Merge pull request #639 from CUQI-DTU/add_non_informative

Add UnboundedUniform distribution

Author: chaozg

cuqi/distribution/__init__.py

@@ -14,6 +14,6 @@
 from ._normal import Normal
 from ._truncated_normal import TruncatedNormal
 from ._posterior import Posterior
-from ._uniform import Uniform
+from ._uniform import Uniform, UnboundedUniform
 from ._custom import UserDefinedDistribution, DistributionGallery
 from ._joint_distribution import JointDistribution, _StackedJointDistribution, MultipleLikelihoodPosterior

cuqi/distribution/_uniform.py

@@ -1,5 +1,6 @@
 import numpy as np
 from cuqi.distribution import Distribution
+from cuqi.geometry import Geometry
 
 class Uniform(Distribution):
 
@@ -57,4 +58,37 @@ def _sample(self,N=1, rng=None):
         else:
             s = np.random.uniform(self.low, self.high, (N,self.dim)).T
 
-        return s
+        return s
+
+class UnboundedUniform(Distribution):
+    """
+    Unbounded uniform distribution. This is a special case of the
+    Uniform distribution, where the lower and upper bounds are set to
+    -inf and inf, respectively. This distribution is not normalizable,
+    and therefore cannot be sampled from. It is mainly used for
+    initializing non-informative priors.
+    Parameters
+    ----------
+    geometry : int or Geometry
+        The geometry of the distribution. If an integer is given, it is
+        interpreted as the dimension of the distribution. If a
+        Geometry object is given, its par_dim attribute is used.
+    """
+    def __init__(self, geometry, is_symmetric=True, **kwargs):
+        super().__init__(geometry=geometry, is_symmetric=is_symmetric, **kwargs) 
+
+    def logpdf(self, x):
+        """
+        Evaluate the logarithm of the unnormalized PDF at the given values of x.
+        """
+        # Always return 1.0 (the unnormalized log PDF)
+        return 1.0
+
+    def gradient(self, x):
+        """
+        Computes the gradient of logpdf at the given values of x.
+        """
+        return np.zeros_like(x)
+
+    def _sample(self, N=1, rng=None):
+        raise NotImplementedError("Cannot sample from UnboundedUniform distribution")

tests/test_distribution.py

@@ -203,7 +203,6 @@ def test_Uniform_logpdf(low, high, toeval, expected):
     UD = cuqi.distribution.Uniform(low, high)
     assert np.allclose(UD.logpdf(toeval), expected) 
 
-
 @pytest.mark.parametrize("low,high,expected",[(np.array([1, .5]), 
                                                np.array([2, 2.5]),
                                                np.array([[1.5507979 , 1.29090474, 1.89294695],
@@ -217,6 +216,19 @@ def test_Uniform_sample(low, high, expected):
     print(cuqi_samples)
     assert np.allclose(cuqi_samples.samples, expected) 
 
+def test_UnboundedUniform_logpdf_and_gradient():
+    x1 = cuqi.distribution.UnboundedUniform(geometry=1)
+    assert np.allclose(x1.logpdf(np.array([1])), 1.0)
+    assert np.allclose(x1.gradient(np.array([0])), np.array([0]))
+    x2 = cuqi.distribution.UnboundedUniform(geometry=cuqi.geometry.Discrete(2))
+    assert np.allclose(x2.logpdf(np.array([1, 2])), 1.0)
+    assert np.allclose(x2.gradient(np.array([0, 0])), np.array([0, 0]))
+
+def test_UnboundedUniform_sample():
+    x = cuqi.distribution.UnboundedUniform(geometry=2)
+    with pytest.raises(NotImplementedError, match="Cannot sample from UnboundedUniform distribution"):
+        x.sample()
+
 @pytest.mark.parametrize("distribution, kwargs",
                          [(cuqi.distribution.Uniform, 
                           {'low':np.array([2, 2.5, 3,5]),

tests/test_distributions_shape.py

@@ -13,6 +13,7 @@
     "Posterior",
     "Distribution",
     "JointGaussianSqrtPrec",
+    "UnboundedUniform",
 ]
 
 # Define cases to skip (these are TODO)