Skip to content

Support 4D ProjectedNormal distribution #3011

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 1 commit into from
Jan 26, 2022
Merged

Support 4D ProjectedNormal distribution #3011

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
21 changes: 21 additions & 0 deletions pyro/distributions/projected_normal.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -170,3 +170,24 @@ def _log_prob_3(concentration, value):
).log()

return para_part + perp_part


@ProjectedNormal._register_log_prob(dim=4)
def _log_prob_4(concentration, value):
# We integrate along a ray, factorizing the integrand as a product of:
# a truncated normal distribution over coordinate t parallel to the ray, and
# a bivariate normal distribution over coordinate r perpendicular to the ray.
t = _dot(concentration, value)
t2 = t.square()
r2 = _dot(concentration, concentration) - t2
perp_part = r2.mul(-0.5) - 1.5 * math.log(2 * math.pi)

# This is the log of a definite integral, computed by mathematica:
# Integrate[x^3/(E^((x-t)^2/2) Sqrt[2 Pi]), {x, 0, Infinity}]
# = (2 + t^2)/(E^(t^2/2) Sqrt[2 Pi]) + (t (3 + t^2) (1 + Erf[t/Sqrt[2]]))/2
para_part = (
(2 + t2) * t2.mul(-0.5).exp() / (2 * math.pi) ** 0.5
+ t * (3 + t2) * (1 + (t * 0.5 ** 0.5).erf()) / 2
).log()

return para_part + perp_part
5 changes: 5 additions & 0 deletions tests/distributions/conftest.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -529,6 +529,11 @@ def __init__(self, von_loc, von_conc, skewness):
{"concentration": [2.0, 3.0], "test_data": [0.0, 1.0]},
{"concentration": [0.0, 0.0, 0.0], "test_data": [1.0, 0.0, 0.0]},
{"concentration": [-1.0, 2.0, 3.0], "test_data": [0.0, 0.0, 1.0]},
{"concentration": [0.0, 0.0, 0.0, 0.0], "test_data": [1.0, 0.0, 0.0, 0.0]},
{
"concentration": [-1.0, 2.0, 0.5, -0.5],
"test_data": [0.0, 1.0, 0.0, 0.0],
},
],
),
Fixture(
Expand Down