improve ABC sampler (#3940)

* Expand ABC features.

* valueerror

* update notebook

* remove unused import update release notes

* fix notebook style and change order params argument

Author: aloctavodia

RELEASE-NOTES.md

@@ -19,6 +19,7 @@
 - `pm.Data` container can now be used as input for other random variables (issue [#3842](https://github.com/pymc-devs/pymc3/issues/3842), fixed by [#3925](https://github.com/pymc-devs/pymc3/pull/3925)).
 - Plots and Stats API sections now link to ArviZ documentation [#3927](https://github.com/pymc-devs/pymc3/pull/3927)
 - Add `SamplerReport` with properties `n_draws`, `t_sampling` and `n_tune` to SMC. `n_tune` is always 0 [#3931](https://github.com/pymc-devs/pymc3/issues/3931).
+- SMC-ABC: add option to define summary statistics, allow to sample from more complex models, remove redundant distances [#3940](https://github.com/pymc-devs/pymc3/issues/3940)
 
 ### Maintenance
 - Tuning results no longer leak into sequentially sampled `Metropolis` chains (see #3733 and #3796).

docs/source/notebooks/SMC-ABC_Lotka-Volterra_example.ipynb

@@ -19,17 +19,20 @@
 
 
 class Simulator(NoDistribution):
-    def __init__(self, function, *args, **kwargs):
+    def __init__(self, function, *args, params=None, **kwargs):
         """
         This class stores a function defined by the user in python language.
         
         function: function
             Simulation function defined by the user.
+        params: list
+            Parameters passed to function.
         *args and **kwargs: 
             Arguments and keywords arguments that the function takes.
         """
 
         self.function = function
+        self.params = params
         observed = self.data
         super().__init__(shape=np.prod(observed.shape), dtype=observed.dtype, *args, **kwargs)
 

pymc3/distributions/simulator.py

@@ -28,8 +28,8 @@ def sample_smc(
     p_acc_rate=0.99,
     threshold=0.5,
     epsilon=1.0,
-    dist_func="absolute_error",
-    sum_stat=False,
+    dist_func="gaussian_kernel",
+    sum_stat="identity",
     progressbar=False,
     model=None,
     random_seed=-1,
@@ -71,11 +71,10 @@ def sample_smc(
     epsilon: float
         Standard deviation of the gaussian pseudo likelihood. Only works with `kernel = ABC`
     dist_func: str
-        Distance function. Available options are ``absolute_error`` (default) and
-        ``sum_of_squared_distance``. Only works with ``kernel = ABC``
-    sum_stat: bool
-        Whether to use or not a summary statistics. Defaults to False. Only works with
-        ``kernel = ABC``
+        Distance function. The only available option is ``gaussian_kernel``
+    sum_stat: str or callable
+        Summary statistics. Available options are ``indentity``, ``sorted``, ``mean``, ``median``.
+        If a callable is based it should return a number or a 1d numpy array.
     progressbar: bool
         Flag for displaying a progress bar. Defaults to False.
     model: Model (optional if in ``with`` context)).

pymc3/smc/sample_smc.py

@@ -31,7 +31,6 @@
 from ..step_methods.metropolis import MultivariateNormalProposal
 from ..backends.ndarray import NDArray
 from ..backends.base import MultiTrace
-from ..util import is_transformed_name
 
 EXPERIMENTAL_WARNING = (
     "Warning: SMC-ABC methods are experimental step methods and not yet"
@@ -53,7 +52,7 @@ def __init__(
         threshold=0.5,
         epsilon=1.0,
         dist_func="absolute_error",
-        sum_stat=False,
+        sum_stat="Identity",
         progressbar=False,
         model=None,
         random_seed=-1,
@@ -140,6 +139,7 @@ def setup_kernel(self):
                 self.epsilon,
                 simulator.observations,
                 simulator.distribution.function,
+                [v.name for v in simulator.distribution.params],
                 self.model,
                 self.var_info,
                 self.variables,
@@ -281,7 +281,7 @@ def mutate(self):
                     self.priors[draw],
                     self.likelihoods[draw],
                     draw,
-                    *parameters
+                    *parameters,
                 )
                 for draw in iterator
             ]
@@ -307,7 +307,7 @@ def posterior_to_trace(self):
             size = 0
             for var in varnames:
                 shape, new_size = self.var_info[var]
-                value.append(self.posterior[i][size: size + new_size].reshape(shape))
+                value.append(self.posterior[i][size : size + new_size].reshape(shape))
                 size += new_size
             strace.record({k: v for k, v in zip(varnames, value)})
         return MultiTrace([strace])
@@ -389,7 +389,16 @@ class PseudoLikelihood:
     """
 
     def __init__(
-        self, epsilon, observations, function, model, var_info, variables, distance, sum_stat
+        self,
+        epsilon,
+        observations,
+        function,
+        params,
+        model,
+        var_info,
+        variables,
+        distance,
+        sum_stat,
     ):
         """
         epsilon: float
@@ -398,34 +407,48 @@ def __init__(
             observed data
         function: python function
             data simulator
+        params: list
+            names of the variables parameterizing the simulator.
         model: PyMC3 model
         var_info: dict
             generated by ``SMC.initialize_population``
-        distance: str
-            Distance function. Available options are ``absolute_error`` (default) and
-            ``sum_of_squared_distance``.
-        sum_stat: bool
-            Whether to use or not a summary statistics.
+        distance : str or callable
+            Distance function. The only available option is ``gaussian_kernel``
+        sum_stat: str or callable
+            Summary statistics. Available options are ``indentity``, ``sorted``, ``mean``,
+            ``median``. The user can pass any valid Python function
         """
         self.epsilon = epsilon
-        self.observations = observations
         self.function = function
+        self.params = params
         self.model = model
         self.var_info = var_info
         self.variables = variables
         self.varnames = [v.name for v in self.variables]
         self.unobserved_RVs = [v.name for v in self.model.unobserved_RVs]
-        self.kernel = self.gauss_kernel
-        self.dist_func = distance
-        self.sum_stat = sum_stat
         self.get_unobserved_fn = self.model.fastfn(self.model.unobserved_RVs)
 
-        if distance == "absolute_error":
-            self.dist_func = self.absolute_error
-        elif distance == "sum_of_squared_distance":
-            self.dist_func = self.sum_of_squared_distance
+        if sum_stat == "identity":
+            self.sum_stat = lambda x: x
+        elif sum_stat == "sorted":
+            self.sum_stat = np.sort
+        elif sum_stat == "mean":
+            self.sum_stat = np.mean
+        elif sum_stat == "median":
+            self.sum_stat = np.median
+        elif hasattr(sum_stat, "__call__"):
+            self.sum_stat = sum_stat
+        else:
+            raise ValueError(f"The summary statistics {sum_stat} is not implemented")
+
+        self.observations = self.sum_stat(observations)
+
+        if distance == "gaussian_kernel":
+            self.distance = self.gaussian_kernel
+        elif hasattr(distance, "__call__"):
+            self.distance = distance
         else:
-            raise ValueError("Distance metric not understood")
+            raise ValueError(f"The distance metric {distance} is not implemented")
 
     def posterior_to_function(self, posterior):
         model = self.model
@@ -436,32 +459,18 @@ def posterior_to_function(self, posterior):
         size = 0
         for var in self.variables:
             shape, new_size = var_info[var.name]
-            varvalues.append(posterior[size: size + new_size].reshape(shape))
+            varvalues.append(posterior[size : size + new_size].reshape(shape))
             size += new_size
         point = {k: v for k, v in zip(self.varnames, varvalues)}
         for varname, value in zip(self.unobserved_RVs, self.get_unobserved_fn(point)):
-            if not is_transformed_name(varname):
+            if varname in self.params:
                 samples[varname] = value
         return samples
 
-    def gauss_kernel(self, value):
-        epsilon = self.epsilon
-        return (-(value ** 2) / epsilon ** 2 + np.log(1 / (2 * np.pi * epsilon ** 2))) / 2.0
-
-    def absolute_error(self, a, b):
-        if self.sum_stat:
-            return np.abs(a.mean() - b.mean())
-        else:
-            return np.mean(np.atleast_2d(np.abs(a - b)))
-
-    def sum_of_squared_distance(self, a, b):
-        if self.sum_stat:
-            return np.sum(np.atleast_2d((a.mean() - b.mean()) ** 2))
-        else:
-            return np.mean(np.sum(np.atleast_2d((a - b) ** 2)))
+    def gaussian_kernel(self, obs_data, sim_data):
+        return np.sum(-0.5 * ((obs_data - sim_data) / self.epsilon) ** 2)
 
     def __call__(self, posterior):
         func_parameters = self.posterior_to_function(posterior)
-        sim_data = self.function(**func_parameters)
-        value = self.dist_func(self.observations, sim_data)
-        return self.kernel(value)
+        sim_data = self.sum_stat(self.function(**func_parameters))
+        return self.distance(self.observations, sim_data)

pymc3/smc/smc.py

@@ -98,19 +98,19 @@ def test_start(self):
 class TestSMCABC(SeededTest):
     def setup_class(self):
         super().setup_class()
-        self.data = np.sort(np.random.normal(loc=0, scale=1, size=1000))
+        self.data = np.random.normal(loc=0, scale=1, size=1000)
 
         def normal_sim(a, b):
-            return np.sort(np.random.normal(a, b, 1000))
+            return np.random.normal(a, b, 1000)
 
         with pm.Model() as self.SMABC_test:
             a = pm.Normal("a", mu=0, sd=5)
             b = pm.HalfNormal("b", sd=2)
-            s = pm.Simulator("s", normal_sim, observed=self.data)
+            s = pm.Simulator("s", normal_sim, params=(a, b), observed=self.data)
 
     def test_one_gaussian(self):
         with self.SMABC_test:
-            trace = pm.sample_smc(draws=2000, kernel="ABC", epsilon=0.1)
+            trace = pm.sample_smc(draws=1000, kernel="ABC", sum_stat="sorted", epsilon=1)
 
         np.testing.assert_almost_equal(self.data.mean(), trace["a"].mean(), decimal=2)
         np.testing.assert_almost_equal(self.data.std(), trace["b"].mean(), decimal=1)