Implement RV censoring logprob and opt

Author: Ricardo

aeppl/opt.py

@@ -5,7 +5,7 @@
 from aesara.compile.mode import optdb
 from aesara.graph.features import Feature
 from aesara.graph.op import compute_test_value
-from aesara.graph.opt import EquilibriumOptimizer, local_optimizer
+from aesara.graph.opt import EquilibriumOptimizer, local_optimizer, out2in
 from aesara.graph.optdb import SequenceDB
 from aesara.tensor.extra_ops import BroadcastTo
 from aesara.tensor.random.op import RandomVariable
@@ -21,6 +21,7 @@
 )
 from aesara.tensor.var import TensorVariable
 
+from aeppl.truncation import censor_rvs
 from aeppl.utils import indices_from_subtensor
 
 inc_subtensor_ops = (IncSubtensor, AdvancedIncSubtensor, AdvancedIncSubtensor1)
@@ -182,4 +183,5 @@ def naive_bcast_rv_lift(fgraph, node):
 
 
 logprob_canonicalize.register("canonicalize", optdb["canonicalize"], -10, "basic")
-logprob_canonicalize.register("rvsinker", RVSinker(), -1, "basic")
+logprob_canonicalize.register("rvsinker", RVSinker(), -5, "basic")
+logprob_canonicalize.register("censor_rvs", out2in(censor_rvs), -1, "basic")

aeppl/truncation.py

@@ -0,0 +1,126 @@
+import warnings
+from typing import List, Optional
+
+import aesara.tensor as at
+import numpy as np
+from aesara.assert_op import Assert
+from aesara.graph.basic import Node
+from aesara.graph.fg import FunctionGraph
+from aesara.graph.opt import local_optimizer
+from aesara.scalar.basic import Clip
+from aesara.tensor.elemwise import Elemwise
+from aesara.tensor.random.op import RandomVariable
+from aesara.tensor.var import TensorConstant
+
+from aeppl.logprob import _logcdf, _logprob
+
+
+# TODO: Add interval transform
+class CensoredRV(RandomVariable):
+    r"""A base class for censored `RandomVariable`\s."""
+
+    def __init__(self, *args, base_op, **kwargs):
+        self.base_op = base_op
+        super().__init__(*args, **kwargs)
+
+
+@_logprob.register(CensoredRV)
+def censor_logprob(op, value, *inputs, name=None, **kwargs):
+
+    *rv_params, lower_bound, upper_bound = inputs
+    logprob = _logprob(op.base_op, value, *rv_params, name=name, **kwargs)
+    logcdf = _logcdf(op.base_op, value, *rv_params, name=name, **kwargs)
+    if op.base_op.name:
+        logprob.name = f"{op.base_op.name}_logprob"
+        logcdf.name = f"{op.base_op.name}_logcdf"
+
+    is_lower_bounded, is_upper_bounded = False, False
+    if not (
+        isinstance(upper_bound, TensorConstant) and np.all(upper_bound.value == np.inf)
+    ):
+        is_upper_bounded = True
+        logprob = at.switch(
+            at.eq(value, upper_bound),
+            at.log(1 - at.exp(logcdf)),
+            at.switch(at.gt(value, upper_bound), -np.inf, logprob),
+        )
+    if not (
+        isinstance(lower_bound, TensorConstant) and np.all(lower_bound.value == -np.inf)
+    ):
+        is_lower_bounded = True
+        logprob = at.switch(
+            at.eq(value, lower_bound),
+            logcdf,
+            at.switch(at.lt(value, lower_bound), -np.inf, logprob),
+        )
+
+    if is_lower_bounded and is_upper_bounded:
+        logprob = Assert("lower_bound <= upper_bound")(
+            logprob, at.all(at.le(lower_bound, upper_bound))
+        )
+
+    return logprob
+
+
+@local_optimizer(tracks=[Elemwise])
+def censor_rvs(fgraph: FunctionGraph, node: Node) -> Optional[List[Node]]:
+    # TODO: Canonicalize x[x>ub] = ub -> clip(x, x, ub)
+
+    rv_map_feature = getattr(fgraph, "preserve_rv_mappings", None)
+    if rv_map_feature is None:
+        return
+
+    if not isinstance(node.op, Elemwise) or not isinstance(node.op.scalar_op, Clip):
+        return
+
+    clipped_var = node.outputs[0]
+    if clipped_var not in rv_map_feature.rv_values:
+        return
+
+    base_var, lower_bound, upper_bound = node.inputs
+    base_op = base_var.owner.op
+
+    if not isinstance(base_op, RandomVariable):
+        return
+
+    if base_var in rv_map_feature.rv_values:
+        warnings.warn(
+            f"Value variables were assigned to both the input ({base_var}) and "
+            f"output ({clipped_var}) of a censored random variable."
+        )
+        return
+
+    censored_rv = CensoredRV(
+        "censored",
+        base_op.ndim_supp,
+        list(base_op.ndims_params) + [base_op.ndim_supp] * 2,
+        base_op.dtype,
+        inplace=False,
+        base_op=base_op,
+    )
+
+    # Replace bounds by +-inf if `y = clip(x, x, ?)` or `y=clip(x, ?, x)`
+    # This is used in `censor_logprob` to generate a more succint logprob graph
+    # for one-sided censored random variables
+    # TODO: This will probably fail for multivariate variables
+    lower_bound = lower_bound if (lower_bound is not base_var) else -np.inf
+    upper_bound = upper_bound if (upper_bound is not base_var) else np.inf
+
+    censored_node = censored_rv.make_node(
+        *base_var.owner.inputs,
+        lower_bound,
+        upper_bound,
+    )
+
+    censored_node_out = censored_node.outputs[1]
+
+    if not censored_node_out.type == clipped_var.type:
+        # TODO: issue warning?
+        return
+
+    if clipped_var.name:
+        censored_node_out.name = clipped_var.name
+    elif base_var.name:
+        censored_node_out.name = f"{base_var.name}_censored"
+
+    return [censored_node_out]

tests/test_truncation.py

@@ -0,0 +1,161 @@
+import aesara
+import aesara.tensor as at
+import numpy as np
+import pytest
+import scipy.stats as st
+
+from aeppl import joint_logprob
+from tests.utils import assert_no_rvs
+
+
+def test_uniform_censoring():
+    x_rv = at.random.uniform(-4, 5)
+    cens_x_rv = at.clip(x_rv, -1, 1)
+    cens_x_rv.name = "cens_x_rv"
+
+    cens_x = cens_x_rv.type()
+
+    logp = joint_logprob(cens_x_rv, {cens_x_rv: cens_x})
+    assert_no_rvs(logp)
+
+    logp_fn = aesara.function([cens_x], logp)
+    ref_scipy = st.uniform(-4, 9)
+
+    assert logp_fn(-5) == -np.inf
+    assert logp_fn(6) == -np.inf
+
+    assert np.isclose(logp_fn(-1), ref_scipy.logcdf(-1))
+    assert np.isclose(logp_fn(5), ref_scipy.logsf(5))
+    assert np.isclose(logp_fn(0), ref_scipy.logpdf(0))
+
+
+def test_normal_censoring():
+    x_rv = at.random.normal(0.5, 1, name="x_rv")
+    cens_x_rv = at.clip(x_rv, -2, 2)
+
+    cens_x = cens_x_rv.type()
+
+    logp = joint_logprob(cens_x_rv, {cens_x_rv: cens_x})
+    assert_no_rvs(logp)
+
+    logp_fn = aesara.function([cens_x], logp)
+    ref_scipy = st.norm(0.5, 1)
+
+    assert logp_fn(-3) == -np.inf
+    assert logp_fn(3) == -np.inf
+
+    assert np.isclose(logp_fn(-2), ref_scipy.logcdf(-2))
+    assert np.isclose(logp_fn(2), ref_scipy.logsf(2))
+    assert np.isclose(logp_fn(0), ref_scipy.logpdf(0))
+
+
+def test_one_sided_censoring():
+    x_rv = at.random.normal(0, 1)
+    lb_cens_x_rv = at.clip(x_rv, -1, x_rv)
+    ub_cens_x_rv = at.clip(x_rv, x_rv, 1)
+
+    lb_cens_x = lb_cens_x_rv.type()
+    ub_cens_x = ub_cens_x_rv.type()
+
+    lb_logp = joint_logprob(lb_cens_x_rv, {lb_cens_x_rv: lb_cens_x})
+    ub_logp = joint_logprob(ub_cens_x_rv, {ub_cens_x_rv: ub_cens_x})
+    assert_no_rvs(lb_logp)
+    assert_no_rvs(ub_logp)
+
+    logp_fn = aesara.function([lb_cens_x, ub_cens_x], [lb_logp, ub_logp])
+    ref_scipy = st.norm(0, 1)
+
+    assert np.all(np.array(logp_fn(-2, 2)) == -np.inf)
+    assert np.all(np.array(logp_fn(2, -2)) != -np.inf)
+    np.testing.assert_almost_equal(logp_fn(-1, 1), ref_scipy.logcdf(-1))
+    np.testing.assert_almost_equal(logp_fn(1, -1), ref_scipy.logpdf(-1))
+
+
+def test_useless_censoring():
+    x_rv = at.random.normal(0.5, 1, size=3)
+    cens_x_rv = at.clip(x_rv, x_rv, x_rv)
+
+    cens_x = cens_x_rv.type()
+
+    logp = joint_logprob(cens_x_rv, {cens_x_rv: cens_x})
+    assert_no_rvs(logp)
+
+    logp_fn = aesara.function([cens_x], logp)
+    ref_scipy = st.norm(0.5, 1)
+
+    np.testing.assert_allclose(logp_fn([-2, 0, 2]), ref_scipy.logpdf([-2, 0, 2]))
+
+
+def test_random_censoring():
+    lb_rv = at.random.normal(0, 1, size=2)
+    x_rv = at.random.normal(0, 2)
+    cens_x_rv = at.clip(x_rv, lb_rv, [1, 1])
+
+    lb = lb_rv.type()
+    cens_x = cens_x_rv.type()
+    logp = joint_logprob(cens_x_rv, {cens_x_rv: cens_x, lb_rv: lb})
+    assert_no_rvs(logp)
+
+    logp_fn = aesara.function([lb, cens_x], logp)
+    res = logp_fn([0, -1], [-1, -1])
+    assert res[0] == -np.inf
+    assert res[1] != -np.inf
+
+
+@pytest.mark.xfail(reason="Broadcasting not properly handled yet")
+def test_broadcasted_censoring_constant():
+    lb_rv = at.random.uniform(0, 1, name="lb_rv")
+    x_rv = at.random.normal(0, 2, name="x_rv")
+    cens_x_rv = at.clip(x_rv, lb_rv, [1, 1])
+
+    lb = lb_rv.type()
+    lb.name = "lb"
+    cens_x = cens_x_rv.type()
+    cens_x.name = "cens_x"
+
+    logp = joint_logprob(cens_x_rv, {cens_x_rv: cens_x, lb_rv: lb})
+    assert_no_rvs(logp)
+
+
+@pytest.mark.xfail(reason="Broadcasting not properly handled yet")
+def test_broadcasted_censoring_random():
+    lb_rv = at.random.normal(0, 1, name="lb_rv")
+    x_rv = at.random.normal(0, 2, size=2, name="x_rv")
+    cens_x_rv = at.clip(x_rv, lb_rv, [1, 1])
+
+    lb = lb_rv.type()
+    lb.name = "lb"
+    cens_x = cens_x_rv.type()
+    cens_x.name = "cens_x"
+
+    logp = joint_logprob(cens_x_rv, {cens_x_rv: cens_x, lb_rv: lb})
+    assert_no_rvs(logp)
+
+
+def test_failed_censoring():
+    # Test that `joint_logprob` fails when both base_rv and clipped_rv are given
+    # value vars
+    x_rv = at.random.normal(0, 1)
+    cens_x_rv = at.clip(x_rv, x_rv, 1)
+
+    x = x_rv.type()
+    cens_x = cens_x_rv.type()
+    with pytest.raises(NotImplementedError):
+        joint_logprob(cens_x_rv, {cens_x_rv: cens_x, x_rv: x})
+
+
+def test_deterministic_clipping():
+    x_rv = at.random.normal(0, 1)
+    clip = at.clip(x_rv, 0, 0)
+    y_rv = at.random.normal(clip, 1)
+
+    x = x_rv.type()
+    y = y_rv.type()
+    logp = joint_logprob(y_rv, {x_rv: x, y_rv: y})
+    assert_no_rvs(logp)
+
+    logp_fn = aesara.function([x, y], logp)
+    assert np.isclose(
+        logp_fn(-1, 1),
+        st.norm(0, 1).logpdf(-1) + st.norm(0, 1).logpdf(1),
+    )