Add unit distribution for adding to log prob

Summary:
Addresses [#1041](#1041). Imported the Unit Dist (with some minor modifications) from pyro. This will allow users to add terms to the model density:
```
bm.random_variable
def increment_log_prob():
    val = Normal(0., 1.).log_prob(1.)
    return Unit(val)
```

In the future we can wrap this with a `factor` statement.

Reviewed By: neerajprad

Differential Revision: D31516303

fbshipit-source-id: b8dc3245e012788c7d5b468aed26535d1cc1b83e

src/beanmachine/ppl/distribution/__init__.py

@@ -1,5 +1,6 @@
 # Copyright (c) Facebook, Inc. and its affiliates.
 from beanmachine.ppl.distribution.flat import Flat
+from beanmachine.ppl.distribution.unit import Unit
 
 
-__all__ = ["Flat"]
+__all__ = ["Flat", "Unit"]

src/beanmachine/ppl/distribution/unit.py

@@ -0,0 +1,66 @@
+# Copyright Contributors to the Pyro project.
+# SPDX-License-Identifier: Apache-2.0
+
+import torch
+from torch.distributions import constraints
+
+
+def broadcast_shape(*shapes, **kwargs):
+    """
+    Similar to ``np.broadcast()`` but for shapes.
+    Equivalent to ``np.broadcast(*map(np.empty, shapes)).shape``.
+    :param tuple shapes: shapes of tensors.
+    :param bool strict: whether to use extend-but-not-resize broadcasting.
+    :returns: broadcasted shape
+    :rtype: tuple
+    :raises: ValueError
+    """
+    strict = kwargs.pop("strict", False)
+    reversed_shape = []
+    for shape in shapes:
+        for i, size in enumerate(reversed(shape)):
+            if i >= len(reversed_shape):
+                reversed_shape.append(size)
+            elif reversed_shape[i] == 1 and not strict:
+                reversed_shape[i] = size
+            elif reversed_shape[i] != size and (size != 1 or strict):
+                raise ValueError(
+                    "shape mismatch: objects cannot be broadcast to a single shape: {}".format(
+                        " vs ".join(map(str, shapes))
+                    )
+                )
+    return tuple(reversed(reversed_shape))
+
+
+class Unit(torch.distributions.Distribution):
+    """
+    Trivial nonnormalized distribution representing the unit type.
+
+    The unit type has a single value with no data, i.e. ``value.numel() == 0``.
+
+    This is used for :func:`pyro.factor` statements.
+    """
+
+    arg_constraints = {"log_factor": constraints.real}
+    support = constraints.real
+
+    def __init__(self, log_factor, validate_args=None):
+        log_factor = torch.as_tensor(log_factor)
+        batch_shape = log_factor.shape
+        event_shape = torch.Size((0,))  # This satisfies .numel() == 0.
+        self.log_factor = log_factor
+        super().__init__(batch_shape, event_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Unit, _instance)
+        new.log_factor = self.log_factor.expand(batch_shape)
+        super(Unit, new).__init__(batch_shape, self.event_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def sample(self, sample_shape=torch.Size()):  # noqa: B008
+        return self.log_factor.new_empty(sample_shape)
+
+    def log_prob(self, value):
+        shape = broadcast_shape(self.batch_shape, value.shape[:-1])
+        return self.log_factor.expand(shape)