Add goal for loc-scale transformation

aemcmc/transforms.py

@@ -0,0 +1,75 @@
+import aesara.tensor as at
+from etuples import etuple, etuplize
+from kanren import eq, lall
+from kanren.facts import Relation, fact
+from unification import var
+
+location_scale_family = Relation("location-scale-family")
+fact(location_scale_family, at.random.cauchy)
+fact(location_scale_family, at.random.gumbel)
+fact(location_scale_family, at.random.laplace)
+fact(location_scale_family, at.random.logistic)
+fact(location_scale_family, at.random.normal)
+
+
+def location_scale_transform(in_expr, out_expr):
+    r"""Produce a goal that represents the action of lifting and sinking
+    the scale and location parameters of distributions in the location-scale
+    family.
+
+    For instance
+
+    .. math::
+
+        \begin{equation*}
+            Y \sim \operatorname{Normal}(\mu, \sigma)
+        \end{equation*}
+
+    can also be written
+
+    .. math::
+
+        \begin{align*}
+            \epsilon &\sim \operatorname{Normal}(0, 1)\\
+            Y = \mu + \sigma\,\epsilon
+        \end{align*}
+
+    Parameters
+    ----------
+    in_expr
+        An expression that represents a random variable whose distribution belongs
+        to the location-scale family.
+    out_expr
+        An expression for the non-centered representation of this random variable.
+
+    """
+
+    # Centered representation
+    rng_lv, size_lv, type_idx_lv = var(), var(), var()
+    mu_lv, sd_lv = var(), var()
+    distribution_lv = var()
+    centered_et = etuple(distribution_lv, rng_lv, size_lv, type_idx_lv, mu_lv, sd_lv)
+
+    # Non-centered representation
+    noncentered_et = etuple(
+        etuplize(at.add),
+        mu_lv,
+        etuple(
+            etuplize(at.mul),
+            sd_lv,
+            etuple(
+                distribution_lv,
+                0.0,
+                1.0,
+                rng=rng_lv,
+                size=size_lv,
+                dtype=type_idx_lv,
+            ),
+        ),
+    )
+
+    return lall(
+        eq(in_expr, centered_et),
+        eq(out_expr, noncentered_et),
+        location_scale_family(distribution_lv),
+    )

tests/test_transforms.py

@@ -0,0 +1,28 @@
+import aesara.tensor as at
+from aesara.graph.fg import FunctionGraph
+from aesara.graph.kanren import KanrenRelationSub
+from aesara.graph.opt import EquilibriumOptimizer
+from aesara.graph.opt_utils import optimize_graph
+
+from aemcmc.transforms import location_scale_transform
+
+
+def test_normal_scale_loc_transform():
+    """"""
+
+    srng = at.random.RandomStream(0)
+    mu_rv = srng.normal(0, 1)
+    sigma_rv = srng.halfcauchy(1)
+    Y_rv = srng.normal(mu_rv, sigma_rv)
+
+    fgraph = FunctionGraph(outputs=[Y_rv], clone=False)
+
+    location_scale_opt = EquilibriumOptimizer(
+        [KanrenRelationSub(location_scale_transform)], max_use_ratio=10
+    )
+    res = optimize_graph(fgraph, include=[], custom_opt=location_scale_opt, clone=False)
+
+    # Make sure that Y_rv gets replaced with an addition
+    assert res.owner.op == at.add
+    rhs = res.owner.inputs[1].owner.inputs[0]
+    assert rhs.owner.op == at.mul