Implement Ordered distribution factory

pymc/distributions/__init__.py

@@ -103,6 +103,7 @@
     WishartBartlett,
     ZeroSumNormal,
 )
+from pymc.distributions.ordered import Ordered
 from pymc.distributions.simulator import Simulator
 from pymc.distributions.timeseries import (
     AR,
@@ -178,6 +179,7 @@
     "NegativeBinomial",
     "Normal",
     "NormalMixture",
+    "Ordered",
     "OrderedLogistic",
     "OrderedMultinomial",
     "OrderedProbit",

pymc/distributions/discrete.py

@@ -1239,8 +1239,7 @@ class OrderedLogistic:
 
         # Ordered logistic regression
         with pm.Model() as model:
-            cutpoints = pm.Normal("cutpoints", mu=[-1,1], sigma=10, shape=2,
-                                  transform=pm.distributions.transforms.ordered)
+            cutpoints = pm.Ordered("cutpoints", dist=pm.Normal.dist(mu=0, sigma=10), shape=2)
             y_ = pm.OrderedLogistic("y", cutpoints=cutpoints, eta=x, observed=y)
             idata = pm.sample()
 
@@ -1343,8 +1342,7 @@ class OrderedProbit:
 
         # Ordered probit regression
         with pm.Model() as model:
-            cutpoints = pm.Normal("cutpoints", mu=[-1,1], sigma=10, shape=2,
-                                  transform=pm.distributions.transforms.ordered)
+            cutpoints = pm.Ordered("cutpoints", dist=pm.Normal.dist(mu=0, sigma=10), shape=2)
             y_ = pm.OrderedProbit("y", cutpoints=cutpoints, eta=x, observed=y)
             idata = pm.sample()
 

pymc/distributions/ordered.py

@@ -0,0 +1,133 @@
+#   Copyright 2024 The PyMC Developers
+#
+#   Licensed under the Apache License, Version 2.0 (the "License");
+#   you may not use this file except in compliance with the License.
+#   You may obtain a copy of the License at
+#
+#       http://www.apache.org/licenses/LICENSE-2.0
+#
+#   Unless required by applicable law or agreed to in writing, software
+#   distributed under the License is distributed on an "AS IS" BASIS,
+#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#   See the License for the specific language governing permissions and
+#   limitations under the License.
+import pytensor.tensor as pt
+
+from pytensor.tensor.random.op import RandomVariable
+from pytensor.tensor.random.utils import normalize_size_param
+from pytensor.tensor.variable import TensorVariable
+
+from pymc.distributions.distribution import (
+    Distribution,
+    SymbolicRandomVariable,
+    _support_point,
+)
+from pymc.distributions.shape_utils import change_dist_size, get_support_shape_1d, rv_size_is_none
+from pymc.distributions.transforms import _default_transform, ordered
+
+
+class OrderedRV(SymbolicRandomVariable):
+    inline_logprob = True
+    extended_signature = "(x)->(x)"
+    _print_name = ("Ordered", "\\operatorname{Ordered}")
+
+    @classmethod
+    def rv_op(cls, dist, *, size=None):
+        # We don't allow passing `rng` because we don't fully control the rng of the components!
+
+        size = normalize_size_param(size)
+
+        if not rv_size_is_none(size):
+            core_shape = tuple(dist.shape)[-1]
+            shape = (*tuple(size), core_shape)
+            dist = change_dist_size(dist, shape)
+
+        sorted_rv = pt.sort(dist, axis=-1)
+
+        return OrderedRV(
+            inputs=[dist],
+            outputs=[sorted_rv],
+        )(dist)
+
+
+class Ordered(Distribution):
+    r"""Univariate IID Ordered distribution.
+
+    The pdf of the oredered distribution is
+
+    .. math::
+        f(x_1, ..., x_n) = n!\prod_{i=1}^n f(x_{(i)}),
+        where x_1 <= x2 <= ... <= x_n
+
+    Parameters
+    ----------
+    dist: unnamed_distribution
+        Univariate IID distribution which will be sorted.
+
+        .. warning:: dist will be cloned, rendering it independent of the one passade as input
+
+    Examples
+    --------
+    .. code-block:: python
+        import pymc as pm
+
+        with pm.Model():
+            x = pm.Normal.dist(mu=0, sigma=1)  # Must be IID
+            ordered_x = pm.Ordered("ordered_x", dist=x, shape=(3,))
+
+        pm.draw(ordered_x, random_seed=52)  # array([0.05172346, 0.43970706, 0.91500416])
+    """
+
+    rv_type = OrderedRV
+    rv_op = OrderedRV.rv_op
+
+    def __new__(cls, name, dist, *, support_shape=None, **kwargs):
+        support_shape = get_support_shape_1d(
+            support_shape=support_shape,
+            shape=None,  # shape will be checked in `cls.dist`
+            dims=kwargs.get("dims", None),
+            observed=kwargs.get("observed", None),
+        )
+        return super().__new__(cls, name, dist, support_shape=support_shape, **kwargs)
+
+    @classmethod
+    def dist(cls, dist, *, support_shape=None, **kwargs):
+        if not isinstance(dist, TensorVariable) or not isinstance(
+            dist.owner.op, RandomVariable | SymbolicRandomVariable
+        ):
+            raise ValueError(
+                f"Ordered dist must be a distribution created via the `.dist()` API, got {type(dist)}"
+            )
+        if dist.owner.op.ndim_supp > 0:
+            raise NotImplementedError("Ordering of multivariate distributions not supported")
+        if not all(
+            all(param.type.broadcastable) for param in dist.owner.op.dist_params(dist.owner)
+        ):
+            raise ValueError("Ordered dist must be an IID variable")
+
+        support_shape = get_support_shape_1d(
+            support_shape=support_shape,
+            shape=kwargs.get("shape", None),
+        )
+        if support_shape is not None:
+            dist = change_dist_size(dist, support_shape)
+
+        dist = pt.atleast_1d(dist)
+
+        return super().dist([dist], **kwargs)
+
+
+@_default_transform.register(OrderedRV)
+def default_transform_ordered(op, rv):
+    if rv.type.dtype.startswith("float"):
+        return ordered
+    else:
+        return None
+
+
+@_support_point.register(OrderedRV)
+def support_point_ordered(op, rv, dist):
+    # FIXME: This does not work with the default ordered transform
+    # which maps [0, 0, 0] to [0, -inf, -inf].
+    # return support_point(dist)
+    return rv  # Draw from the prior

pymc/logprob/order.py

@@ -41,21 +41,65 @@
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.rewriting.basic import node_rewriter
 from pytensor.tensor.math import Max
+from pytensor.tensor.random.op import RandomVariable
+from pytensor.tensor.sort import SortOp
 from pytensor.tensor.variable import TensorVariable
 
 from pymc.logprob.abstract import (
-    MeasurableElemwise,
     MeasurableOp,
     _logcdf_helper,
     _logprob,
     _logprob_helper,
 )
 from pymc.logprob.rewriting import measurable_ir_rewrites_db
-from pymc.logprob.utils import filter_measurable_variables
+from pymc.logprob.utils import (
+    CheckParameterValue,
+    check_potential_measurability,
+    filter_measurable_variables,
+)
 from pymc.math import logdiffexp
 from pymc.pytensorf import constant_fold
 
 
+def _underlying_iid_rv(variable) -> TensorVariable | None:
+    # Check whether an IID base RV is connected to the variable through identical elemwise operations
+    from pymc.distributions.distribution import SymbolicRandomVariable
+    from pymc.logprob.transforms import MeasurableTransform
+
+    def iid_elemwise_root(var: TensorVariable) -> TensorVariable | None:
+        node = var.owner
+        if isinstance(node.op, RandomVariable | SymbolicRandomVariable):
+            return var
+        elif isinstance(node.op, MeasurableTransform):
+            if len(node.inputs == 1):
+                return iid_elemwise_root(node.inputs[0])
+            else:
+                # If the non-measurable inputs are broadcasted, it is still an IID operation.
+                measurable_inp = node.op.measurable_input_idx
+                other_inputs = [inp for i, inp in node.inputs if i != measurable_inp]
+                if all(all(other_inp.type.broadcastable) for other_inp in other_inputs):
+                    return iid_elemwise_root(node.inputs[measurable_inp])
+        return None
+
+    # Check that the root is a univariate distribution linked by only elemwise operations
+    latent_base_var = iid_elemwise_root(variable)
+
+    if latent_base_var is None:
+        return None
+
+    latent_op = latent_base_var.owner.op
+
+    if not (hasattr(latent_op, "dist_params") and getattr(latent_op, "ndim_supp") == 0):
+        return None
+
+    if not all(
+        all(params.type.broadcastable) for params in latent_op.dist_params(latent_base_var.owner)
+    ):
+        return None
+
+    return cast(TensorVariable, latent_base_var)
+
+
 class MeasurableMax(MeasurableOp, Max):
     """A placeholder used to specify a log-likelihood for a max sub-graph."""
 
@@ -77,31 +121,12 @@ def find_measurable_max(fgraph: FunctionGraph, node: Apply) -> list[TensorVariab
     if not filter_measurable_variables(node.inputs):
         return None
 
-    # We allow Max of RandomVariables or Elemwise of univariate RandomVariables
-    if isinstance(base_var.owner.op, MeasurableElemwise):
-        latent_base_vars = [
-            var
-            for var in base_var.owner.inputs
-            if (var.owner and isinstance(var.owner.op, MeasurableOp))
-        ]
-        if len(latent_base_vars) != 1:
-            return None
-        [latent_base_var] = latent_base_vars
-    else:
-        latent_base_var = base_var
-
-    latent_op = latent_base_var.owner.op
-    if not (hasattr(latent_op, "dist_params") and getattr(latent_op, "ndim_supp") == 0):
-        return None
+    # We allow Max of RandomVariables or IID Elemwise of univariate RandomVariables
+    latent_base_var = _underlying_iid_rv(base_var)
 
-    # univariate i.i.d. test which also rules out other distributions
-    if not all(
-        all(params.type.broadcastable) for params in latent_op.dist_params(latent_base_var.owner)
-    ):
+    if not latent_base_var:
         return None
 
-    base_var = cast(TensorVariable, base_var)
-
     if node.op.axis is None:
         axis = tuple(range(base_var.ndim))
     else:
@@ -119,7 +144,7 @@ def find_measurable_max(fgraph: FunctionGraph, node: Apply) -> list[TensorVariab
 
 
 measurable_ir_rewrites_db.register(
-    "find_measurable_max",
+    find_measurable_max.__name__,
     find_measurable_max,
     "basic",
     "max",
@@ -158,3 +183,54 @@ def max_logprob_discrete(op, values, base_rv, **kwargs):
 
     n = pt.prod(base_rv_shape)
     return logdiffexp(n * logcdf, n * logcdf_prev)
+
+
+class MeasurableSort(MeasurableOp, SortOp):
+    """A placeholder used to specify a log-likelihood for a sort sub-graph."""
+
+
+@_logprob.register(MeasurableSort)
+def sort_logprob(op, values, base_rv, axis, **kwargs):
+    r"""Compute the log-likelihood graph for the `Sort` operation."""
+    (value,) = values
+
+    logprob = _logprob_helper(base_rv, value).sum(axis=-1)
+
+    base_rv_shape = constant_fold(tuple(base_rv.shape), raise_not_constant=False)
+    n = pt.prod(base_rv_shape, axis=-1)
+    sorted_logp = pt.gammaln(n + 1) + logprob
+
+    # The sorted value is not really a parameter, but we include the check in
+    # `CheckParameterValue` to avoid costly sorting if `check_bounds=False` in a PyMC model
+    return CheckParameterValue("value must be sorted", can_be_replaced_by_ninf=True)(
+        sorted_logp, pt.eq(value, value.sort(axis=axis, kind=op.kind)).all()
+    )
+
+
+@node_rewriter(tracks=[SortOp])
+def find_measurable_sort(fgraph, node):
+    if isinstance(node.op, MeasurableSort):
+        return None
+
+    if not filter_measurable_variables(node.inputs):
+        return None
+
+    [base_var, axis] = node.inputs
+
+    # We allow Max of RandomVariables or IID Elemwise of univariate RandomVariables
+    if _underlying_iid_rv(base_var) is None:
+        return None
+
+    # Check axis is not potentially measurable
+    if check_potential_measurability([axis]):
+        return None
+
+    return [MeasurableSort(**node.op._props_dict())(base_var, axis)]
+
+
+measurable_ir_rewrites_db.register(
+    find_measurable_sort.__name__,
+    find_measurable_sort,
+    "basic",
+    "sort",
+)