def _expectation(self, z):
with torch.no_grad():
# computing wik
pdf = df.gaussianPDF(z,
self._mu,
self._sigma,
norm_func=self.zeta_phi.zeta)
if (pdf.mean() != pdf.mean()):
print("EXPECTATION : pdf contain not a number elements")
quit()
p_pdf = pdf * self._w.unsqueeze(0).expand_as(pdf)
# it can happens sometime to get (due to machine precision) a node with all pdf to zero
# in this case we must detect it. There is severall solution, in our case we affect it
# equally to each gaussian.
if (p_pdf.sum(-1).min() <= 1e-15):
if (self._verbose):
print("EXPECTATION : pdf.sum(-1) contain zero for ",
(p_pdf.sum(-1) <= 1e-15).sum().item(), "items")
p_pdf[p_pdf.sum(-1) <= 1e-15] = 1
wik = p_pdf / p_pdf.sum(-1, keepdim=True).expand_as(pdf)
if (wik.mean() != wik.mean()):
print("EXPECTATION : wik contain not a number elements")
quit()
# print(wik.mean(0))
if (wik.sum(1).mean() <= 1 - 1e-4
and wik.sum(1).mean() >= 1 + 1e-4):
print("EXPECTATION : wik don't sum to 1")
print(wik.sum(1))
quit()
return wik
def get_density(self, z):
N, D, M = z.shape + (self._mu.shape[0], )
pdf = df.gaussianPDF(z,
self._mu,
self._sigma,
norm_func=self.zeta_phi.zeta)
density = (pdf * self._w.unsqueeze(0).expand_as(pdf)).sum(-1)
return density
def get_unormalized_probs(self, z):
N, D, M = z.shape + (self._mu.shape[0], )
pdf = df.gaussianPDF(z,
self._mu,
self._sigma,
norm_func=self.zeta_phi.zeta)
p_pdf = pdf * self._w.unsqueeze(0).expand_as(pdf)
return p_pdf
def predict(self, z):
N, D, M = z.shape + (self._mu.shape[0], )
pdf = df.gaussianPDF(z,
self._mu,
self._sigma,
norm_func=self.zeta_phi.zeta)
p_pdf = pdf * self._w.unsqueeze(0).expand_as(pdf)
return p_pdf.max(-1)[1]
def get_pik(self, z):
N, D, M = z.shape + (self._mu.shape[0], )
pdf = df.gaussianPDF(z,
self._mu,
self._sigma,
norm_func=self.zeta_phi.zeta)
p_pdf = pdf * self._w.unsqueeze(0).expand_as(pdf)
if (p_pdf.sum(-1).min() == 0):
print(
"EXPECTATION (function get_pik) : pdf.sum(-1) contain zero for ",
(p_pdf.sum(-1) <= 1e-15).sum().item(), "items")
p_pdf[p_pdf.sum(-1) == 0] = 1e-8
wik = p_pdf / p_pdf.sum(-1, keepdim=True).expand_as(pdf)
return wik
def get_pik(self, z):
N, D, M = z.shape + (self._mu.shape[0], )
pdf = df.gaussianPDF(z,
self._mu,
self._sigma,
norm_func=self.norm_ff,
distance=self._distance)
print("pdf mean", pdf[20])
p_pdf = pdf * self._w.unsqueeze(0).expand_as(pdf)
print("ppd", p_pdf.size())
if (p_pdf.sum(-1).min() == 0):
print("EXPECTATION : pdf.sum(-1) contain zero -> ",
(p_pdf.sum(-1) == 0).sum())
#same if we set = 1
p_pdf[p_pdf.sum(-1) == 0] = 1e-8
wik = p_pdf / p_pdf.sum(-1, keepdim=True).expand_as(pdf)
# print("wik 1", wik.mean(1))
# print("wik 2", wik.mean(0))
# wik[torch.arange(len(wik)), wik.max(1)[1]] = 1
# wik = wik.long().float()
# print("wik 2", wik.mean(0))
return wik
from rcome.function_tools import distribution_function as df
# Define the barycentre mu and variance sigma
mu = torch.Tensor([[0.7, 0.7]])
sigma = torch.Tensor([2.2])
# Precompute the normalisation factor
norm_factor = df.ZetaPhiStorage(torch.arange(5e-2, 2., 0.001), 2)
# Sample a number of points on the manifold
points = (torch.rand(200000, 2) - 0.5) * 2
points = points[points.norm(2, -1) < 0.9999]
#Compute the probability density of each point
probs = df.gaussianPDF(points, mu, sigma, norm_func=norm_factor.zeta).squeeze()
#Divide into two classes
points_high = points[probs > 0.001]
points_med = points[probs > 0.003]
points_low = points[probs <= 0.003]
plt.figure()
plt.gca().set_aspect('equal', adjustable='box')
plt.axis('off')
plt.scatter(points_low[:, 0].numpy(), points_low[:, 1].numpy(), c='red')
plt.scatter(points_high[:, 0].numpy(), points_high[:, 1].numpy(), c='blue')
plt.scatter(points_med[:, 0].numpy(), points_med[:, 1].numpy(), c='green')
plt.scatter(mu[:, 0].numpy(), mu[:, 1].numpy(), c='orange', marker='*', s=150)
plt.savefig('gaussian.png')
plt.show()