Source code for pyro.distributions.transforms.cholesky

# Copyright (c) 2017-2019 Uber Technologies, Inc.

import math

import torch
from torch.distributions.transforms import Transform

from .. import constraints

def _vector_to_l_cholesky(z):
D = (1.0 + math.sqrt(1.0 + 8.0 * z.shape[-1])) / 2.0
if D % 1 != 0:
raise ValueError("Correlation matrix transformation requires d choose 2 inputs")
D = int(D)
x = torch.zeros(z.shape[:-1] + (D, D), dtype=z.dtype, device=z.device)

x[..., 0, 0] = 1
x[..., 1:, 0] = z[..., : (D - 1)]
i = D - 1
last_squared_x = torch.zeros(z.shape[:-1] + (D,), dtype=z.dtype, device=z.device)
for j in range(1, D):
distance_to_copy = D - 1 - j
last_squared_x = last_squared_x[..., 1:] + x[..., j:, (j - 1)].clone() ** 2
x[..., j, j] = (1 - last_squared_x[..., 0]).sqrt()
x[..., (j + 1) :, j] = (
z[..., i : (i + distance_to_copy)] * (1 - last_squared_x[..., 1:]).sqrt()
)
i += distance_to_copy
return x

[docs]class CorrLCholeskyTransform(Transform):
"""
Transforms a vector into the cholesky factor of a correlation matrix.

The input should have shape [batch_shape] + [d * (d-1)/2]. The output will
have shape [batch_shape] + [d, d].

References:

[1] Cholesky Factors of Correlation Matrices. Stan Reference Manual v2.18,
Section 10.12.

"""

domain = constraints.real_vector
codomain = constraints.corr_cholesky
bijective = True

def __eq__(self, other):
return isinstance(other, CorrLCholeskyTransform)

def _call(self, x):
z = x.tanh()
return _vector_to_l_cholesky(z)

def _inverse(self, y):
if y.shape[-2] != y.shape[-1]:
raise ValueError(
"A matrix that isn't square can't be a Cholesky factor of a correlation matrix"
)
D = y.shape[-1]

z_tri = torch.zeros(
y.shape[:-2] + (D - 2, D - 2), dtype=y.dtype, device=y.device
)
z_stack = [y[..., 1:, 0]]

for i in range(2, D):
z_tri[..., i - 2, 0 : (i - 1)] = (
y[..., i, 1:i] / (1 - y[..., i, 0 : (i - 1)].pow(2).cumsum(-1)).sqrt()
)
for j in range(D - 2):
z_stack.append(z_tri[..., j:, j])

z = torch.cat(z_stack, -1)

[docs]    def log_abs_det_jacobian(self, x, y):
# Note dependence on pytorch 1.0.1 for batched tril
tanpart = x.cosh().log().sum(-1).mul(-2)
matpart = (
(1 - y.pow(2).cumsum(-1).tril(diagonal=-2)).log().div(2).sum(-1).sum(-1)
)
return tanpart + matpart

[docs]class CholeskyTransform(Transform):
r"""
Transform via the mapping :math:y = cholesky(x), where x is a
positive definite matrix.
"""
bijective = True
domain = constraints.positive_definite
codomain = constraints.lower_cholesky

def __eq__(self, other):
return isinstance(other, CholeskyTransform)

def _call(self, x):

def _inverse(self, y):

[docs]    def log_abs_det_jacobian(self, x, y):
# Ref: http://web.mit.edu/18.325/www/handouts/handout2.pdf page 13
n = x.shape[-1]
order = torch.arange(n, 0, -1, dtype=x.dtype, device=x.device)
return -n * math.log(2) - (
order * torch.diagonal(y, dim1=-2, dim2=-1).log()
).sum(-1)

[docs]class CorrMatrixCholeskyTransform(CholeskyTransform):
r"""
Transform via the mapping :math:y = cholesky(x), where x is a
correlation matrix.
"""
bijective = True
domain = constraints.corr_matrix
# TODO: change corr_cholesky_constraint to corr_cholesky when the latter is availabler
codomain = constraints.corr_cholesky_constraint

def __eq__(self, other):
return isinstance(other, CorrMatrixCholeskyTransform)

[docs]    def log_abs_det_jacobian(self, x, y):
# NB: see derivation in LKJCholesky implementation
n = x.shape[-1]
order = torch.arange(n - 1, -1, -1, dtype=x.dtype, device=x.device)
return -(order * torch.diagonal(y, dim1=-2, dim2=-1).log()).sum(-1)