Add Beta-Binomial conjugacy optimization

Author: ricardoV94

pymc_experimental/model/marginal/distributions.py

@@ -7,7 +7,6 @@
 from pymc.logprob.abstract import MeasurableOp, _logprob
 from pymc.logprob.basic import conditional_logp, logp
 from pymc.pytensorf import constant_fold
-from pytensor import Variable
 from pytensor.compile.builders import OpFromGraph
 from pytensor.compile.mode import Mode
 from pytensor.graph import Op, vectorize_graph
@@ -17,6 +16,7 @@
 from pytensor.tensor import TensorVariable
 
 from pymc_experimental.distributions import DiscreteMarkovChain
+from pymc_experimental.utils.ofg import inline_ofg_outputs
 
 
 class MarginalRV(OpFromGraph, MeasurableOp):
@@ -126,18 +126,6 @@ def align_logp_dims(dims: tuple[tuple[int, None]], logp: TensorVariable) -> Tens
     return logp.transpose(*dims_alignment)
 
 
-def inline_ofg_outputs(op: OpFromGraph, inputs: Sequence[Variable]) -> tuple[Variable]:
-    """Inline the inner graph (outputs) of an OpFromGraph Op.
-
-    Whereas `OpFromGraph` "wraps" a graph inside a single Op, this function "unwraps"
-    the inner graph.
-    """
-    return clone_replace(
-        op.inner_outputs,
-        replace=tuple(zip(op.inner_inputs, inputs)),
-    )
-
-
 DUMMY_ZERO = pt.constant(0, name="dummy_zero")
 
 

pymc_experimental/sampling/mcmc.py

@@ -52,6 +52,44 @@ def opt_sample(
             y = pm.Binomial("y", n=100, p=p, observed=[1, 50, 99, 50]*250)
 
             idata = pmx.opt_sample(verbose=True)
+
+        # Applied optimization: beta_binomial_conjugacy 1x
+        # ConjugateRVSampler: [p]
+
+
+    You can control which optimizations are applied using the `include` and `exclude` arguments:
+
+    .. code:: python
+        import pymc as pm
+        import pymc_experimental as pmx
+
+        with pm.Model() as m:
+            p = pm.Beta("p", 1, 1, shape=(1000,))
+            y = pm.Binomial("y", n=100, p=p, observed=[1, 50, 99, 50]*250)
+
+            idata = pmx.opt_sample(exclude="conjugacy", verbose=True)
+
+        # No optimizations applied
+        # NUTS: [p]
+
+    .. code:: python
+        import pymc as pm
+        import pymc_experimental as pmx
+
+        with pm.Model() as m:
+            a = pm.InverseGamma("a", 1, 1)
+            b = pm.InverseGamma("b", 1, 1)
+            p = pm.Beta("p", a, b, shape=(1000,))
+            y = pm.Binomial("y", n=100, p=p, observed=[1, 50, 99, 50]*250)
+
+            # By default, the conjugacy of p will not be applied because it depends on other free variables
+            idata = pmx.opt_sample(include="conjugacy-eager", verbose=True)
+
+        # Applied optimization: beta_binomial_conjugacy_eager 1x
+        # CompoundStep
+        # >NUTS: [a, b]
+        # >ConjugateRVSampler: [p]
+
     """
     if kwargs.get("step", None) is not None:
         raise ValueError(

pymc_experimental/sampling/optimizations/__init__.py

@@ -1,5 +1,6 @@
 # ruff: noqa: F401
 # Add rewrites to the optimization DBs
+import pymc_experimental.sampling.optimizations.conjugacy
 import pymc_experimental.sampling.optimizations.summary_stats
 
 from pymc_experimental.sampling.optimizations.optimize import (

pymc_experimental/sampling/optimizations/conjugacy.py

@@ -0,0 +1,205 @@
+from collections.abc import Sequence
+from functools import partial
+
+from pymc.distributions import Beta, Binomial
+from pymc.model.fgraph import ModelFreeRV, ModelValuedVar, model_free_rv
+from pymc.pytensorf import collect_default_updates
+from pytensor.graph.basic import Variable, ancestors
+from pytensor.graph.fg import FunctionGraph, Output
+from pytensor.graph.rewriting.basic import node_rewriter
+from pytensor.tensor.elemwise import DimShuffle
+from pytensor.tensor.subtensor import _sum_grad_over_bcasted_dims as sum_bcasted_dims
+
+from pymc_experimental.sampling.optimizations.conjugate_sampler import (
+    ConjugateRV,
+)
+from pymc_experimental.sampling.optimizations.optimize import posterior_optimization_db
+
+
+def register_conjugacy_rewrites_variants(rewrite_fn, tracks=(ModelFreeRV,)):
+    """Register a rewrite function and its force variant in the posterior optimization DB."""
+    name = rewrite_fn.__name__
+
+    rewrite_fn_default = partial(rewrite_fn, eager=False)
+    rewrite_fn_default.__name__ = name
+    rewrite_default = node_rewriter(tracks=tracks)(rewrite_fn_default)
+
+    rewrite_fn_eager = partial(rewrite_fn, eager=True)
+    rewrite_fn_eager.__name__ = f"{name}_eager"
+    rewrite_eager = node_rewriter(tracks=tracks)(rewrite_fn_eager)
+
+    posterior_optimization_db.register(
+        rewrite_default.__name__,
+        rewrite_default,
+        "default",
+        "conjugacy",
+    )
+
+    posterior_optimization_db.register(
+        rewrite_eager.__name__,
+        rewrite_eager,
+        "non-default",
+        "conjugacy-eager",
+    )
+
+    return rewrite_default, rewrite_eager
+
+
+def has_free_rv_ancestor(vars: Variable | Sequence[Variable]) -> bool:
+    """Return True if any of the variables have a model variable as an ancestor."""
+    if not isinstance(vars, Sequence):
+        vars = (vars,)
+
+    # TODO: It should stop at observed RVs, it doesn't matter if they have a free RV above
+    #  Did not implement due to laziness and it being a rare case
+    return any(
+        var.owner is not None and isinstance(var.owner.op, ModelFreeRV) for var in ancestors(vars)
+    )
+
+
+def get_model_var_of_rv(fgraph: FunctionGraph, rv: Variable) -> Variable:
+    """Return the Model dummy var that wraps the RV"""
+    for client, _ in fgraph.clients[rv]:
+        if isinstance(client.op, ModelValuedVar):
+            return client.outputs[0]
+
+
+def get_dist_params(rv: Variable) -> tuple[Variable]:
+    return rv.owner.op.dist_params(rv.owner)
+
+
+def get_size_param(rv: Variable) -> Variable:
+    return rv.owner.op.size_param(rv.owner)
+
+
+def rv_used_by(
+    fgraph: FunctionGraph,
+    rv: Variable,
+    used_by_type: type,
+    used_as_arg_idx: int | Sequence[int],
+    arg_idx_offset: int = 2,  # Ignore the first two arguments (rng and size)
+    strict: bool = True,
+) -> list[Variable]:
+    """Return the RVs that use `rv` as an argument in an operation of type `used_by_type`.
+
+    RV may be used directly or broadcasted before being used.
+
+    Parameters
+    ----------
+    fgraph : FunctionGraph
+        The function graph containing the RVs
+    rv : Variable
+        The RV to check for uses.
+    used_by_type : type
+        The type of operation that may use the RV.
+    used_as_arg_idx : int | Sequence[int]
+        The index of the RV in the operation's inputs.
+    strict : bool, default=True
+        If True, return no results when the RV is used in an unrecognized way.
+
+    """
+    if isinstance(used_as_arg_idx, int):
+        used_as_arg_idx = (used_as_arg_idx,)
+    used_as_arg_idx = tuple(arg_idx + arg_idx_offset for arg_idx in used_as_arg_idx)
+
+    clients = fgraph.clients
+    used_by: list[Variable] = []
+    for client, inp_idx in clients[rv]:
+        if isinstance(client.op, Output):
+            continue
+
+        if isinstance(client.op, used_by_type) and inp_idx in used_as_arg_idx:
+            # RV is directly used by the RV type
+            used_by.append(client.default_output())
+
+        elif isinstance(client.op, DimShuffle) and client.op.is_left_expand_dims:
+            for sub_client, sub_inp_idx in clients[client.outputs[0]]:
+                if isinstance(sub_client.op, used_by_type) and sub_inp_idx in used_as_arg_idx:
+                    # RV is broadcasted and then used by the RV type
+                    used_by.append(sub_client.default_output())
+                elif strict:
+                    # Some other unrecognized use, bail out
+                    return []
+        elif strict:
+            # Some other unrecognized use, bail out
+            return []
+
+    return used_by
+
+
+def wrap_rv_and_conjugate_rv(
+    fgraph: FunctionGraph, rv: Variable, conjugate_rv: Variable, inputs: Sequence[Variable]
+) -> Variable:
+    """Wrap the RV and its conjugate posterior RV in a ConjugateRV node.
+
+    Also takes care of handling the random number generators used in the conjugate posterior.
+    """
+    rngs, next_rngs = zip(*collect_default_updates(conjugate_rv, inputs=[rv, *inputs]).items())
+    for rng in rngs:
+        if rng not in fgraph.inputs:
+            fgraph.add_input(rng)
+    conjugate_op = ConjugateRV(inputs=[rv, *inputs, *rngs], outputs=[rv, conjugate_rv, *next_rngs])
+    return conjugate_op(rv, *inputs, *rngs)[0]
+
+
+def create_untransformed_free_rv(
+    fgraph: FunctionGraph, rv: Variable, name: str, dims: Sequence[str | Variable]
+) -> Variable:
+    """Create a model FreeRV without transform."""
+    transform = None
+    value = rv.type(name=name)
+    fgraph.add_input(value)
+    free_rv = model_free_rv(rv, value, transform, *dims)
+    free_rv.name = name
+    return free_rv
+
+
+def beta_binomial_conjugacy(fgraph: FunctionGraph, node, eager: bool = False):
+    if not isinstance(node.op, ModelFreeRV):
+        return None
+
+    [beta_free_rv] = node.outputs
+    beta_rv, _, *beta_dims = node.inputs
+
+    if not isinstance(beta_rv.owner.op, Beta):
+        return None
+
+    a, b = get_dist_params(beta_rv)
+    if not eager and has_free_rv_ancestor([a, b]):
+        # Don't apply rewrite if a, b depend on other model variables as that will force a Gibbs sampling scheme
+        return None
+
+    p_arg_idx = 1  # Params to the Binomial are (n, p)
+    binomial_rvs = rv_used_by(fgraph, beta_free_rv, Binomial, p_arg_idx)
+
+    if len(binomial_rvs) != 1:
+        # Question: Can we apply conjugacy when RV is used by more than one binomial?
+        return None
+
+    [binomial_rv] = binomial_rvs
+
+    binomial_model_var = get_model_var_of_rv(fgraph, binomial_rv)
+    if binomial_model_var is None:
+        return None
+
+    # We want to replace free_rv by ConjugateRV()->(free_rv, conjugate_posterior_rv)
+    n, _ = get_dist_params(binomial_rv)
+
+    # Use value of y in new graph to avoid circularity
+    y = binomial_model_var.owner.inputs[1]
+
+    conjugate_a = sum_bcasted_dims(beta_rv, a + y)
+    conjugate_b = sum_bcasted_dims(beta_rv, b + (n - y))
+
+    conjugate_beta_rv = Beta.dist(conjugate_a, conjugate_b, size=get_size_param(beta_rv))
+
+    new_beta_rv = wrap_rv_and_conjugate_rv(fgraph, beta_rv, conjugate_beta_rv, [a, b, n, y])
+    new_beta_free_rv = create_untransformed_free_rv(
+        fgraph, new_beta_rv, beta_free_rv.name, beta_dims
+    )
+    return [new_beta_free_rv]
+
+
+beta_binomial_conjugacy_default, beta_binomial_conjugacy_force = (
+    register_conjugacy_rewrites_variants(beta_binomial_conjugacy)
+)