Fixed norm const for SBVM (#3411)

* added lognorm terms for high conc sbvm

* lint

pyro/distributions/sine_bivariate_von_mises.py

@@ -35,7 +35,6 @@ class SineBivariateVonMises(TorchDistribution):
     This distribution is a submodel of the Bivariate von Mises distribution, called the Sine Distribution [2] in
     directional statistics.
 
-
     This distribution is helpful for modeling coupled angles such as torsion angles in peptide chains.
     To infer parameters, use :class:`~pyro.infer.NUTS` or :class:`~pyro.infer.HMC` with priors that
     avoid parameterizations where the distribution becomes bimodal; see note below.
@@ -44,10 +43,12 @@ class SineBivariateVonMises(TorchDistribution):
 
         .. math::
 
-            \frac{\rho}{\kappa_1\kappa_2} \rightarrow 1
+            \frac{\rho^2}{\kappa_1\kappa_2} \rightarrow 1
 
-        because the distribution becomes increasingly bimodal. To avoid bimodality use the `weighted_correlation`
-        parameter with a skew away from one (e.g., Beta(1,3)). The `weighted_correlation` should be in [0,1].
+        because the distribution becomes increasingly bimodal. To avoid inefficient sampling use the
+        `weighted_correlation` parameter with a skew away from one (e.g.,
+        `TransformedDistribution(Beta(5,5), AffineTransform(loc=-1, scale=2))`). The `weighted_correlation`
+        should be in [-1,1].
 
     .. note:: The correlation and weighted_correlation params are mutually exclusive.
 
@@ -65,7 +66,7 @@ class SineBivariateVonMises(TorchDistribution):
     :param torch.Tensor psi_concentration: concentration of second angle
     :param torch.Tensor correlation: correlation between the two angles
     :param torch.Tensor weighted_correlation: set correlation to weighted_corr * sqrt(phi_conc*psi_conc)
-        to avoid bimodality (see note). The `weighted_correlation` should be in [0,1].
+        to avoid bimodality (see note). The `weighted_correlation` should be in [-1,1].
     """
 
     arg_constraints = {
@@ -139,7 +140,13 @@ def norm_const(self):
             + m * torch.log((corr**2).clamp(min=tiny))
             - m * torch.log(4 * torch.prod(conc, dim=-1))
         )
-        fs += log_I1(m.max(), conc, 51).sum(-1)
+        num_I1terms = torch.maximum(
+            torch.tensor(501),
+            torch.max(self.phi_concentration) + torch.max(self.psi_concentration),
+        ).int()
+
+        fs += log_I1(m.max(), conc, num_I1terms).sum(-1)
+
         mfs = fs.max()
         norm_const = 2 * torch.log(torch.tensor(2 * pi)) + mfs + (fs - mfs).logsumexp(0)
         return norm_const.reshape(self.phi_loc.shape)

tests/distributions/test_sine_bivariate_von_mises.py

@@ -130,3 +130,16 @@ def guide(data):
             )  # k == 'corr'
 
         assert_equal(expected[k].squeeze(), actual.squeeze(), 9e-2)
+
+
+@pytest.mark.parametrize("conc", [1.0, 10.0, 1000.0, 10000.0])
+def test_sine_bivariate_von_mises_norm(conc):
+    dist = SineBivariateVonMises(0, 0, conc, conc, 0.0)
+    num_samples = 500
+    x = torch.linspace(-torch.pi, torch.pi, num_samples)
+    y = torch.linspace(-torch.pi, torch.pi, num_samples)
+    mesh = torch.stack(torch.meshgrid(x, y, indexing="ij"), axis=-1)
+    integral_torus = (
+        torch.exp(dist.log_prob(mesh)) * (2 * torch.pi) ** 2 / num_samples**2
+    ).sum()
+    assert torch.allclose(integral_torus, torch.tensor(1.0), rtol=1e-2)