使用 pytorch 学习多元正态协方差矩阵

Question

I am trying to learn a multivariate normal covariance matrix (Sigma, ∑) using some observations.

The way I went at it is by using pytorch.distributions.MultivariateNormal:

import torch
from torch.distributions import MultivariateNormal

# I tried both the scale_tril parameter and the covariance parameter.
mvn = MultivariateNormal(loc=torch.tensor([0.0, 0.0], requires_grad=False).view(1,2),
                        scale_tril=torch.tensor([[1.0 , 0.0], [0.0, 1.0]],
                                                requires_grad=True).view(-1, 2, 2))

loss = -mvn.log_prob(torch.ones((1, 2))).mean()
loss.backward()
print(mvn.loc.grad)

I get None. I tried fiddling with the dimensions of the both the loc and the scale_tril parameters. Nothing appears to work. Any ideas?

• I can obviously implement this myself, but I have a strong preference using existing tools.

Bests, Eyal.

Answer 1

You are not calling.grad on your leaf nodes (on .view rather than tensor itself), also you have requires_grad=False on a mean, lets make things more explicit

import torch
from torch.distributions import MultivariateNormal

mean = torch.tensor([0.0, 0.0], requires_grad=True)
cov = torch.tensor([[1.0 , 0.0], [0.0, 1.0]], requires_grad=True)

mvn = MultivariateNormal(loc=mean.view(1,2),
                         scale_tril=cov.view(-1, 2, 2))

loss = -mvn.log_prob(torch.ones((1, 2))).mean()
loss.backward()

print(mean.grad)
print(cov.grad)