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Stabilize zero-inflated variance at large base means #3487

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6 changes: 3 additions & 3 deletions pyro/distributions/zero_inflated.py
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Original file line number Diff line number Diff line change
Expand Up @@ -97,9 +97,9 @@ def mean(self):

@lazy_property
def variance(self):
return (1 - self.gate) * (self.base_dist.mean**2 + self.base_dist.variance) - (
self.mean
) ** 2
return (1 - self.gate) * self.base_dist.variance + (
self.gate * self.base_dist.mean
) * self.mean

def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(type(self), _instance)
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20 changes: 20 additions & 0 deletions tests/distributions/test_zero_inflated.py
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Expand Up @@ -75,6 +75,26 @@ def test_zip_mean_variance(gate, rate):
assert_close(expected_std, estimated_std, atol=1e-02)


@pytest.mark.parametrize("dtype", [torch.float32, torch.float64])
@pytest.mark.parametrize("base_type", [Poisson, Normal])
def test_zero_inflated_variance_large_mean(dtype, base_type):
mean = torch.tensor([1e3, 1e10, 1e20, 1e20], dtype=dtype, requires_grad=True)
gate = torch.tensor([0.25, 0.0, 1e-20, 1.0], dtype=dtype)
base = base_type(mean) if base_type is Poisson else Normal(mean, 1.0)
distribution = ZeroInflatedDistribution(base, gate=gate)
# Law of total variance, evaluated in double precision around each mean.
g, m, v = gate.double(), mean.double(), base.variance.double()
mixture_mean = (1 - g) * m
expected = (1 - g) * (v + (m - mixture_mean).square())
expected = expected + g * mixture_mean.square()
torch.testing.assert_close(distribution.variance, expected.to(dtype))
gradient = torch.autograd.grad(distribution.variance.sum(), mean)[0]
expected_gradient = 2 * g * (1 - g) * m
if base_type is Poisson:
expected_gradient = expected_gradient + (1 - g)
torch.testing.assert_close(gradient, expected_gradient.to(dtype))


@pytest.mark.parametrize("total_count", [0.1, 0.5, 0.9, 1.0, 1.1, 2.0, 10.0])
@pytest.mark.parametrize("probs", [0.1, 0.5, 0.9])
def test_zinb_0_gate(total_count, probs):
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