PlanarFlow

docs/source/distributions.rst

@@ -179,6 +179,13 @@ PermuteTransform
     :undoc-members:
     :show-inheritance:
 
+PlanarFlow
+----------------
+.. autoclass:: pyro.distributions.PlanarFlow
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
 TransformModule
 ----------------
 .. autoclass:: pyro.distributions.TransformModule

pyro/distributions/__init__.py

@@ -15,6 +15,7 @@
 from pyro.distributions.mixture import MaskedMixture
 from pyro.distributions.omt_mvn import OMTMultivariateNormal
 from pyro.distributions.permute import PermuteTransform
+from pyro.distributions.planar import PlanarFlow
 from pyro.distributions.rejector import Rejector
 from pyro.distributions.relaxed_straight_through import (RelaxedBernoulliStraightThrough,
                                                          RelaxedOneHotCategoricalStraightThrough)
@@ -46,6 +47,7 @@
     "MixtureOfDiagNormals",
     "OMTMultivariateNormal",
     "PermuteTransform",
+    "PlanarFlow",
     "Rejector",
     "RelaxedBernoulliStraightThrough",
     "RelaxedOneHotCategoricalStraightThrough",

pyro/distributions/iaf.py

@@ -118,6 +118,8 @@ def _inverse(self, y):
                 x[idx] = (y[..., idx] - mean) * inverse_scale
 
             x = torch.stack(x, dim=-1)
+            log_scale = clamp_preserve_gradients(log_scale, min=self.log_scale_min_clip, max=self.log_scale_max_clip)
+            self._add_intermediate_to_cache(log_scale, y, 'log_scale')
             return x
 
     def _add_intermediate_to_cache(self, intermediate, y, name):
@@ -132,11 +134,7 @@ def log_abs_det_jacobian(self, x, y):
         """
         Calculates the elementwise determinant of the log jacobian
         """
-        if (y, 'log_scale') in self._intermediates_cache:
-            log_scale = self._intermediates_cache.pop((y, 'log_scale'))
-        else:
-            _, log_scale = self.arn(x)
-            log_scale = clamp_preserve_gradients(log_scale, min=self.log_scale_min_clip, max=self.log_scale_max_clip)
+        log_scale = self._intermediates_cache.pop((y, 'log_scale'))
         return log_scale
 
 

pyro/distributions/planar.py

@@ -0,0 +1,126 @@
+from __future__ import absolute_import, division, print_function
+
+import math
+
+import torch
+import torch.nn as nn
+from torch.distributions import constraints
+import torch.nn.functional as F
+
+from pyro.distributions.torch_transform import TransformModule
+from pyro.distributions.util import copy_docs_from
+
+
+@copy_docs_from(TransformModule)
+class PlanarFlow(TransformModule):
+    """
+    A 'planar' normalizing flow that uses the transformation
+
+        :math:`\\mathbf{y} = \\mathbf{x} + \\mathbf{u}\\tanh(\\mathbf{w}^T\\mathbf{z}+b)`
+
+    where :math:`\\mathbf{x}` are the inputs, :math:`\\mathbf{y}` are the outputs, and the learnable parameters
+    are :math:`b\\in\\mathbb{R}`, :math:`\\mathbf{u}\\in\\mathbb{R}^D`, :math:`\\mathbf{w}\\in\\mathbb{R}^D` for input
+    dimension :math:`D`. For this to be an invertible transformation, the condition
+    :math:`\\mathbf{w}^T\\mathbf{u}>-1` is enforced.
+
+    Together with `TransformedDistribution` this provides a way to create richer variational approximations.
+
+    Example usage:
+
+    >>> base_dist = dist.Normal(torch.zeros(10), torch.ones(10))
+    >>> plf = PlanarFlow(10)
+    >>> plf_module = pyro.module("my_plf", plf)
+    >>> plf_dist = dist.TransformedDistribution(base_dist, [plf])
+    >>> plf_dist.sample()  # doctest: +SKIP
+        tensor([-0.4071, -0.5030,  0.7924, -0.2366, -0.2387, -0.1417,  0.0868,
+                0.1389, -0.4629,  0.0986])
+
+    The inverse of this transform does not possess an analytical solution and is left unimplemented. However,
+    the inverse is cached when the forward operation is called during sampling, and so samples drawn using
+    planar flow can be scored.
+
+    :param input_dim: the dimension of the input (and output) variable.
+    :type autoregressive_nn: int
+
+    References:
+
+    Variational Inference with Normalizing Flows [arXiv:1505.05770]
+    Danilo Jimenez Rezende, Shakir Mohamed
+
+    """
+
+    codomain = constraints.real
+
+    def __init__(self, input_dim):
+        super(PlanarFlow, self).__init__()
+
+        self.input_dim = input_dim
+        self.lin = nn.Linear(input_dim, 1)
+        self.u = nn.Parameter(torch.Tensor(input_dim))
+        self.reset_parameters()
+        self._intermediates_cache = {}
+        self.add_inverse_to_cache = True
+
+    def reset_parameters(self):
+        stdv = 1. / math.sqrt(self.u.size(0))
+        self.lin.weight.data.uniform_(-stdv, stdv)
+        self.u.data.uniform_(-stdv, stdv)
+
+    def __hash__(self):
+        return super(nn.Module, self).__hash__()
+
+    # This method ensures that torch(u_hat, w) > -1, required for invertibility
+    def u_hat(self):
+        u = self.u
+        w = self.lin.weight.squeeze(0)
+        alpha = torch.dot(u, w)
+        a_prime = -1 + F.softplus(alpha)
+        return u + (a_prime - alpha) * w.div(w.norm())
+
+    def _call(self, x):
+        """
+        :param x: the input into the bijection
+        :type x: torch.Tensor
+
+        Invokes the bijection x=>y; in the prototypical context of a TransformedDistribution `x` is a
+        sample from the base distribution (or the output of a previous flow)
+        """
+
+        y = x + self.u_hat() * torch.tanh(self.lin(x))
+
+        self._add_intermediate_to_cache(x, y, 'x')
+        return y
+
+    def _inverse(self, y):
+        """
+        :param y: the output of the bijection
+        :type y: torch.Tensor
+
+        Inverts y => x. As noted above, this implementation is incapable of inverting arbitrary values
+        `y`; rather it assumes `y` is the result of a previously computed application of the bijector
+        to some `x` (which was cached on the forward call)
+        """
+        if (y, 'x') in self._intermediates_cache:
+            x = self._intermediates_cache.pop((y, 'x'))
+            return x
+        else:
+            raise KeyError("PlanarFlow expected to find "
+                           "key in intermediates cache but didn't")
+
+    def _add_intermediate_to_cache(self, intermediate, y, name):
+        """
+        Internal function used to cache intermediate results computed during the forward call
+        """
+        assert((y, name) not in self._intermediates_cache),\
+            "key collision in _add_intermediate_to_cache"
+        self._intermediates_cache[(y, name)] = intermediate
+
+    def log_abs_det_jacobian(self, x, y):
+        """
+        Calculates the elementwise determinant of the log jacobian
+        """
+        psi_z = (1 - torch.tanh(self.lin(x)).pow(2)) * self.lin.weight
+
+        # TODO: Simplify following line once using multivariate base distributions for multivariate flows
+        return torch.log(torch.abs(1 + torch.matmul(psi_z, self.u_hat())).unsqueeze(-1)) * \
+            torch.ones_like(x) / x.size(-1)

tests/distributions/test_flows.py

@@ -12,7 +12,7 @@
 pytestmark = pytest.mark.init(rng_seed=123)
 
 
-class AutoregressiveFlowTests(TestCase):
+class FlowTests(TestCase):
     def setUp(self):
         # Epsilon is used to compare numerical gradient to analytical one
         self.epsilon = 1e-3
@@ -22,57 +22,69 @@ def setUp(self):
 
     def _test_jacobian(self, input_dim, make_flow):
         jacobian = torch.zeros(input_dim, input_dim)
-        iaf = make_flow(input_dim)
+        flow = make_flow(input_dim)
 
         def nonzero(x):
             return torch.sign(torch.abs(x))
 
         x = torch.randn(1, input_dim)
-        iaf_x = iaf(x)
-        analytic_ldt = iaf.log_abs_det_jacobian(x, iaf_x).data.sum()
+        flow_x = flow(x)
+        analytic_ldt = flow.log_abs_det_jacobian(x, flow_x).data.sum()
 
         for j in range(input_dim):
             for k in range(input_dim):
                 epsilon_vector = torch.zeros(1, input_dim)
                 epsilon_vector[0, j] = self.epsilon
-                delta = (iaf(x + 0.5 * epsilon_vector) - iaf(x - 0.5 * epsilon_vector)) / self.epsilon
+                delta = (flow(x + 0.5 * epsilon_vector) - flow(x - 0.5 * epsilon_vector)) / self.epsilon
                 jacobian[j, k] = float(delta[0, k].data.sum())
 
-        permutation = iaf.arn.get_permutation()
-        permuted_jacobian = jacobian.clone()
-        for j in range(input_dim):
-            for k in range(input_dim):
-                permuted_jacobian[j, k] = jacobian[permutation[j], permutation[k]]
-        numeric_ldt = torch.sum(torch.log(torch.diag(permuted_jacobian)))
-        ldt_discrepancy = np.fabs(analytic_ldt - numeric_ldt)
-
-        diag_sum = torch.sum(torch.diag(nonzero(permuted_jacobian)))
-        lower_sum = torch.sum(torch.tril(nonzero(permuted_jacobian), diagonal=-1))
+        # Apply permutation for autoregressive flows
+        if hasattr(flow, 'arn'):
+            permutation = flow.arn.get_permutation()
+            permuted_jacobian = jacobian.clone()
+            for j in range(input_dim):
+                for k in range(input_dim):
+                    permuted_jacobian[j, k] = jacobian[permutation[j], permutation[k]]
+            jacobian = permuted_jacobian
+
+        # For autoregressive flow, Jacobian is sum of diagonal, otherwise need full determinate
+        if hasattr(flow, 'arn'):
+            numeric_ldt = torch.sum(torch.log(torch.diag(jacobian)))
+        else:
+            numeric_ldt = torch.log(torch.abs(jacobian.det()))
 
+        ldt_discrepancy = np.fabs(analytic_ldt - numeric_ldt)
         assert ldt_discrepancy < self.epsilon
-        assert diag_sum == float(input_dim)
-        assert lower_sum == float(0.0)
+
+        # Test that lower triangular with unit diagonal for autoregressive flows
+        if hasattr(flow, 'arn'):
+            diag_sum = torch.sum(torch.diag(nonzero(jacobian)))
+            lower_sum = torch.sum(torch.tril(nonzero(jacobian), diagonal=-1))
+            assert diag_sum == float(input_dim)
+            assert lower_sum == float(0.0)
 
     def _test_inverse(self, input_dim, make_flow):
         base_dist = dist.Normal(torch.zeros(input_dim), torch.ones(input_dim))
-        iaf = make_flow(input_dim)
+        flow = make_flow(input_dim)
 
         x_true = base_dist.sample(torch.Size([10]))
-        y = iaf._call(x_true)
+        y = flow._call(x_true)
 
         # This line empties the inverse cache, if the flow uses it
-        iaf._inverse(y)
+        if hasattr(flow, '_intermediates_cache'):
+            flow._intermediates_cache.pop((y, 'log_scale'))
+            flow._intermediates_cache.pop((y, 'x'))
 
         # Cache is empty, hence must be calculating inverse afresh
-        x_calculated = iaf._inverse(y)
+        x_calculated = flow._inverse(y)
 
         assert torch.norm(x_true - x_calculated, dim=-1).max().item() < self.delta
 
     def _test_shape(self, base_shape, make_flow):
         base_dist = dist.Normal(torch.zeros(base_shape), torch.ones(base_shape))
         last_dim = base_shape[-1] if isinstance(base_shape, tuple) else base_shape
-        iaf = make_flow(input_dim=last_dim)
-        sample = dist.TransformedDistribution(base_dist, [iaf]).sample()
+        flow = make_flow(input_dim=last_dim)
+        sample = dist.TransformedDistribution(base_dist, [flow]).sample()
         assert sample.shape == base_shape
 
     def _make_iaf(self, input_dim):
@@ -87,6 +99,9 @@ def _make_flipflow(self, input_dim):
         permutation = torch.randperm(input_dim, device='cpu').to(torch.Tensor().device)
         return dist.PermuteTransform(permutation)
 
+    def _make_planar(self, input_dim):
+        return dist.PlanarFlow(input_dim)
+
     def test_iaf_jacobians(self):
         for input_dim in [2, 3, 5, 7, 9, 11]:
             self._test_jacobian(input_dim, self._make_iaf)
@@ -95,6 +110,10 @@ def test_iaf_stable_jacobians(self):
         for input_dim in [2, 3, 5, 7, 9, 11]:
             self._test_jacobian(input_dim, self._make_iaf_stable)
 
+    def test_planar_jacobians(self):
+        for input_dim in [2, 3, 5, 7, 9, 11]:
+            self._test_jacobian(input_dim, self._make_planar)
+
     def test_iaf_inverses(self):
         for input_dim in [2, 3, 5, 7, 9, 11]:
             self._test_inverse(input_dim, self._make_iaf)
@@ -118,3 +137,7 @@ def test_iaf_stable_shapes(self):
     def test_flipflow_shapes(self):
         for shape in [(3,), (3, 4), (3, 4, 2)]:
             self._test_shape(shape, self._make_flipflow)
+
+    def test_planar_shapes(self):
+        for shape in [(3,), (3, 4), (3, 4, 2)]:
+            self._test_shape(shape, self._make_planar)