This implements a PositivePowerTransform. Whereas PowerTransform allows arbitrary exponent and requires positive domain and codomain, this requires positive exponent and allows real domain and codomain.

The intended use case is in sparse regression problems where this can be combined with TransformReparam and AutoNormal / AutoLowRankMultivariateNormal guides, achieving a horseshoe-like prior while attempting to keep the transformed posterior unimodal:

scale = pyro.sample("scale", LogNormal(0, 1))
sparsity = pyro.sample("sparsity", LogNormal(0, 1))
with poutine.reparam(config={"x": TransformReparam()}):
    x = pyro.sample(
        "x",
        TransformedDistribution(
            Normal(0, scale),
            PositivePowerReparam(sparsity),
        ),
    )

Tested

• added a transform test