Use Aeppl for implementing GaussianRandomWalk

Co-authored-by: Ricardo Vieira <[email protected]>

Co-authored-by: lucianopaz <[email protected]>

Author: 2 people

pymc/aesaraf.py

@@ -33,11 +33,12 @@
 import scipy.sparse as sps
 
 from aeppl.abstract import MeasurableVariable
-from aeppl.logprob import CheckParameterValue
+from aeppl.logprob import CheckParameterValue, _logprob, logprob
+from aeppl.tensor import MeasurableJoin
 from aesara import config, scalar
 from aesara.compile.mode import Mode, get_mode
 from aesara.gradient import grad
-from aesara.graph import local_optimizer
+from aesara.graph import local_optimizer, optimize_graph
 from aesara.graph.basic import (
     Apply,
     Constant,
@@ -52,6 +53,7 @@
 from aesara.sandbox.rng_mrg import MRG_RandomStream as RandomStream
 from aesara.scalar.basic import Cast
 from aesara.tensor.basic import _as_tensor_variable
+from aesara.tensor.basic_opt import topo_constant_folding
 from aesara.tensor.elemwise import Elemwise
 from aesara.tensor.random.op import RandomVariable
 from aesara.tensor.random.var import (
@@ -875,6 +877,52 @@ def largest_common_dtype(tensors):
     return np.stack([np.ones((), dtype=dtype) for dtype in dtypes]).dtype
 
 
+@_logprob.register(MeasurableJoin)
+def logprob_join_constant_shapes(op, values, axis, *base_vars, **kwargs):
+    """Compute the log-likelihood graph for a `Join`.
+
+    This overrides the implementation in Aeppl, to constant fold the shapes
+    of the base vars so that RandomVariables do not show up in the logp graph
+    """
+    (value,) = values
+
+    base_var_shapes = at.stack([base_var.shape[axis] for base_var in base_vars])
+
+    base_var_shapes = optimize_graph(
+        base_var_shapes,
+        custom_opt=topo_constant_folding,
+    )
+
+    split_values = at.split(
+        value,
+        splits_size=[base_var_shape for base_var_shape in base_var_shapes],
+        n_splits=len(base_vars),
+        axis=axis,
+    )
+
+    logps = [
+        logprob(base_var, split_value)
+        for base_var, split_value in zip(base_vars, split_values)
+    ]
+
+    if len(set(logp.ndim for logp in logps)) != 1:
+        raise ValueError(
+            "Joined logps have different number of dimensions, this can happen when "
+            "joining univariate and multivariate distributions",
+        )
+
+    base_vars_ndim_supp = split_values[0].ndim - logps[0].ndim
+    join_logprob = at.concatenate(
+        [
+            at.atleast_1d(logprob(base_var, split_value))
+            for base_var, split_value in zip(base_vars, split_values)
+        ],
+        axis=axis - base_vars_ndim_supp,
+    )
+
+    return join_logprob
+
+
 @local_optimizer(tracks=[CheckParameterValue])
 def local_remove_check_parameter(fgraph, node):
     """Rewrite that removes Aeppl's CheckParameterValue

pymc/distributions/timeseries.py

@@ -13,7 +13,7 @@
 #   limitations under the License.
 import warnings
 
-from typing import Any, Optional, Tuple, Union
+from typing import Any, Optional, Union
 
 import aesara
 import aesara.tensor as at
@@ -28,22 +28,15 @@
 from aesara.raise_op import Assert
 from aesara.tensor import TensorVariable
 from aesara.tensor.basic_opt import ShapeFeature, topo_constant_folding
+from aesara.tensor.extra_ops import CumOp
 from aesara.tensor.random.op import RandomVariable
-from aesara.tensor.random.utils import normalize_size_param
 
 from pymc.aesaraf import change_rv_size, convert_observed_data, floatX, intX
 from pymc.distributions import distribution, multivariate
 from pymc.distributions.continuous import Flat, Normal, get_tau_sigma
-from pymc.distributions.dist_math import check_parameters
 from pymc.distributions.distribution import SymbolicDistribution, _moment, moment
 from pymc.distributions.logprob import ignore_logprob, logp
-from pymc.distributions.shape_utils import (
-    Dims,
-    Shape,
-    convert_dims,
-    rv_size_is_none,
-    to_tuple,
-)
+from pymc.distributions.shape_utils import Dims, Shape, convert_dims, to_tuple
 from pymc.model import modelcontext
 from pymc.util import check_dist_not_registered
 
@@ -114,110 +107,8 @@ def get_steps(
     return inferred_steps
 
 
-class GaussianRandomWalkRV(RandomVariable):
-    """
-    GaussianRandomWalk Random Variable
-    """
-
-    name = "GaussianRandomWalk"
-    ndim_supp = 1
-    ndims_params = [0, 0, 0, 0]
-    dtype = "floatX"
-    _print_name = ("GaussianRandomWalk", "\\operatorname{GaussianRandomWalk}")
-
-    def make_node(self, rng, size, dtype, mu, sigma, init_dist, steps):
-        steps = at.as_tensor_variable(steps)
-        if not steps.ndim == 0 or not steps.dtype.startswith("int"):
-            raise ValueError("steps must be an integer scalar (ndim=0).")
-
-        mu = at.as_tensor_variable(mu)
-        sigma = at.as_tensor_variable(sigma)
-        init_dist = at.as_tensor_variable(init_dist)
-
-        # Resize init distribution
-        size = normalize_size_param(size)
-        # If not explicit, size is determined by the shapes of mu, sigma, and init
-        init_dist_size = (
-            size if not rv_size_is_none(size) else at.broadcast_shape(mu, sigma, init_dist)
-        )
-        init_dist = change_rv_size(init_dist, init_dist_size)
-
-        return super().make_node(rng, size, dtype, mu, sigma, init_dist, steps)
-
-    def _supp_shape_from_params(self, dist_params, reop_param_idx=0, param_shapes=None):
-        steps = dist_params[3]
-
-        return (steps + 1,)
-
-    @classmethod
-    def rng_fn(
-        cls,
-        rng: np.random.RandomState,
-        mu: Union[np.ndarray, float],
-        sigma: Union[np.ndarray, float],
-        init_dist: Union[np.ndarray, float],
-        steps: int,
-        size: Tuple[int],
-    ) -> np.ndarray:
-        """Gaussian Random Walk generator.
-
-        The init value is drawn from the Normal distribution with the same sigma as the
-        innovations.
-
-        Notes
-        -----
-        Currently does not support custom init distribution
-
-        Parameters
-        ----------
-        rng: np.random.RandomState
-           Numpy random number generator
-        mu: array_like of float
-           Random walk mean
-        sigma: array_like of float
-            Standard deviation of innovation (sigma > 0)
-        init_dist: array_like of float
-            Initialization value for GaussianRandomWalk
-        steps: int
-            Length of random walk, must be greater than 1. Returned array will be of size+1 to
-            account as first value is initial value
-        size: tuple of int
-            The number of Random Walk time series generated
-
-        Returns
-        -------
-        ndarray
-        """
-
-        if steps < 1:
-            raise ValueError("Steps must be greater than 0")
-
-        # If size is None then the returned series should be (*implied_dims, 1+steps)
-        if size is None:
-            # broadcast parameters with each other to find implied dims
-            bcast_shape = np.broadcast_shapes(
-                np.asarray(mu).shape,
-                np.asarray(sigma).shape,
-                np.asarray(init_dist).shape,
-            )
-            dist_shape = (*bcast_shape, int(steps))
-
-        # If size is None then the returned series should be (*size, 1+steps)
-        else:
-            dist_shape = (*size, int(steps))
-
-        # Add one dimension to the right, so that mu and sigma broadcast safely along
-        # the steps dimension
-        innovations = rng.normal(loc=mu[..., None], scale=sigma[..., None], size=dist_shape)
-        grw = np.concatenate([init_dist[..., None], innovations], axis=-1)
-        return np.cumsum(grw, axis=-1)
-
-
-gaussianrandomwalk = GaussianRandomWalkRV()
-
-
-class GaussianRandomWalk(distribution.Continuous):
-    r"""Random Walk with Normal innovations.
+class GaussianRandomWalk(SymbolicDistribution):
+    r"""Random Walk with Normal innovations
 
     Parameters
     ----------
@@ -236,8 +127,6 @@ class GaussianRandomWalk(distribution.Continuous):
         provided.
     """
 
-    rv_op = gaussianrandomwalk
-
     def __new__(cls, *args, steps=None, **kwargs):
         steps = get_steps(
             steps=steps,
@@ -269,6 +158,8 @@ def dist(cls, mu=0.0, sigma=1.0, *, init_dist=None, steps=None, **kwargs) -> at.
                 FutureWarning,
             )
             init_dist = kwargs.pop("init")
+        if not steps.ndim == 0:
+            raise ValueError("steps must be an integer scalar (ndim=0).")
 
         # If no scalar distribution is passed then initialize with a Normal of same mu and sigma
         if init_dist is None:
@@ -293,39 +184,67 @@ def dist(cls, mu=0.0, sigma=1.0, *, init_dist=None, steps=None, **kwargs) -> at.
 
         return super().dist([mu, sigma, init_dist, steps], **kwargs)
 
-    def moment(rv, size, mu, sigma, init_dist, steps):
-        grw_moment = at.zeros_like(rv)
-        grw_moment = at.set_subtensor(grw_moment[..., 0], moment(init_dist))
-        # Add one dimension to the right, so that mu broadcasts safely along the steps
-        # dimension
-        grw_moment = at.set_subtensor(grw_moment[..., 1:], mu[..., None])
-        return at.cumsum(grw_moment, axis=-1)
-
-    def logp(
-        value: at.Variable,
-        mu: at.Variable,
-        sigma: at.Variable,
-        init_dist: at.Variable,
-        steps: at.Variable,
-    ) -> at.TensorVariable:
-        """Calculate log-probability of Gaussian Random Walk distribution at specified value."""
-
-        # Calculate initialization logp
-        init_logp = logp(init_dist, value[..., 0])
-
-        # Make time series stationary around the mean value
-        stationary_series = value[..., 1:] - value[..., :-1]
-        # Add one dimension to the right, so that mu and sigma broadcast safely along
-        # the steps dimension
-        series_logp = logp(Normal.dist(mu[..., None], sigma[..., None]), stationary_series)
-
-        return check_parameters(
-            init_logp + series_logp.sum(axis=-1),
-            steps > 0,
-            msg="steps > 0",
+    @classmethod
+    def ndim_supp(cls, *args):
+        return 1
+
+    @classmethod
+    def rv_op(cls, mu, sigma, init_dist, steps, size=None):
+        # If not explicit, size is determined by the shapes of mu, sigma, and init
+        if size is not None:
+            # we have all the information regarding size from users or .dist()
+            init_size = size
+        else:
+            # we infer size from parameters
+            init_size = at.broadcast_shape(
+                mu,
+                sigma,
+                init_dist,
+            )
+
+        # TODO: extend for multivariate init
+        init_dist = change_rv_size(init_dist, init_size)
+        innovation_dist = Normal.dist(mu[..., None], sigma[..., None], size=(*init_size, steps))
+        rv_out = at.cumsum(at.concatenate([init_dist[..., None], innovation_dist], axis=-1), axis=-1)
+
+        rv_out.tag.mu = mu
+        rv_out.tag.sigma = sigma
+        rv_out.tag.init_dist = init_dist
+        rv_out.tag.innovation_dist = innovation_dist
+        rv_out.tag.steps = steps
+        rv_out.tag.is_grw = True  # for moment dispatching
+
+        return rv_out
+
+    @classmethod
+    def change_size(cls, rv, new_size, expand=False):
+        if expand:
+            new_size = at.concatenate([new_size, rv.shape[:-1]])
+
+        return cls.rv_op(
+            mu=rv.tag.mu,
+            sigma=rv.tag.sigma,
+            init_dist=rv.tag.init_dist,
+            steps=rv.tag.steps,
+            size=new_size,
         )
 
 
+@_moment.register(CumOp)
+def moment_grw(op, rv, dist_params):
+    """
+    This moment dispatch is currently only applicable for a GaussianRandomWalk.
+    TODO: Encapsulate GRW graph in an OpFromGraph so that we can dispatch
+     the moment directly on it
+    """
+    if not getattr(rv.tag, "is_grw", False):
+        raise NotImplementedError("Moment not implemented for `CumOp`")
+    init_dist = rv.tag.init_dist
+    innovation_dist = rv.tag.innovation_dist
+    grw_moment = at.concatenate([moment(init_dist)[..., None], moment(innovation_dist)], axis=-1)
+    return at.cumsum(grw_moment, axis=-1)
+
+
 class AutoRegressiveRV(OpFromGraph):
     """A placeholder used to specify a log-likelihood for an AR sub-graph."""
 

pymc/tests/test_distributions_moments.py

@@ -28,6 +28,7 @@
     Exponential,
     Flat,
     Gamma,
+    GaussianRandomWalk,
     Geometric,
     Gumbel,
     HalfCauchy,
@@ -1506,3 +1507,43 @@ def test_dirichlet_multinomial_moment(a, n, size, expected):
     with Model() as model:
         DirichletMultinomial("x", n=n, a=a, size=size)
     assert_moment_is_expected(model, expected)
+
+
+even_numbers = np.insert(np.cumsum(np.tile(2, 10)), 0, 0)  # for test_gaussianrandomwalk below
+
+
+@pytest.mark.parametrize(
+    "mu, sigma, init_dist, steps, size, expected",
+    [
+        (0, 3, StudentT.dist(5), 10, None, np.zeros(11)),
+        (Normal.dist(2, 3), Gamma.dist(1, 1), StudentT.dist(5), 10, None, even_numbers),
+        (
+            Normal.dist(2, 3, size=(3, 5)),
+            Gamma.dist(1, 1),
+            StudentT.dist(5),
+            10,
+            None,
+            np.broadcast_to(even_numbers, shape=(3, 5, 11)),
+        ),
+        (
+            Normal.dist(2, 3, size=(3, 1)),
+            Gamma.dist(1, 1, size=(1, 5)),
+            StudentT.dist(5),
+            10,
+            (3, 5),
+            np.broadcast_to(even_numbers, shape=(3, 5, 11)),
+        ),
+        (
+            Normal.dist(2, 3),
+            Gamma.dist(1, 1),
+            StudentT.dist(5),
+            10,
+            (3, 5),
+            np.broadcast_to(even_numbers, shape=(3, 5, 11)),
+        ),
+    ],
+)
+def test_gaussianrandomwalk(mu, sigma, init_dist, steps, size, expected):
+    with Model() as model:
+        GaussianRandomWalk("x", mu=mu, sigma=sigma, init_dist=init_dist, steps=steps, size=size)
+    assert_moment_is_expected(model, expected)