Add a SoftLaplace distribution

docs/source/distributions.rst

@@ -316,6 +316,13 @@ Rejector
     :undoc-members:
     :show-inheritance:
 
+SoftLaplace
+-------------
+.. autoclass:: pyro.distributions.SoftLaplace
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
 SpanningTree
 ------------
 .. autoclass:: pyro.distributions.SpanningTree

pyro/distributions/__init__.py

@@ -58,6 +58,7 @@
     RelaxedBernoulliStraightThrough,
     RelaxedOneHotCategoricalStraightThrough,
 )
+from pyro.distributions.softlaplace import SoftLaplace
 from pyro.distributions.spanning_tree import SpanningTree
 from pyro.distributions.stable import Stable
 from pyro.distributions.torch import __all__ as torch_dists
@@ -127,6 +128,7 @@
     "Rejector",
     "RelaxedBernoulliStraightThrough",
     "RelaxedOneHotCategoricalStraightThrough",
+    "SoftLaplace",
     "SpanningTree",
     "Stable",
     "TorchDistribution",

pyro/distributions/softlaplace.py

@@ -0,0 +1,66 @@
+# Copyright Contributors to the Pyro project.
+# SPDX-License-Identifier: Apache-2.0
+
+import math
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.utils import broadcast_all
+
+from .torch_distribution import TorchDistribution
+
+
+class SoftLaplace(TorchDistribution):
+    """
+    Smooth distribution with Laplace-like tail behavior.
+
+    This distribution corresponds to the log-convex density::
+
+        z = (value - loc) / scale
+        log_prob = log(2 / pi) - log(scale) - logaddexp(z, -z)
+
+    Like the Laplace density, this density has the heaviest possible tails
+    (asymptotically) while still being log-convex. Unlike the Laplace
+    distribution, this distribution is infinitely differentiable everywhere,
+    and is thus suitable for constructing Laplace approximations.
+
+    :param loc: Location parameter.
+    :param scale: Scale parameter.
+    """
+
+    arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
+    support = constraints.real
+    has_rsample = True
+
+    def __init__(self, loc, scale, *, validate_args=None):
+        self.loc, self.scale = broadcast_all(loc, scale)
+        super().__init__(self.loc.shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(SoftLaplace, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.loc = self.loc.expand(batch_shape)
+        new.scale = self.scale.expand(batch_shape)
+        super(SoftLaplace, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        z = (value - self.loc) / self.scale
+        return math.log(2 / math.pi) - self.scale.log() - torch.logaddexp(z, -z)
+
+    def rsample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        u = self.loc.new_empty(shape).uniform_()
+        return self.icdf(u)
+
+    def cdf(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        z = (value - self.loc) / self.scale
+        return z.exp().atan().mul(2 / math.pi)
+
+    def icdf(self, value):
+        return value.mul(math.pi / 2).tan().log().mul(self.scale).add(self.loc)

tests/distributions/conftest.py

@@ -313,6 +313,17 @@ def scale(self):
                 {'concentration': [0., 0., 0.], 'test_data': [1., 0., 0.]},
                 {'concentration': [-1., 2., 3.], 'test_data': [0., 0., 1.]},
                 ]),
+    Fixture(pyro_dist=dist.SoftLaplace,
+            examples=[
+                {'loc': [2.0], 'scale': [4.0],
+                 'test_data': [2.0]},
+                {'loc': [[2.0]], 'scale': [[4.0]],
+                 'test_data': [[2.0]]},
+                {'loc': [[[2.0]]], 'scale': [[[4.0]]],
+                 'test_data': [[[2.0]]]},
+                {'loc': [2.0, 50.0], 'scale': [4.0, 100.0],
+                 'test_data': [[2.0, 50.0], [2.0, 50.0]]},
+                ]),
 ]
 
 discrete_dists = [