.WIP

Author: ricardoV94

pymc_experimental/__init__.py

@@ -15,7 +15,7 @@
 
 from pymc_experimental import distributions, gp, statespace, utils
 from pymc_experimental.inference.fit import fit
-from pymc_experimental.model.marginal_model import MarginalModel
+from pymc_experimental.model.marginal.marginal_model import MarginalModel
 from pymc_experimental.model.model_api import as_model
 from pymc_experimental.version import __version__
 

pymc_experimental/model/marginal/__init__.py

@@ -0,0 +1,196 @@
+from typing import Sequence
+
+import numpy as np
+import pytensor.tensor as pt
+from pymc.distributions import (
+    Bernoulli,
+    Categorical,
+    DiscreteUniform,
+    SymbolicRandomVariable
+)
+from pymc.logprob.basic import conditional_logp, logp
+from pymc.logprob.abstract import _logprob
+from pymc.pytensorf import constant_fold
+from pytensor.graph.replace import clone_replace, graph_replace
+from pytensor.scan import scan, map as scan_map
+from pytensor.compile.mode import Mode
+from pytensor.graph import vectorize_graph
+from pytensor.tensor import TensorVariable, TensorType
+
+from pymc_experimental.distributions import DiscreteMarkovChain
+
+
+class MarginalRV(SymbolicRandomVariable):
+    """Base class for Marginalized RVs"""
+
+
+class FiniteDiscreteMarginalRV(MarginalRV):
+    """Base class for Finite Discrete Marginalized RVs"""
+
+
+class DiscreteMarginalMarkovChainRV(MarginalRV):
+    """Base class for Discrete Marginal Markov Chain RVs"""
+
+
+def get_domain_of_finite_discrete_rv(rv: TensorVariable) -> tuple[int, ...]:
+    op = rv.owner.op
+    dist_params = rv.owner.op.dist_params(rv.owner)
+    if isinstance(op, Bernoulli):
+        return (0, 1)
+    elif isinstance(op, Categorical):
+        [p_param] = dist_params
+        return tuple(range(pt.get_vector_length(p_param)))
+    elif isinstance(op, DiscreteUniform):
+        lower, upper = constant_fold(dist_params)
+        return tuple(np.arange(lower, upper + 1))
+    elif isinstance(op, DiscreteMarkovChain):
+        P, *_ = dist_params
+        return tuple(range(pt.get_vector_length(P[-1])))
+
+    raise NotImplementedError(f"Cannot compute domain for op {op}")
+
+
+def _add_reduce_batch_dependent_logps(
+    marginalized_type: TensorType, dependent_logps: Sequence[TensorVariable]
+):
+    """Add the logps of dependent RVs while reducing extra batch dims relative to `marginalized_type`."""
+
+    mbcast = marginalized_type.broadcastable
+    reduced_logps = []
+    for dependent_logp in dependent_logps:
+        dbcast = dependent_logp.type.broadcastable
+        dim_diff = len(dbcast) - len(mbcast)
+        mbcast_aligned = (True,) * dim_diff + mbcast
+        vbcast_axis = [i for i, (m, v) in enumerate(zip(mbcast_aligned, dbcast)) if m and not v]
+        reduced_logps.append(dependent_logp.sum(vbcast_axis))
+    return pt.add(*reduced_logps)
+
+
+@_logprob.register(FiniteDiscreteMarginalRV)
+def finite_discrete_marginal_rv_logp(op, values, *inputs, **kwargs):
+    # Clone the inner RV graph of the Marginalized RV
+    marginalized_rvs_node = op.make_node(*inputs)
+    marginalized_rv, *inner_rvs = clone_replace(
+        op.inner_outputs,
+        replace={u: v for u, v in zip(op.inner_inputs, marginalized_rvs_node.inputs)},
+    )
+
+    # Obtain the joint_logp graph of the inner RV graph
+    inner_rv_values = dict(zip(inner_rvs, values))
+    marginalized_vv = marginalized_rv.clone()
+    rv_values = inner_rv_values | {marginalized_rv: marginalized_vv}
+    logps_dict = conditional_logp(rv_values=rv_values, **kwargs)
+
+    # Reduce logp dimensions corresponding to broadcasted variables
+    marginalized_logp = logps_dict.pop(marginalized_vv)
+    joint_logp = marginalized_logp + _add_reduce_batch_dependent_logps(
+        marginalized_rv.type, logps_dict.values()
+    )
+
+    # Compute the joint_logp for all possible n values of the marginalized RV. We assume
+    # each original dimension is independent so that it suffices to evaluate the graph
+    # n times, once with each possible value of the marginalized RV replicated across
+    # batched dimensions of the marginalized RV
+
+    # PyMC does not allow RVs in the logp graph, even if we are just using the shape
+    marginalized_rv_shape = constant_fold(tuple(marginalized_rv.shape), raise_not_constant=False)
+    marginalized_rv_domain = get_domain_of_finite_discrete_rv(marginalized_rv)
+    marginalized_rv_domain_tensor = pt.moveaxis(
+        pt.full(
+            (*marginalized_rv_shape, len(marginalized_rv_domain)),
+            marginalized_rv_domain,
+            dtype=marginalized_rv.dtype,
+        ),
+        -1,
+        0,
+    )
+
+    try:
+        joint_logps = vectorize_graph(
+            joint_logp, replace={marginalized_vv: marginalized_rv_domain_tensor}
+        )
+    except Exception:
+        # Fallback to Scan
+        def logp_fn(marginalized_rv_const, *non_sequences):
+            return graph_replace(joint_logp, replace={marginalized_vv: marginalized_rv_const})
+
+        joint_logps, _ = scan_map(
+            fn=logp_fn,
+            sequences=marginalized_rv_domain_tensor,
+            non_sequences=[*values, *inputs],
+            mode=Mode().including("local_remove_check_parameter"),
+        )
+
+    joint_logps = pt.logsumexp(joint_logps, axis=0)
+
+    # We have to add dummy logps for the remaining value variables, otherwise PyMC will raise
+    return joint_logps, *(pt.constant(0),) * (len(values) - 1)
+
+
+@_logprob.register(DiscreteMarginalMarkovChainRV)
+def marginal_hmm_logp(op, values, *inputs, **kwargs):
+    marginalized_rvs_node = op.make_node(*inputs)
+    inner_rvs = clone_replace(
+        op.inner_outputs,
+        replace={u: v for u, v in zip(op.inner_inputs, marginalized_rvs_node.inputs)},
+    )
+
+    chain_rv, *dependent_rvs = inner_rvs
+    P, n_steps_, init_dist_, rng = chain_rv.owner.inputs
+    domain = pt.arange(P.shape[-1], dtype="int32")
+
+    # Construct logp in two steps
+    # Step 1: Compute the probability of the data ("emissions") under every possible state (vec_logp_emission)
+
+    # First we need to vectorize the conditional logp graph of the data, in case there are batch dimensions floating
+    # around. To do this, we need to break the dependency between chain and the init_dist_ random variable. Otherwise,
+    # PyMC will detect a random variable in the logp graph (init_dist_), that isn't relevant at this step.
+    chain_value = chain_rv.clone()
+    dependent_rvs = clone_replace(dependent_rvs, {chain_rv: chain_value})
+    logp_emissions_dict = conditional_logp(dict(zip(dependent_rvs, values)))
+
+    # Reduce and add the batch dims beyond the chain dimension
+    reduced_logp_emissions = _add_reduce_batch_dependent_logps(
+        chain_rv.type, logp_emissions_dict.values()
+    )
+
+    # Add a batch dimension for the domain of the chain
+    chain_shape = constant_fold(tuple(chain_rv.shape))
+    batch_chain_value = pt.moveaxis(pt.full((*chain_shape, domain.size), domain), -1, 0)
+    batch_logp_emissions = vectorize_graph(reduced_logp_emissions, {chain_value: batch_chain_value})
+
+    # Step 2: Compute the transition probabilities
+    # This is the "forward algorithm", alpha_t = p(y | s_t) * sum_{s_{t-1}}(p(s_t | s_{t-1}) * alpha_{t-1})
+    # We do it entirely in logs, though.
+
+    # To compute the prior probabilities of each state, we evaluate the logp of the domain (all possible states)
+    # under the initial distribution. This is robust to everything the user can throw at it.
+    init_dist_value = init_dist_.type()
+    logp_init_dist = logp(init_dist_, init_dist_value)
+    # There is a degerate batch dim for lags=1 (the only supported case),
+    # that we have to work around, by expanding the batch value and then squeezing it out of the logp
+    batch_logp_init_dist = vectorize_graph(
+        logp_init_dist, {init_dist_value: batch_chain_value[:, None, ..., 0]}
+    ).squeeze(1)
+    log_alpha_init = batch_logp_init_dist + batch_logp_emissions[..., 0]
+
+    def step_alpha(logp_emission, log_alpha, log_P):
+        step_log_prob = pt.logsumexp(log_alpha[:, None] + log_P, axis=0)
+        return logp_emission + step_log_prob
+
+    P_bcast_dims = (len(chain_shape) - 1) - (P.type.ndim - 2)
+    log_P = pt.shape_padright(pt.log(P), P_bcast_dims)
+    log_alpha_seq, _ = scan(
+        step_alpha,
+        non_sequences=[log_P],
+        outputs_info=[log_alpha_init],
+        # Scan needs the time dimension first, and we already consumed the 1st logp computing the initial value
+        sequences=pt.moveaxis(batch_logp_emissions[..., 1:], -1, 0),
+    )
+    # Final logp is just the sum of the last scan state
+    joint_logp = pt.logsumexp(log_alpha_seq[-1], axis=0)
+
+    # If there are multiple emission streams, we have to add dummy logps for the remaining value variables. The first
+    # return is the joint probability of everything together, but PyMC still expects one logp for each one.
+    dummy_logps = (pt.constant(0),) * (len(values) - 1)
+    return joint_logp, *dummy_logps