def simulate_data(self, Sigma_x=None, seed=None):
"""Simulate data from the model.
Returns models.common.data instance
Parameters
----------
Sigma_x : {None, 'rand', ndarray}
The covariance structure of the explanatory variable. This is
scaled to regulate the uncertainty. If not provided or None,
identity matrix is used. Providing string 'rand' uses method
common.rand_corr_vine to randomise one.
"""
# Localise params
J = self.J
D = self.D
npg = self.npg
# Set seed
rnd_data = np.random.RandomState(seed=seed)
# Draw random seed for input covariance for consistency in randomness
# even if not needed
seed_input_cov = rnd_data.randint(2**31-1)
# Randomise input covariance structure if needed
if Sigma_x == 'rand':
Sigma_x = rand_corr_vine(D, seed=seed_input_cov)
# Parameters
# Number of observations for each group
if hasattr(npg, '__getitem__') and len(npg) == 2:
Nj = rnd_data.randint(npg[0],npg[1]+1, size=J)
else:
Nj = npg*np.ones(J, dtype=np.int64)
# Total number of observations
N = np.sum(Nj)
# Observation index limits for J groups
j_lim = np.concatenate(([0], np.cumsum(Nj)))
# Group indices for each sample
j_ind = np.empty(N, dtype=np.int64)
for j in xrange(J):
j_ind[j_lim[j]:j_lim[j+1]] = j
# Assign parameters
if SIGMA is None:
sigma = np.exp(rnd_data.randn()*SIGMA_H)
else:
sigma = SIGMA
if SIGMA_A is None:
sigma_a = np.exp(rnd_data.randn()*SIGMA_AH)
else:
sigma_a = SIGMA_A
if BETA is None:
beta = rnd_data.randn(D)*SIGMA_B
else:
beta = BETA
# Regulate beta
beta_sum = np.sum(beta)
while np.abs(beta_sum) < B_ABS_MIN_SUM:
# Replace one random element in beta
index = rnd_data.randint(D)
beta_sum -= beta[index]
beta[index] = rnd_data.randn()*SIGMA_B
beta_sum += beta[index]
alpha_j = rnd_data.randn(J)*sigma_a
phi_true = np.empty(self.dphi)
phi_true[0] = np.log(sigma)
phi_true[1] = np.log(sigma_a)
phi_true[2:] = beta
# Determine suitable sigma_x
sigma_x = calc_input_param_lin_reg(beta, sigma, Sigma_x)
# Simulate data
if Sigma_x is None:
X = rnd_data.randn(N,D)*sigma_x
else:
cho_x = cholesky(Sigma_x)
X = rnd_data.randn(N,D).dot(sigma_x*cho_x)
y_true = alpha_j[j_ind] + X.dot(beta)
y = y_true + rnd_data.randn(N)*sigma
return data(
X, y, {'sigma_x':sigma_x, 'Sigma_x':Sigma_x}, y_true, Nj, j_lim,
j_ind, {'phi':phi_true, 'alpha':alpha_j, 'beta':beta,
'sigma':sigma}
)
def simulate_data(self, Sigma_x=None, seed=None):
"""Simulate data from the model.
Returns models.common.data instance
Parameters
----------
Sigma_x : {None, 'rand', ndarray}
The covariance structure of the explanatory variable. This is
scaled to regulate the uncertainty. If not provided or None,
identity matrix is used. Providing string 'rand' uses method
common.rand_corr_vine to randomise one.
"""
# Localise params
J = self.J
D = self.D
npg = self.npg
# Set seed
rnd_data = np.random.RandomState(seed=seed)
# Draw random seed for input covariance for consistency in randomness
# even if not needed
seed_input_cov = rnd_data.randint(2 ** 31 - 1)
# Randomise input covariance structure if needed
if Sigma_x == "rand":
Sigma_x = rand_corr_vine(D, seed=seed_input_cov)
# Parameters
# Number of observations for each group
if hasattr(npg, "__getitem__") and len(npg) == 2:
Nj = rnd_data.randint(npg[0], npg[1] + 1, size=J)
else:
Nj = npg * np.ones(J, dtype=np.int64)
# Total number of observations
N = np.sum(Nj)
# Observation index limits for J groups
j_lim = np.concatenate(([0], np.cumsum(Nj)))
# Group indices for each sample
j_ind = np.empty(N, dtype=np.int64)
for j in xrange(J):
j_ind[j_lim[j] : j_lim[j + 1]] = j
# Assign parameters
if SIGMA is None:
sigma = np.exp(rnd_data.randn() * SIGMA_H)
else:
sigma = SIGMA
if SIGMA_A is None:
sigma_a = np.exp(rnd_data.randn() * SIGMA_SA)
else:
sigma_a = SIGMA_A
if MU_A is None:
mu_a = rnd_data.randn() * SIGMA_MA
else:
mu_a = MU_A
sigma_b = np.exp(rnd_data.randn(D) * SIGMA_SB)
mu_b = rnd_data.randn(D) * SIGMA_MB
alpha_j = mu_a + rnd_data.randn(J) * sigma_a
beta_j = mu_b + rnd_data.randn(J, D) * sigma_b
# Regulate beta
for j in xrange(J):
beta_sum = np.sum(beta_j[j])
while np.abs(beta_sum) < B_ABS_MIN_SUM:
# Replace one random element in beta
index = rnd_data.randint(D)
beta_sum -= beta_j[j, index]
beta_j[j, index] = mu_b[index] + rnd_data.randn() * sigma_b[index]
beta_sum += beta_j[j, index]
phi_true = np.empty(self.dphi)
phi_true[0] = np.log(sigma)
phi_true[1] = mu_a
phi_true[2] = np.log(sigma_a)
phi_true[3 : 3 + D] = mu_b
phi_true[3 + D :] = np.log(sigma_b)
# Determine suitable sigma_x
sigma_x_j = calc_input_param_lin_reg(beta_j, sigma, Sigma_x)
# Simulate data
# Different sigma_x for every group
X = np.empty((N, D))
if Sigma_x is None:
for j in xrange(J):
X[j_lim[j] : j_lim[j + 1], :] = rnd_data.randn(Nj[j], D) * sigma_x_j[j]
else:
cho_x = cholesky(Sigma_x)
for j in xrange(J):
X[j_lim[j] : j_lim[j + 1], :] = rnd_data.randn(Nj[j], D).dot(sigma_x_j[j] * cho_x)
y_true = np.empty(N)
for n in xrange(N):
y_true[n] = alpha_j[j_ind[n]] + X[n].dot(beta_j[j_ind[n]])
y = y_true + rnd_data.randn(N) * sigma
return data(
X,
y,
{"sigma_x": sigma_x_j, "Sigma_x": Sigma_x},
y_true,
Nj,
j_lim,
j_ind,
{"phi": phi_true, "alpha": alpha_j, "beta": beta_j, "sigma": sigma},
)