Allow parametrization through either shape, dims or size

Always treats `size` as being in addition to dimensions implied by RV parameters.

All resizing beyond parameter-implied dimensionality is done from:
- `shape` or `size` in `Distribution.dist()`
- `dims` or `observed` in `Distribution.__new__`
and only in those two places.

Closes #4552.

RELEASE-NOTES.md

@@ -8,6 +8,11 @@
 
 ### New Features
 - The `CAR` distribution has been added to allow for use of conditional autoregressions which often are used in spatial and network models.
+- The dimensionality of model variables can now be parametrized through either of `shape`, `dims` or `size` (see [#4625](https://github.com/pymc-devs/pymc3/pull/4625)):
+  - With `shape` the length of dimensions must be given numerically or as scalar Aesara `Variables`. Using `shape` restricts the model variable to the exact length and re-sizing is no longer possible.
+  - `dims` keeps model variables re-sizeable (for example through `pm.Data`) and leads to well defined coordinates in `InferenceData` objects.
+  - The `size` kwarg creates new dimensions in addition to what is implied by RV parameters.
+  - An `Ellipsis` (`...`) in the last position of `shape` or `dims` can be used as short-hand notation for implied dimensions.
 - ...
 
 ### Maintenance

pymc3/distributions/distribution.py

@@ -20,21 +20,17 @@
 
 from abc import ABCMeta
 from copy import copy
-from typing import TYPE_CHECKING
+from typing import Any, Optional, Sequence, Tuple, Union
 
+import aesara
+import aesara.tensor as at
 import dill
 
+from aesara.graph.basic import Variable
 from aesara.tensor.random.op import RandomVariable
 
+from pymc3.aesaraf import change_rv_size, pandas_to_array
 from pymc3.distributions import _logcdf, _logp
-
-if TYPE_CHECKING:
-    from typing import Optional, Callable
-
-import aesara
-import aesara.graph.basic
-import aesara.tensor as at
-
 from pymc3.util import UNSET, get_repr_for_variable
 from pymc3.vartypes import string_types
 
@@ -52,6 +48,10 @@
 
 PLATFORM = sys.platform
 
+Shape = Union[int, Sequence[Union[str, type(Ellipsis)]], Variable]
+Dims = Union[str, Sequence[Union[str, None, type(Ellipsis)]]]
+Size = Union[int, Tuple[int, ...]]
+
 
 class _Unpickling:
     pass
@@ -122,13 +122,111 @@ def logcdf(op, var, rvs_to_values, *dist_params, **kwargs):
         return new_cls
 
 
+def _valid_ellipsis_position(items: Union[None, Shape, Dims, Size]) -> bool:
+    if items is not None and not isinstance(items, Variable) and Ellipsis in items:
+        if any(i == Ellipsis for i in items[:-1]):
+            return False
+    return True
+
+
+def _validate_shape_dims_size(
+    shape: Any = None, dims: Any = None, size: Any = None
+) -> Tuple[Optional[Shape], Optional[Dims], Optional[Size]]:
+    # Raise on unsupported parametrization
+    if shape is not None and dims is not None:
+        raise ValueError("Passing both `shape` ({shape}) and `dims` ({dims}) is not supported!")
+    if dims is not None and size is not None:
+        raise ValueError("Passing both `dims` ({dims}) and `size` ({size}) is not supported!")
+    if shape is not None and size is not None:
+        raise ValueError("Passing both `shape` ({shape}) and `size` ({size}) is not supported!")
+
+    # Raise on invalid types
+    if not isinstance(shape, (type(None), int, list, tuple, Variable)):
+        raise ValueError("The `shape` parameter must be an int, list or tuple.")
+    if not isinstance(dims, (type(None), str, list, tuple)):
+        raise ValueError("The `dims` parameter must be a str, list or tuple.")
+    if not isinstance(size, (type(None), int, list, tuple)):
+        raise ValueError("The `size` parameter must be an int, list or tuple.")
+
+    # Auto-convert non-tupled parameters
+    if isinstance(shape, int):
+        shape = (shape,)
+    if isinstance(dims, str):
+        dims = (dims,)
+    if isinstance(size, int):
+        size = (size,)
+
+    # Convert to actual tuples
+    if not isinstance(shape, (type(None), tuple, Variable)):
+        shape = tuple(shape)
+    if not isinstance(dims, (type(None), tuple)):
+        dims = tuple(dims)
+    if not isinstance(size, (type(None), tuple)):
+        size = tuple(size)
+
+    if not _valid_ellipsis_position(shape):
+        raise ValueError(
+            f"Ellipsis in `shape` may only appear in the last position. Actual: {shape}"
+        )
+    if not _valid_ellipsis_position(dims):
+        raise ValueError(f"Ellipsis in `dims` may only appear in the last position. Actual: {dims}")
+    if size is not None and Ellipsis in size:
+        raise ValueError("The `size` parameter cannot contain an Ellipsis. Actual: {size}")
+    return shape, dims, size
+
+
 class Distribution(metaclass=DistributionMeta):
     """Statistical distribution"""
 
     rv_class = None
     rv_op = None
 
-    def __new__(cls, name, *args, **kwargs):
+    def __new__(
+        cls,
+        name: str,
+        *args,
+        rng=None,
+        dims: Optional[Dims] = None,
+        testval=None,
+        observed=None,
+        total_size=None,
+        transform=UNSET,
+        **kwargs,
+    ) -> RandomVariable:
+        """Adds a RandomVariable corresponding to a PyMC3 distribution to the current model.
+
+        Note that all remaining kwargs must be compatible with ``.dist()``
+
+        Parameters
+        ----------
+        cls : type
+            A PyMC3 distribution.
+        name : str
+            Name for the new model variable.
+        rng : optional
+            Random number generator to use with the RandomVariable.
+        dims : tuple, optional
+            A tuple of dimension names known to the model.
+        testval : optional
+            Test value to be attached to the output RV.
+            Must match its shape exactly.
+        observed : optional
+            Observed data to be passed when registering the random variable in the model.
+            See ``Model.register_rv``.
+        total_size : float, optional
+            See ``Model.register_rv``.
+        transform : optional
+            See ``Model.register_rv``.
+        **kwargs
+            Keyword arguments that will be forwarded to ``.dist()``.
+            Most prominently: ``shape`` and ``size``
+
+        Returns
+        -------
+        rv : RandomVariable
+            The created RV, registered in the Model.
+        """
+
         try:
             from pymc3.model import Model
 
@@ -141,40 +239,125 @@ def __new__(cls, name, *args, **kwargs):
                 "for a standalone distribution."
             )
 
-        rng = kwargs.pop("rng", None)
+        if not isinstance(name, string_types):
+            raise TypeError(f"Name needs to be a string but got: {name}")
 
         if rng is None:
             rng = model.default_rng
 
-        if not isinstance(name, string_types):
-            raise TypeError(f"Name needs to be a string but got: {name}")
+        _, dims, _ = _validate_shape_dims_size(dims=dims)
+        resize = None
 
-        data = kwargs.pop("observed", None)
+        # Create the RV without specifying testval, because the testval may have a shape
+        # that only matches after replicating with a size implied by dims (see below).
+        rv_out = cls.dist(*args, rng=rng, testval=None, **kwargs)
+        n_implied = rv_out.ndim
 
-        total_size = kwargs.pop("total_size", None)
+        # `dims` are only available with this API, because `.dist()` can be used
+        # without a modelcontext and dims are not tracked at the Aesara level.
+        if dims is not None:
+            if Ellipsis in dims:
+                # Auto-complete the dims tuple to the full length
+                dims = (*dims[:-1], *[None] * rv_out.ndim)
 
-        dims = kwargs.pop("dims", None)
+            n_resize = len(dims) - n_implied
 
-        if "shape" in kwargs:
-            raise DeprecationWarning("The `shape` keyword is deprecated; use `size`.")
+            # All resize dims must be known already (numerically or symbolically).
+            unknown_resize_dims = set(dims[:n_resize]) - set(model.dim_lengths)
+            if unknown_resize_dims:
+                raise KeyError(
+                    f"Dimensions {unknown_resize_dims} are unknown to the model and cannot be used to specify a `size`."
+                )
 
-        transform = kwargs.pop("transform", UNSET)
+            # The numeric/symbolic resize tuple can be created using model.RV_dim_lengths
+            resize = tuple(model.dim_lengths[dname] for dname in dims[:n_resize])
+        elif observed is not None:
+            if not hasattr(observed, "shape"):
+                observed = pandas_to_array(observed)
+            n_resize = observed.ndim - n_implied
+            resize = tuple(observed.shape[d] for d in range(n_resize))
+
+        if resize:
+            # A batch size was specified through `dims`, or implied by `observed`.
+            rv_out = change_rv_size(rv_var=rv_out, new_size=resize, expand=True)
+
+        if dims is not None:
+            # Now that we have a handle on the output RV, we can register named implied dimensions that
+            # were not yet known to the model, such that they can be used for size further downstream.
+            for di, dname in enumerate(dims[n_resize:]):
+                if not dname in model.dim_lengths:
+                    model.add_coord(dname, values=None, length=rv_out.shape[n_resize + di])
 
-        rv_out = cls.dist(*args, rng=rng, **kwargs)
+        if testval is not None:
+            # Assigning the testval earlier causes trouble because the RV may not be created with the final shape already.
+            rv_out.tag.test_value = testval
 
-        return model.register_rv(rv_out, name, data, total_size, dims=dims, transform=transform)
+        return model.register_rv(rv_out, name, observed, total_size, dims=dims, transform=transform)
 
     @classmethod
-    def dist(cls, dist_params, **kwargs):
+    def dist(
+        cls,
+        dist_params,
+        *,
+        shape: Optional[Shape] = None,
+        size: Optional[Size] = None,
+        testval=None,
+        **kwargs,
+    ) -> RandomVariable:
+        """Creates a RandomVariable corresponding to the `cls` distribution.
 
-        testval = kwargs.pop("testval", None)
+        Parameters
+        ----------
+        dist_params
+        shape : tuple, optional
+            A tuple of sizes for each dimension of the new RV.
+
+            Ellipsis (...) may be used in the last position of the tuple,
+            and automatically expand to the shape implied by RV inputs.
+        size : int, tuple, Variable, optional
+            A scalar or tuple for replicating the RV in addition
+            to its implied shape/dimensionality.
+        testval : optional
+            Test value to be attached to the output RV.
+            Must match its shape exactly.
+
+        Returns
+        -------
+        rv : RandomVariable
+            The created RV.
+        """
+        if "dims" in kwargs:
+            raise NotImplementedError("The use of a `.dist(dims=...)` API is not yet supported.")
+
+        shape, _, size = _validate_shape_dims_size(shape=shape, size=size)
+
+        # Create the RV without specifying size or testval.
+        # The size will be expanded later (if necessary) and only then the testval fits.
+        rv_native = cls.rv_op(*dist_params, size=None, **kwargs)
 
-        rv_var = cls.rv_op(*dist_params, **kwargs)
+        if shape is None and size is None:
+            size = ()
+        elif shape is not None:
+            if isinstance(shape, Variable):
+                size = ()
+            else:
+                if Ellipsis in shape:
+                    size = tuple(shape[:-1])
+                else:
+                    size = tuple(shape[: len(shape) - rv_native.ndim])
+        # no-op conditions:
+        # `elif size is not None` (User already specified how to expand the RV)
+        # `else` (Unreachable)
+
+        if size:
+            rv_out = change_rv_size(rv_var=rv_native, new_size=size, expand=True)
+        else:
+            rv_out = rv_native
 
         if testval is not None:
-            rv_var.tag.test_value = testval
+            rv_out.tag.test_value = testval
 
-        return rv_var
+        return rv_out
 
     def _distr_parameters_for_repr(self):
         """Return the names of the parameters for this distribution (e.g. "mu"