Implement step method sampler for DiscreteMarkovChain

Author: ricardoV94

pymc_experimental/distributions/timeseries.py

@@ -20,7 +20,12 @@
 from pymc.logprob.abstract import _logprob
 from pymc.logprob.basic import logp
 from pymc.pytensorf import constant_fold, intX
-from pymc.util import check_dist_not_registered
+from pymc.step_methods import STEP_METHODS
+from pymc.step_methods.arraystep import ArrayStep
+from pymc.step_methods.compound import Competence
+from pymc.step_methods.metropolis import CategoricalGibbsMetropolis
+from pymc.util import check_dist_not_registered, get_value_vars_from_user_vars
+from pytensor import Mode
 from pytensor.graph.basic import Node
 from pytensor.tensor import TensorVariable
 from pytensor.tensor.random.op import RandomVariable
@@ -101,10 +106,15 @@ class DiscreteMarkovChain(Distribution):
      Create a Markov Chain of length 100 with 3 states. The number of states is given by the shape of P,
      3 in this case.
 
-    >>> with pm.Model() as markov_chain:
-    >>>     P = pm.Dirichlet("P", a=[1, 1, 1], size=(3,))
-    >>>     init_dist = pm.Categorical.dist(p = np.full(3, 1 / 3))
-    >>>     markov_chain = pm.DiscreteMarkovChain("markov_chain", P=P, init_dist=init_dist, shape=(100,))
+    .. code-block:: python
+
+        import pymc as pm
+        import pymc_experimental as pmx
+
+        with pm.Model() as markov_chain:
+            P = pm.Dirichlet("P", a=[1, 1, 1], size=(3,))
+            init_dist = pm.Categorical.dist(p = np.full(3, 1 / 3))
+            markov_chain = pmx.DiscreteMarkovChain("markov_chain", P=P, init_dist=init_dist, shape=(100,))
 
     """
 
@@ -266,3 +276,70 @@ def discrete_mc_logp(op, values, P, steps, init_dist, state_rng, **kwargs):
         "P must sum to 1 along the last axis, "
         "First dimension of init_dist must be n_lags",
     )
+
+
+class DiscreteMarkovChainGibbsMetropolis(CategoricalGibbsMetropolis):
+
+    name = "discrete_markov_chain_gibbs_metropolis"
+
+    def __init__(self, vars, proposal="uniform", order="random", model=None):
+        model = pm.modelcontext(model)
+        vars = get_value_vars_from_user_vars(vars, model)
+        initial_point = model.initial_point()
+
+        dimcats = []
+        # The above variable is a list of pairs (aggregate dimension, number
+        # of categories). For example, if vars = [x, y] with x being a 2-D
+        # variable with M categories and y being a 3-D variable with N
+        # categories, we will have dimcats = [(0, M), (1, M), (2, N), (3, N), (4, N)].
+        for v in vars:
+            v_init_val = initial_point[v.name]
+            rv_var = model.values_to_rvs[v]
+            rv_op = rv_var.owner.op
+
+            if not isinstance(rv_op, DiscreteMarkovChainRV):
+                raise TypeError("All variables must be DiscreteMarkovChainRV")
+
+            k_graph = rv_var.owner.inputs[0].shape[-1]
+            (k_graph,) = model.replace_rvs_by_values((k_graph,))
+            k = model.compile_fn(
+                k_graph,
+                inputs=model.value_vars,
+                on_unused_input="ignore",
+                mode=Mode(linker="py", optimizer=None),
+            )(initial_point)
+            start = len(dimcats)
+            dimcats += [(dim, k) for dim in range(start, start + v_init_val.size)]
+
+        if order == "random":
+            self.shuffle_dims = True
+            self.dimcats = dimcats
+        else:
+            if sorted(order) != list(range(len(dimcats))):
+                raise ValueError("Argument 'order' has to be a permutation")
+            self.shuffle_dims = False
+            self.dimcats = [dimcats[j] for j in order]
+
+        if proposal == "uniform":
+            self.astep = self.astep_unif
+        elif proposal == "proportional":
+            # Use the optimized "Metropolized Gibbs Sampler" described in Liu96.
+            self.astep = self.astep_prop
+        else:
+            raise ValueError("Argument 'proposal' should either be 'uniform' or 'proportional'")
+
+        # Doesn't actually tune, but it's required to emit a sampler stat
+        # that indicates whether a draw was done in a tuning phase.
+        self.tune = True
+
+        # We bypass CategoryGibbsMetropolis's __init__ to avoid it's specialiazed initialization logic
+        ArrayStep.__init__(self, vars, [model.compile_logp()])
+
+    @staticmethod
+    def competence(var):
+        if isinstance(var.owner.op, DiscreteMarkovChainRV):
+            return Competence.IDEAL
+        return Competence.INCOMPATIBLE
+
+
+STEP_METHODS.append(DiscreteMarkovChainGibbsMetropolis)

pymc_experimental/tests/distributions/test_discrete_markov_chain.py

@@ -4,10 +4,15 @@
 # general imports
 import pytensor.tensor as pt
 import pytest
+from pymc.distributions import Categorical
 from pymc.distributions.shape_utils import change_dist_size
 from pymc.logprob.utils import ParameterValueError
+from pymc.sampling.mcmc import assign_step_methods
 
-from pymc_experimental.distributions.timeseries import DiscreteMarkovChain
+from pymc_experimental.distributions.timeseries import (
+    DiscreteMarkovChain,
+    DiscreteMarkovChainGibbsMetropolis,
+)
 
 
 def transition_probability_tests(steps, n_states, n_lags, n_draws, atol):
@@ -215,3 +220,37 @@ def test_change_size_univariate(self):
 
         new_rw = change_dist_size(chain, new_size=(4, 3), expand=True)
         assert tuple(new_rw.shape.eval()) == (4, 3, 100, 5)
+
+    def test_mcmc_sampling(self):
+
+        with pm.Model(coords={"step": range(100)}) as model:
+            init_dist = Categorical.dist(p=[0.5, 0.5])
+            DiscreteMarkovChain(
+                "markov_chain",
+                P=[[0.1, 0.9], [0.1, 0.9]],
+                init_dist=init_dist,
+                shape=(100,),
+                dims="step",
+            )
+
+            step_method = assign_step_methods(model)
+            assert isinstance(step_method, DiscreteMarkovChainGibbsMetropolis)
+
+            # Sampler needs no tuning
+            idata = pm.sample(
+                tune=0, chains=4, draws=250, progressbar=False, compute_convergence_checks=False
+            )
+
+        np.testing.assert_allclose(
+            idata.posterior["markov_chain"].isel(step=0).mean(("chain", "draw")),
+            0.5,
+            atol=0.05,
+        )
+
+        np.testing.assert_allclose(
+            idata.posterior["markov_chain"].isel(step=slice(1, None)).mean(("chain", "draw")),
+            0.9,
+            atol=0.05,
+        )
+
+        assert pm.stats.ess(idata, method="tail").min() > 950