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Address precision matrix instability of MVN distribution #21366

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Address precision matrix instability of MVN distribution #21366

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b659b14
address precision matrix instability
fehiepsi Jun 4, 2019
2c1c7c7
add comment for the reference
fehiepsi Jun 4, 2019
4623239
fix typo in mvn test
fehiepsi Jun 4, 2019
90d9d0e
use triangular solve for inverse of triangular matrix
fehiepsi Jun 4, 2019
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5 changes: 5 additions & 0 deletions test/test_distributions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1781,6 +1781,11 @@ def gradcheck_func(samples, mu, sigma, prec, scale_tril):
multivariate_normal_log_prob_gradcheck(mean, None, None, scale_tril)
multivariate_normal_log_prob_gradcheck(mean_no_batch, None, None, scale_tril_batched)

def test_multivariate_normal_stable_with_precision_matrix(self):
x = torch.randn(10)
P = torch.exp(-(x - x.unsqueeze(-1)) ** 2) # RBF kernel
MultivariateNormal(x.new_zeros(10), precision_matrix=P)

@unittest.skipIf(not TEST_NUMPY, "Numpy not found")
def test_multivariate_normal_log_prob(self):
mean = torch.randn(3, requires_grad=True)
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17 changes: 13 additions & 4 deletions torch/distributions/multivariate_normal.py
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Expand Up @@ -66,6 +66,15 @@ def _batch_mahalanobis(bL, bx):
return reshaped_M.reshape(bx_batch_shape)


def _precision_to_scale_tril(P):
# Ref: https://nbviewer.jupyter.org/gist/fehiepsi/5ef8e09e61604f10607380467eb82006#Precision-to-scale_tril
Lf = torch.cholesky(torch.flip(P, (-2, -1)))
L_inv = torch.transpose(torch.flip(Lf, (-2, -1)), -2, -1)
L = torch.triangular_solve(torch.eye(P.shape[-1], dtype=P.dtype, device=P.device),
L_inv, upper=False)[0]
return L


class MultivariateNormal(Distribution):
r"""
Creates a multivariate normal (also called Gaussian) distribution
Expand Down Expand Up @@ -136,10 +145,10 @@ def __init__(self, loc, covariance_matrix=None, precision_matrix=None, scale_tri

if scale_tril is not None:
self._unbroadcasted_scale_tril = scale_tril
else:
if precision_matrix is not None:
self.covariance_matrix = torch.inverse(precision_matrix).expand_as(loc_)
self._unbroadcasted_scale_tril = torch.cholesky(self.covariance_matrix)
elif covariance_matrix is not None:
self._unbroadcasted_scale_tril = torch.cholesky(covariance_matrix)
else: # precision_matrix is not None
self._unbroadcasted_scale_tril = _precision_to_scale_tril(precision_matrix)

def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(MultivariateNormal, _instance)
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