the mean of the data
the_mean = mean(data)
# sum of squared differences between data and mean
SSD = sum( (data - the_mean)**2 )
# combining the prior with the data - page 79 of Gelman et al.
# to make sense of this note that
# inv-chi-sq(v,s^2) = inv-gamma(v/2,(v*s^2)/2)
kN = float(k0 + N)
mN = (k0/kN)*m0 + (N/kN)*the_mean
vN = v0 + N
vN_times_s_sqN = v0*s_sq0 + SSD + (N*k0*(m0-the_mean)**2)/kN
# 1) draw the variances from an inverse gamma
# (params: alpha, beta)
alpha = vN/2
beta = vN_times_s_sqN/2
# thanks to wikipedia, we know that:
# if X ~ inv-gamma(a,1) then b*X ~ inv-gamma(a,b)
sig_sq_samples = beta*invgamma.rvs(alpha,size=n_samples)
# 2) draw means from a normal conditioned on the drawn sigmas
# (params: mean_norm, var_norm)
mean_norm = mN
var_norm = sqrt(sig_sq_samples/kN)
mu_samples = norm.rvs(mean_norm,scale=var_norm,size=n_samples)
# 3) return the mu_samples and sig_sq_samples
return mu_samples, sig_sq_samples
def _sampling_s2_ep(self):
A_ep = self.A_ep
B_ep = self.B_ep
y = self.y
X = self.X
XTX = np.dot(X.T, X)
k = self.k
beta0 = self.params['beta0'][-1]
beta1 = self.params['beta1'][-1]
beta = np.array([beta0, beta1])
# parameters of full conditionals
shape = self.n / 2
scale = np.dot(
np.dot(X, beta).reshape(self.n) - y,
np.dot(X, beta).reshape(self.n) - y) / 2
# sampling from full conditionals
s2_ep = invgamma.rvs(a=shape, scale=scale, size=1)[0]
# update posterior samples
self.params['s2_ep'].append(s2_ep)
def action(self):
"""Samples beta's from posterior, and chooses best action accordingly."""
if len(self.data.positive_actions) == 0:
# Return fake positive action if run out of positives
return -1, np.zeros(
self.data.actions_dim
), self.data.positive_reward, self.data.positive_reward
# Sample sigma2, and beta conditional on sigma2
sigma2_s = self.b * invgamma.rvs(self.a)
try:
beta_s = np.random.multivariate_normal(self.mu,
sigma2_s * self.cov)
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling for {}.'.format(self.hparams.name))
print('Details: {} | {}.'.format(str(e), e.args))
d = self.latent_dim
beta_s = np.random.multivariate_normal(np.zeros(d), np.eye(d))
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
z_actions = self.bnn.sess.run(
self.bnn.nn, feed_dict={self.bnn.x: self.data.actions})
# Apply Thompson Sampling to last-layer representation
pred_rs = np.dot(beta_s, z_actions.T)
action_i = np.argmax(pred_rs)
return action_i, self.data.actions[action_i], pred_rs[
action_i], self.data.rewards[action_i]
def choose_arm(self, x: np.ndarray, step) -> np.ndarray:
"""腕の中から1つ選択肢し、インデックスを返す"""
if True in (self.counts < self.warmup):
result = np.argmax(np.array(self.counts < self.warmup))
else:
sigma2 = [
self._ig_b[i] * invgamma.rvs(self._ig_a[i])
for i in range(self.n_arms)
]
try:
beta = [
np.random.multivariate_normal(self._mu[i],
sigma2[i] * self._cov[i])
for i in range(self.n_arms)
]
except np.linalg.LinAlgError as e:
print('except')
d = self.n_features + 1
beta = [
np.random.multivariate_normal(np.zeros(d), np.identity(d))
for _ in range(self.n_arms)
]
vals = [
beta[i][:-1] @ x.T + beta[i][-1] for i in range(self.n_arms)
]
result = np.argmax(vals)
return result
def draw_mus(N, xbar, SSD, m0, k0, s_sq0, v0, n_samples=10000):
# SSD = variance
# combining the prior with the datva - page 79 of Gelman et al.
# to make sense of this note that
# inv-chi-sq(v,s^2) = inv-gamma(v/2,(v*s^2)/2)
kN = float(k0 + N)
mN = (k0 / kN) * m0 + (N / kN) * xbar
vN = v0 + N
vN_times_s_sqN = v0 * s_sq0 + SSD + (N * k0 * (m0 - xbar)**2) / kN
# 1) draw the variances from an inverse gamma
# (params: alpha, beta)
alpha = vN / 2
beta = vN_times_s_sqN / 2
# thanks to wikipedia, we know that:
# if X ~ inv-gamma(a,1) then b*X ~ inv-gamma(a,b)
sig_sq_samples = beta * invgamma.rvs(alpha, size=n_samples)
# 2) draw means from a normal conditioned on the drawn sigmas
# (params: mean_norm, var_norm)
mean_norm = mN
var_norm = sqrt(sig_sq_samples / kN)
mu_samples = norm.rvs(mean_norm, scale=var_norm, size=n_samples)
# 3) return the mu_samples and sig_sq_samples
return mu_samples
def gibbs_sampler(X, y, beta0, sigma_squared0, B0inv, alpha0, delta0, burn_in, sample_size):
'''Gibbs sampler for Bayesian normal linear regression model
See Greenberg p. 116, adapted for better numerical stability
'''
n = len(X)
k = len(beta0)
assert X.shape == (n, k)
alpha1 = alpha0 + n
# set up beta and sigma_squared chains
beta = np.zeros((burn_in + sample_size, k))
beta[0] = beta0
sigma_squared = np.zeros(burn_in + sample_size)
sigma_squared[0] = sigma_squared0
# compute some operations to save time later
XT = X.T
XTX = XT.dot(X)
XTy = XT.dot(y)
for i in range(1, burn_in + sample_size):
if i % 1000 == 0 or i == burn_in + sample_size - 1:
print(f'Sampling {i} / {burn_in + sample_size}')
B1inv = XTX / sigma_squared[i-1] + B0inv
# using cholesky decomp (since we need cholesky anyway), compute beta_bar
L = np.linalg.cholesky(B1inv)
beta_bar = solve_triangular(L.T, solve_triangular(L, XTy / sigma_squared[i-1] + B0inv.dot(beta0), lower=True))
beta[i] = multnorm_sampler(beta_bar, L=L)
Z = y - X.dot(beta[i])
delta = delta0 + Z.T.dot(Z)
sigma_squared[i] = invgamma.rvs(a=alpha1/2, scale=delta/2)
return beta, sigma_squared
def _sampling_s2_d(self):
A_d = self.A_d
B_d = self.B_d
n = self.n
z = self.z
one_vec = np.ones(n)
if self.current_iteration == 0:
x = self.params['x']
else:
x = self.params['x'][:, -1]
X = np.c_[one_vec, x]
gam0 = self.params['gam0'][-1]
gam1 = self.params['gam1'][-1]
gam = np.array([gam0, gam1])
# parameters of full conditionals
shape = A_d + n / 2
scale = B_d + np.dot(
np.dot(X, gam).reshape(self.n) - z,
np.dot(X, gam).reshape(self.n) - z) / 2
# sampling from full conditionals
s2_d = invgamma.rvs(a=shape, scale=scale, size=1)[0]
# update posterior samples
self.params['s2_d'].append(s2_d)
def _sampling_s2_ep(self):
A_ep = self.A_ep
B_ep = self.B_ep
if self.current_iteration == 0:
x = self.params['x']
else:
x = self.params['x'][:, -1]
y = self.y
one_vec = np.ones(self.n)
X = np.c_[one_vec, x]
beta0 = self.params['beta0'][-1]
beta1 = self.params['beta1'][-1]
beta = np.array([beta0, beta1])
# parameters of full conditionals
shape = A_ep + self.n / 2
scale = B_ep + np.dot(
np.dot(X, beta).reshape(self.n) - y,
np.dot(X, beta).reshape(self.n) - y) / 2
# sampling from full conditionals
s2_ep = invgamma.rvs(a=shape, scale=scale, size=1)[0]
# update posterior samples
self.params['s2_ep'].append(s2_ep)
def draw_mus_and_sigmas(data):
# number of samples
N = size(data)
# find the mean of the data
the_mean = mean(data)
# sum of squared differences between data and mean
SSD = sum((data - the_mean)**2)
# combining the prior with the data - page 79 of Gelman et al.
# to make sense of this note that
# inv-chi-sq(v,s^2) = inv-gamma(v/2,(v*s^2)/2)
kN = float(k0 + N)
mN = (k0 / kN) * m0 + (N / kN) * the_mean
vN = v0 + N
vN_times_s_sqN = v0 * s_sq0 + SSD + (N * k0 * (m0 - the_mean)**2) / kN
# 1) draw the variances from an inverse gamma
# (params: alpha, beta)
alpha = vN / 2
beta = vN_times_s_sqN / 2
# thanks to wikipedia, we know that:
# if X ~ inv-gamma(a,1) then b*X ~ inv-gamma(a,b)
sig_sq_samples = beta * invgamma.rvs(alpha)
# 2) draw means from a normal conditioned on the drawn sigmas
# (params: mean_norm, var_norm)
mean_norm = mN
var_norm = sqrt(sig_sq_samples / kN)
mu_samples = np.random.normal(mean_norm, var_norm)
# 3) return the mu_samples and std_devs
return mu_samples, sqrt(sig_sq_samples)
def sampleMeanAndVarianceForGaussianDataAndGelmansPriori(data,m0=0,k0=1,s_sq0=1,v0=1,samples=10000):
# actual observations
N = size(data)
data_mean = mean(data)
sum_sd = sum( (data - data_mean)**2 )
# combining the prior with the data - page 79 of Gelman et al.
# to make sense of this note that
# inv-chi-sq(v,s^2) = inv-gamma(v/2,(v*s^2)/2)
kN = float(k0 + N)
mN = (k0/kN)*m0 + (N/kN)*data_mean
vN = v0 + N
vN_times_s_sqN = v0*s_sq0 + sum_sd + (N*k0*(m0-data_mean)**2)/kN
# Sample \sigma^2 from the Inverse Gamma
# (params: alpha, beta)
# Note: if X ~ inv-gamma(a,1) then b*X ~ inv-gamma(a,b)
alpha = vN/2
beta = vN_times_s_sqN/2
variance_samples = beta*invgamma.rvs(alpha,size=samples)
# Sample \mu from a normal conditioned on the sampled \sigma^2
# (params: mean_norm, var_norm)
mean_norm = mN
var_norm = sqrt(variance_samples/kN)
mean_samples = norm.rvs(mean_norm,scale=var_norm,size=samples)
return mean_samples, variance_samples
def select_action(self, context: torch.Tensor) -> int:
"""Select an action based on given context.
Selects an action by computing a forward pass through network to output
a representation of the context on which bayesian linear regression is
performed to select an action.
Args:
context (torch.Tensor): The context vector to select action for.
Returns:
int: The action to take.
"""
self.model.use_dropout = self.eval_with_dropout
self.t += 1
if self.t < self.n_actions * self.init_pulls:
return torch.tensor(
self.t % self.n_actions, device=self.device, dtype=torch.int
)
var = torch.tensor(
[self.b[i] * invgamma.rvs(self.a[i]) for i in range(self.n_actions)],
device=self.device,
dtype=torch.float,
)
try:
beta = (
torch.tensor(
np.stack(
[
np.random.multivariate_normal(
self.mu[i], var[i] * self.cov[i]
)
for i in range(self.n_actions)
]
)
)
.to(self.device)
.to(torch.float)
)
except np.linalg.LinAlgError as e: # noqa F841
beta = (
(
torch.stack(
[
torch.distributions.MultivariateNormal(
torch.zeros(self.context_dim + 1),
torch.eye(self.context_dim + 1),
).sample()
for i in range(self.n_actions)
]
)
)
.to(self.device)
.to(torch.float)
)
results = self.model(context)
latent_context = results["x"]
values = torch.mv(beta, torch.cat([latent_context.squeeze(0), torch.ones(1)]))
action = torch.argmax(values).to(torch.int)
return action
def calculate_difference((hh, Xs)):
# step3の階差の計算--------------------------------------
# step3の階差計算の和の計算で使用する変数の初期化
dift = 0.
difw = 0.
difbeta = np.array([np.float(0)]*nz)
#
dift = sum( (Xs[hh,0,1:TIMES] - Xs[hh,0,0:TIMES-1])**2 )
difw = sum( (Xs[hh,k,1:TIMES]+sum(Xs[hh, k:(k-1)+SEASONALYTY-1, 0:TIMES-1]))**2 )
for d in xrange(nz):
difbeta[d] = sum( (Xs[hh, (k-1)+SEASONALYTY+d, 1:TIMES]
- Xs[hh, (k-1)+ SEASONALYTY+d, 0:TIMES-1])**2 )
# step3--------------------------------------
Sita_sys[hh,0,0] = invgamma.rvs((nu0+TIMES)/2, scale=(s0+dift)/2, size=1)[0]
Sita_sys[hh,1,1] = invgamma.rvs((nu0+TIMES)/2, scale=(s0+difw)/2, size=1)[0]
for d in xrange(nz):
Sita_sys[hh,2+d,2+d] = invgamma.rvs((nu0+TIMES)/2, scale=(s0+difbeta[d])/2, size=1)[0]
return Sita_sys[hh,:,:]
def draw_posterior_sigma2(model, states, phi, mu, prior_params=(5, 0.05)):
sigma_r, S_sigma = prior_params
v1 = sigma_r + model.nobs
tmp1 = (states[0, 0] - mu)**2 * (1 - phi**2)
tmp = np.sum(((states[0, 1:] - mu) - phi * (states[0, :-1] - mu))**2)
delta1 = S_sigma + tmp1 + tmp
return invgamma.rvs(v1, scale=delta1)
def calculate_difference_m(Xs): # 人間すべてに対応
# step3の階差の計算--------------------------------------
# step3の階差計算の和の計算で使用する変数の初期化
dift = np.zeros(nhh, dtype=np.float)
difw = np.zeros(nhh, dtype=np.float)
difbeta = np.zeros((nhh,nz), dtype=np.float)
dift = np.sum( (Xs[:,0,1:TIMES] - Xs[:,0,0:TIMES-1])**2, axis=1 )
difw = np.sum( (Xs[:,k,1:TIMES]+np.sum(Xs[:, k:(k-1)+SEASONALYTY-1, 0:TIMES-1], axis=1))**2, axis=1 )
for d in xrange(nz):
difbeta[:,d] = np.sum( (Xs[:, (k-1)+SEASONALYTY+d, 1:TIMES]
- Xs[:, (k-1)+ SEASONALYTY+d, 0:TIMES-1])**2, axis=1 )
# step3--------------------------------------
Sita_sys[:,0,0] = invgamma.rvs((nu0+TIMES)/2, scale=(s0+dift)/2, size=nhh)
Sita_sys[:,1,1] = invgamma.rvs((nu0+TIMES)/2, scale=(s0+difw)/2, size=nhh)
for d in xrange(nz):
Sita_sys[:,2+d,2+d] = invgamma.rvs((nu0+TIMES)/2, scale=(s0+difbeta[:,d])/2, size=nhh)
return Sita_sys[:,:,:]
def updatePriorVals(self,weights,biases):
new_sW = np.zeros(self.sW.shape)
weights_cpu = weights.get()
n_w = np.float32(weights_cpu.shape[0])
shape_new = self.shape + n_w/2.0
for i in range(0,weights_cpu.shape[1]):
scale_new = self.scale + ((weights_cpu[:,i])**2).sum()/2.0
new_val = invgamma.rvs(shape_new,scale=scale_new,size=1)
new_sW[0,i] = np.float32(new_val)
self.sW = gpuarray.to_gpu(new_sW.astype(self.precision))
## Biases have common variance
biases_cpu = biases.get()
n_b = np.float32(biases.shape[1])
shape_new = self.shape + n_b/2.0
scale_new = self.scale + ((biases_cpu)**2).sum()/2.0
new_val = invgamma.rvs(shape_new,scale=scale_new,size=1)
new_sB = np.float32(new_val)
self.sB = gpuarray.to_gpu(new_sB)
def updatePriorVals(self,weights,biases):
new_sW = np.zeros(self.sW.shape)
weights_cpu = weights.get()
n_w = np.float32(weights_cpu.shape[0]*weights_cpu.shape[1])
shape_new = self.shape + n_w/2.0
scale_new = self.scale + (weights_cpu**2).sum()/2.0
new_val = invgamma.rvs(shape_new,scale=scale_new,size=1)
#print 'New standard deviation for feature ' + ': ' + str(new_val)
new_sW = np.float32(new_val)
self.sW = gpuarray.to_gpu(new_sW.astype(self.precision))
## Biases have common variance
biases_cpu = biases.get()
n_b = np.float32(biases.shape[1])
shape_new = self.shape + n_b/2.0
scale_new = self.scale + ((biases_cpu)**2).sum()/2.0
new_val = invgamma.rvs(shape_new,scale=scale_new,size=1)
new_sB = np.float32(new_val)
self.sB = gpuarray.to_gpu(new_sB)
def simple_model_sample_prior():
vals = np.zeros(3 * components)
vals[:components] = \
np.exp(multivariate_normal.rvs(cov=COV_ALPHA*np.eye(components)))
for i in range(components, 2*components):
vals[i] = random.random() * (END - START) + START
vals[(2*components):(3*components)] = \
invgamma.rvs(A, LOC, SCALE, size=components)
return vals
def _resample_eta(self):
"""
Resample sigma under an inverse gamma prior, sigma ~ IG(1,1)
:return:
"""
L = self.L
a_prior = 1.0
b_prior = 1.0
a_post = a_prior + L.size / 2.0
b_post = b_prior + (L**2).sum() / 2.0
from scipy.stats import invgamma
self.eta = invgamma.rvs(a=a_post, scale=b_post)
def __init__(self,shape,scale,layer,precision=np.float32,init=100):
self.precision = precision
self.shape = shape
self.scale = scale
##initialize with random draw
#init_var = invgamma.rvs(shape,scale=scale,size=(1,layer.weights.shape[0])).astype(precision)
init_var = (np.tile(init,reps=layer.weights.shape[0]).reshape(1,layer.weights.shape[0])).astype(precision)
self.sW = gpuarray.to_gpu(init_var)
init_mean = (np.tile(self.scale/(self.shape-1),reps=layer.weights.shape[0]).reshape(1,layer.weights.shape[0])).astype(precision)
self.mean = gpuarray.to_gpu(init_mean)
init_var = invgamma.rvs(1.0,scale=1.0,size=(1,1)).astype(precision)
self.sB = gpuarray.to_gpu(init_var)
kernels = SourceModule(open(path+'/kernels.cu', "r").read())
self.add_prior_kernel = kernels.get_function("add_ARD_grad")
self.add_prior_b_kernel = kernels.get_function("add_bias_grad")
self.scale_momentum_kernel = kernels.get_function("scale_momentum_ARD")
self.scale_stepsize_kernel = kernels.get_function("scale_stepsize_ARD")
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly.
Args:
context: Context for which the action need to be chosen.
Returns:
action: Selected action for the context.
"""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i], sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling from {}.'.format(self.name))
print('Details: {} | {}.'.format(e.message, e.args))
d = self.hparams.context_dim + 1
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute sampled expected values, intercept is last component of beta
vals = [
np.dot(beta_s[i][:-1], context.T) + beta_s[i][-1]
for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i], sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling for {}.'.format(self.name))
print('Details: {} | {}.'.format(e.message, e.args))
d = self.latent_dim
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
# Apply Thompson Sampling to last-layer representation
vals = [
np.dot(beta_s[i], z_context.T) for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def resample(self,data=[]):
return
if self.bayesian:
# Compute the states matrix of the whole sequence given the other chains' states
global_state = self.l + self.others
# Correct the overflow in the bias term
global_state[-1, :] = 1.
# Sanity check
assert global_state[global_state > 1].any() == False, "There is a problem rebuilding the global state matrix"
w = self.W*global_state #These should be numpy's matrix objects so this works
# Reconstruct the indices of the data
data = data[0]
idx = np.zeros(data.shape[0], dtype=int)
for i in xrange(data.shape[0]):
idx[i] = np.where(np.all(self.global_data == data[i, :], axis=1))[0]
# Compute the sum of squared errors
centered = np.power(data - w.T[idx, :], 2)
sse = np.sum(centered, axis=0)
variances = np.ones(sse.shape[1])
# Resample the variances
for i in xrange(sse.shape[1]):
alpha = self.ah + (self.global_data.shape[0]/2.)
beta = 1. /(self.bh + (sse[0, i]/2.))
sample = invgamma.rvs(alpha, beta)
variances[i] = sample
self.variances = variances
#
# step3の階差の計算--------------------------------------
dift = sum((Xs[hh, 0, 1:TIMES] - Xs[hh, 0, 0 : TIMES - 1]) ** 2)
difw = sum((Xs[hh, k, 1:TIMES] + sum(Xs[hh, k : (k - 1) + SEASONALYTY - 1, 0 : TIMES - 1])) ** 2)
for d in range(nz):
difbeta[d] = sum(
(Xs[hh, (k - 1) + SEASONALYTY + d, 1:TIMES] - Xs[hh, (k - 1) + SEASONALYTY + d, 0 : TIMES - 1]) ** 2
)
# --------------------------------------------------------
#
# step4の効用値の誤差計算(step4のθの尤度計算)------------
Lsita = sum((u[hh, :] - np.diag(np.dot(Ztld[:, :, hh].T, Xs[hh, :, :]))) ** 2)
# --------------------------------------------------------
#
# step3--------------------------------------
Sita_sys[hh, 0, 0] = invgamma.rvs((nu0 + TIMES) / 2, scale=(s0 + dift) / 2, size=1)[0]
Sita_sys[hh, 1, 1] = invgamma.rvs((nu0 + TIMES) / 2, scale=(s0 + difw) / 2, size=1)[0]
for d in range(nz):
Sita_sys[hh, 2 + d, 2 + d] = invgamma.rvs((nu0 + TIMES) / 2, scale=(s0 + difbeta[d]) / 2, size=1)[0]
# --------------------------------------------
#
### step4--------------------------------------
## '''dlt側の計算'''
# 現状のθを確保する
old_sita_dlt = Sita_dlt[hh]
# 新しいθをサンプリング（酔歩サンプリング）
new_sita_dlt = Sita_dlt[hh] + ss.norm.rvs(loc=0, scale=sigma_dlt, size=1)[0]
#
# 尤度の計算（対数尤度の場合はヤコビアンで調整）
new_Lsita_dlt = Lsita + hbm.Nkernel(new_sita_dlt, Hdlt, D[hh, :], Vsita_dlt)
new_Lsita_dlt = math.exp(-0.5 * new_Lsita_dlt)
for i, component in enumerate(components):
states[i, :] = component.states_list[0].stateseq
# Now compute the means
means = np.matrix(weights)*states
# Squared summed error
sse = np.power(observations - means.T, 2).sum(axis=0)
# Learn the new variances
new_variances = np.zeros((1, sse.shape[1]))
for i in xrange(sse.shape[1]):
alpha = .05 + (observations.shape[0]/ 2.)
beta = (.05 + (sse[0, i]/2.))
new_variances[0, i] = invgamma.rvs(alpha, scale=beta)
# Delete the states to avoid memory leaks
del states
for component in components:
# The number of components plus a bias term
global_states = np.zeros((COMP+1, observations.shape[0]))
global_states[-1, :] = 1. # The bias term
for i, other in enumerate(components):
# Only if this is another chain
if other != component:
seq = other.states_list[0].stateseq
global_states[i, :] = seq
def getUpdates(self):
return invgamma.rvs(a = self.a, scale = self.scale, size = 1)
def sample(self):
''' Samples a mean and stdev from the Normal-InverseGamma distribution. '''
variance = invgamma.rvs(self.a, scale=self.b)
mean = np.random.normal(self.mu, np.sqrt(variance / self.nu))
return (mean, np.sqrt(variance))
def _sample(self, shape, scale, size):
return invgamma.rvs(shape, scale=scale, size=size)
def estimate(self, xs, max_iterations=10000):
self.n = len(xs)
self.s2 = invgamma.rvs(self.alpha, scale=self.beta)
self.means = []
response_sums = []
self.counts = []
assignments = []
assignments.append(0)
response_sums.append(xs[0])
self.counts.append(1)
self.means.append(self.sample_posterior_mean(response_sums[0], 1,
self.s2, self.m0,
self.s20))
for i in range(1, len(xs)):
weights = self.__create_weight_vector(xs[i], self.means,
self.counts, self.s2,
self.m0, self.s20,
self.m)
# Sample an assignment for each item and update statistics
assignment = multinomial_sampling.sample(weights)
if assignment < len(self.means):
response_sums[assignment] += xs[i]
self.counts[assignment] += 1
# Create a new component
elif assignment == len(self.means):
response_sums.append(xs[i])
self.counts.append(1)
self.means.append(self.sample_posterior_mean(xs[i], 1,
self.s2, self.m0,
self.s20))
else:
print("WWWWW Should never get here. WWWWWW")
assignments.append(assignment)
for i in xrange(max_iterations):
# First sample an assignment for each data item
for j in xrange(len(xs)):
old_assignment = assignments[j]
response_sums[old_assignment] -= xs[j]
self.counts[old_assignment] -= 1
if self.counts[old_assignment] == 0:
self.__fix_hole(assignments, response_sums, self.means,
self.counts, old_assignment)
weights = self.__create_weight_vector(xs[j], self.means,
self.counts,
self.s2, self.m0,
self.s20, self.m)
new_assignment = multinomial_sampling.sample(weights)
# Create a new component
if new_assignment < len(self.means):
response_sums[new_assignment] += xs[j]
self.counts[new_assignment] += 1
elif new_assignment == len(self.means):
response_sums.append(xs[j])
self.counts.append(1)
self.means.append(self.sample_posterior_mean(xs[j], 1,
self.s2,
self.m0,
self.s20))
else:
print("EEEEEEE This should never happenEEEEEEEEEE")
assignments[j] = new_assignment
# Sample new values for the means
for j in xrange(len(self.means)):
self.means[j] = self.sample_posterior_mean(response_sums[j],
self.counts[j],
self.s2, self.m0,
self.s20)
# Sample new value for the component variance
res_sum_squares = self.calculate_res_sum_squares(xs, assignments,
self.means)
self.s2 = self.sample_posterior_var(self.n, res_sum_squares,
self.alpha, self.beta)
return self
def sample_posterior_var(self, n, res_sum_squares, alpha, beta):
alpha_star = alpha + (n / 2.)
beta_star = beta + (res_sum_squares / 2.)
return invgamma.rvs(alpha_star, scale=beta_star)
def rchisquare_inv_scaled(df,scale,size=None):
a = df/2.0
b = (df*scale)/2.0
# size=None returns a scalar
return invgamma.rvs(a,scale=b,size=size)
def sample_physics():
"""
Return a physics object with all the model parameters sampled from their
appropriate hyperpriors.
"""
T = 3600 # an episode is 3600 seconds
R = 6371 # the radius of the earth in km
# event rate
lambda_e = gamma.rvs(6.0, loc=0, scale = 1/(4 * pi * R**2 * T))
# event magnitude
mu_m = 3.0
theta_m = 4.0
gamma_m = 6.0
# Note: the correct choice of theta_m should be 0.75.
# We have chosen a large value here to force larger events and hence
# allow for easier detection. If the full set of 180 stations are ever used
# then we can correct theta_m.
# station-specific attributes
mu_d0, mu_d1, mu_d2 = [], [], []
mu_t, theta_t, mu_z, theta_z, mu_s, theta_s = [], [], [], [], [], []
mu_a0, mu_a1, mu_a2, sigma_a = [], [], [], []
lambda_f, mu_f, theta_f = [], [], []
for sta in STATIONS:
# per-station detection probability
(d0, d1, d2) = mvar_norm_sample(array([-10.4, 3.26, -0.0499]),
array([[13.43,-2.36, -.0122],
[-2.36, 0.452, .000112],
[-.0122, .000112, .000125]]))
mu_d0.append(d0)
mu_d1.append(d1)
mu_d2.append(d2)
# time
mu_t.append(0.0)
theta_t.append(invgamma.rvs(120, 0.0, 118))
# azimuth
mu_z.append(0.0)
theta_z.append(invgamma.rvs(5.2, 0.0, 44.0))
# slowness
mu_s.append(0.0)
theta_s.append(invgamma.rvs(6.7, 0.0, 7.5))
# amplitude
(a0, a1, a2) = mvar_norm_sample(array([-7.3, 2.03, -.00196]),
array([[1.23, -.227, -.000175],
[-.227, .0461, .0000245],
[-.000175, .0000245, .000000302]]))
mu_a0.append(a0)
mu_a1.append(a1)
mu_a2.append(a2)
sigma_a.append(sqrt(invgamma.rvs(21.1, 0, 12.6)))
# false arrivals
lambda_f.append(gamma.rvs(2.1, 0, 0.0013))
mu_f.append(norm.rvs(-0.68, 0.68))
theta_f.append(invgamma.rvs(23.5, 0, 12.45))
return Physics(T, R, lambda_e, mu_m, theta_m, gamma_m, mu_d0, mu_d1, mu_d2,
mu_t, theta_t, mu_z, theta_z, mu_s, theta_s,
mu_a0, mu_a1, mu_a2, sigma_a,
lambda_f, mu_f, theta_f)
