def rvs(self, size):
# if self.df == np.inf:
# x = 1.
# else:
# x = np.random.chisquare(self.df, size)/self.df
# z = np.random.multivariate_normal(np.zeros(self.d), self.cov, (size,))
# return self.loc + z/np.sqrt(x)[:,None]
if isinstance(self.loc, list):
assert size in self.loc.shape, "If loc is a list of vectors, it should have same length with size."
return [stats.multivariate_t(df=self.df, loc=mu, shape=self.cov).rvs(size=1) for mu in self.loc]
else:
return stats.multivariate_t(df=self.df, loc=self.loc, shape=self.cov).rvs(size=size)
def simulate_data(self, p_sample, n_obs):
"""
Returns a dataset given a sample from the prior.
"""
D = p_sample.shape[0] // 2
mu, sd = p_sample[:D], p_sample[D:]
x = stats.multivariate_t(loc=mu, shape=np.diag(sd),
df=self.df).rvs(n_obs)
return x
def get_trajectories(self,
J,
H_grid,
parameter,
distr_name: str,
log_hubs=False,
quantile=float('nan'),
matrix='hard'):
multivariate = False
if distr_name == 'no_distr':
distribution = sps.norm(loc=0, scale=0)
elif distr_name == 'norm':
distribution = sps.norm(loc=0, scale=parameter)
elif distr_name == 'student':
distribution = sps.t(df=parameter)
elif distr_name == 'multivariate_norm':
multivariate = True
if matrix == 'simple':
cov_matrix = (1 - parameter) * np.eye(
self.N) + parameter * np.ones((self.N, self.N))
distribution = sps.multivariate_normal(cov=cov_matrix)
else:
distribution = sps.multivariate_normal(
cov=self.__get_correlation_matrix(parameter))
elif distr_name == 'multivariate_student':
multivariate = True
distribution = sps.multivariate_t(
df=3.5, shape=3 / 7 * self.__get_correlation_matrix(parameter))
else:
raise NotImplementedError('Unknown distribution')
fractions_low_to_high, fractions_high_to_low = [], []
self.sample_fields(distribution, multivariate)
self.set_state(-np.ones(self.N))
if not log_hubs:
for H in H_grid:
new_state = self.get_stable_state(H, J)
fractions_low_to_high.append(np.mean(new_state + 1) / 2)
for H in np.flip(H_grid):
new_state = self.get_stable_state(H, J)
fractions_high_to_low.append(np.mean(new_state + 1) / 2)
return fractions_low_to_high, fractions_high_to_low
hubs_low_to_high, hubs_high_to_low = [], []
for H in H_grid:
new_state, changed_hubs = self.get_stable_state(
H, J, log_hubs, quantile)
fractions_low_to_high.append(np.mean(new_state + 1) / 2)
hubs_low_to_high.append(changed_hubs)
for H in np.flip(H_grid):
new_state, changed_hubs = self.get_stable_state(
H, J, log_hubs, quantile)
fractions_high_to_low.append(np.mean(new_state + 1) / 2)
hubs_high_to_low.append(changed_hubs)
return fractions_low_to_high, fractions_high_to_low, hubs_low_to_high, hubs_high_to_low
def mv_student_neg_logpdf_packed(x, ndim, data, corr=None, verbose=False):
if corr is not None:
rho_mapped = map_rho(corr)
x = np.insert(x, 1, rho_mapped)
df, loc, scale = unpack_mv_t_args(x, ndim)
try:
dist = stats.multivariate_t(loc=loc, shape=scale, df=df)
except (np.linalg.LinAlgError, ValueError) as e:
if verbose:
print(e, df, loc, scale)
return np.inf
return -dist.logpdf(data).sum()
def simulate_data(self, p_sample, n_obs):
"""
Returns a single dataset given a sample from the prior.
Parameters
----------
p_sample: np.ndarray
One set of parameter samples for one multivariate t distribution
n_obs: int
Number of observations
"""
D = p_sample.shape[0] // 2
mu, sd = p_sample[:D], p_sample[D:]
x = stats.multivariate_t(loc=mu, shape=np.diag(sd),
df=self.df).rvs(n_obs)
return x
def radial_student_t_integral(r_max, df, ndim):
from scipy import integrate
vec = np.zeros(ndim)
vec[0] = 1
if ndim == 1:
dist = stats.t(df=df, loc=0, scale=1)
def _integrand(r):
return 2 * dist.pdf(r * vec)
elif ndim == 2:
dist = stats.multivariate_t(df=df, loc=np.zeros(ndim), shape=np.eye(ndim))
def _integrand(r):
return r * 2 * np.pi * dist.pdf(r * vec)
else:
raise NotImplementedError("Not implemented for ndim > 2")
integral, err = integrate.quad(_integrand, a=0, b=r_max)
return integral
def _kth_likelihood(self, k):
return stats.multivariate_t(loc=self.means_[:,k],
shape=self.covariance_[k,:,:],
df=self.dofs_[k],
allow_singular=True)
def logpdf(self, x):
return stats.multivariate_t(df=self.df, loc=self.loc, shape=self.cov).logpdf(x=x)