def covariance_pdf(density, x_cond, n_samples=10**6):
covs = np.zeros((x_cond.shape[0], density.ndim_y, density.ndim_y))
mean = density.mean_(x_cond)
for i in range(x_cond.shape[0]):
x = x = np.tile(x_cond[i].reshape((1, x_cond[i].shape[0])),
(n_samples, 1))
def cov(y):
a = (y - mean[i])
#compute cov matrices c for sampled instances and weight them with the probability p from the pdf
c = np.empty((a.shape[0], a.shape[1]**2))
for j in range(a.shape[0]):
c[j, :] = np.outer(a[j], a[j]).flatten()
p = np.tile(np.expand_dims(density.pdf(x, y), axis=1),
(1, density.ndim_y**2))
res = c * p
return res
integral = mc_integration_student_t(cov,
ndim=density.ndim_y,
n_samples=n_samples)
covs[i] = integral.reshape((density.ndim_y, density.ndim_y))
return covs
def _divergence_mc(p, q, x_cond, divergenc_fun, n_samples=10**5, n_measures=1):
assert x_cond.ndim == 2 and x_cond.shape[1] == q.ndim_x
P = p.pdf
Q = q.pdf
def _div(x_tiled, y_samples):
p = P(x_tiled, y_samples).flatten()
q = Q(x_tiled, y_samples).flatten()
q = np.ma.masked_where(q < 10**-64, q).flatten()
p = np.ma.masked_where(p < 10**-64, p).flatten()
r = divergenc_fun(p, q)
return r.filled(0)
if n_measures == 1:
distances = np.zeros(x_cond.shape[0])
else:
distances = np.zeros((x_cond.shape[0], n_measures))
mu_proposal, std_proposal = p._determine_mc_proposal_dist()
for i in range(x_cond.shape[0]):
x = np.tile(x_cond[i].reshape((1, x_cond[i].shape[0])), (n_samples, 1))
func = lambda y: _make_2d(_div(x, y))
distances[i] = mc_integration_student_t(func,
q.ndim_y,
n_samples=n_samples,
loc_proposal=mu_proposal,
scale_proposal=std_proposal)
assert distances.shape[0] == x_cond.shape[0]
return distances
def test_mc_integration_t_1(self):
func = lambda y: np.expand_dims(stats.multivariate_normal.pdf(
y, mean=[0, 0], cov=np.diag([2, 2])),
axis=1)
integral = mc_integration_student_t(func,
ndim=2,
n_samples=10**7,
batch_size=10**6)
self.assertAlmostEqual(1.0, integral[0], places=2)
def mean_pdf(density, x_cond, n_samples=10**6):
means = np.zeros((x_cond.shape[0], density.ndim_y))
for i in range(x_cond.shape[0]):
x = x = np.tile(x_cond[i].reshape((1, x_cond[i].shape[0])),
(n_samples, 1))
func = lambda y: y * np.tile(np.expand_dims(density.pdf(x, y), axis=1),
(1, density.ndim_y))
integral = mc_integration_student_t(func, ndim=2, n_samples=n_samples)
means[i] = integral
return means
def _mean_pdf(self, x_cond, n_samples=10**6):
means = np.zeros((x_cond.shape[0], self.ndim_y))
for i in range(x_cond.shape[0]):
mean_fun = lambda y: y
if self.ndim_y == 1:
n_samples_int, lower, upper = self._determine_integration_bounds(
)
func_to_integrate = lambda y: mean_fun(y) * np.squeeze(
self._tiled_pdf(y, x_cond[i], n_samples_int))
integral = numeric_integation(func_to_integrate, n_samples_int,
lower, upper)
else:
loc_proposal, scale_proposal = self._determine_mc_proposal_dist(
)
func_to_integrate = lambda y: mean_fun(y) * self._tiled_pdf(
y, x_cond[i], n_samples)
integral = mc_integration_student_t(
func_to_integrate,
ndim=self.ndim_y,
n_samples=n_samples,
loc_proposal=loc_proposal,
scale_proposal=scale_proposal)
means[i] = integral
return means
def _covariance_pdf(self, x_cond, n_samples=10**6, mean=None):
assert hasattr(self, "mean_")
assert hasattr(self, "pdf")
assert mean is None or mean.shape == (x_cond.shape[0], self.ndim_y)
loc_proposal, scale_proposal = self._determine_mc_proposal_dist()
if mean is None:
mean = self.mean_(x_cond, n_samples=n_samples)
covs = np.zeros((x_cond.shape[0], self.ndim_y, self.ndim_y))
for i in range(x_cond.shape[0]):
x = x = np.tile(x_cond[i].reshape((1, x_cond[i].shape[0])),
(n_samples, 1))
def cov(y):
a = (y - mean[i])
# compute cov matrices c for sampled instances and weight them with the probability p from the pdf
c = np.empty((a.shape[0], a.shape[1]**2))
for j in range(a.shape[0]):
c[j, :] = np.reshape(np.outer(a[j], a[j]),
(a.shape[1]**2, ))
p = np.tile(np.expand_dims(self.pdf(x, y), axis=1),
(1, self.ndim_y**2))
res = c * p
return res
integral = mc_integration_student_t(cov,
ndim=self.ndim_y,
n_samples=n_samples,
loc_proposal=loc_proposal,
scale_proposal=scale_proposal)
covs[i] = integral.reshape((self.ndim_y, self.ndim_y))
return covs