Implement more robust jitter init (resolves #4107)

RELEASE-NOTES.md

@@ -48,6 +48,7 @@ This new version of `Theano-PyMC` comes with an experimental JAX backend which,
 - Fix bug in `model.check_test_point` that caused the `test_point` argument to be ignored. (see [PR #4211](https://github.com/pymc-devs/pymc3/pull/4211#issuecomment-727142721))
 - Refactored MvNormal.random method with better handling of sample, batch and event shapes. [#4207](https://github.com/pymc-devs/pymc3/pull/4207)
 - The `InverseGamma` distribution now implements a `logcdf`. [#3944](https://github.com/pymc-devs/pymc3/pull/3944)
+- Make starting jitter methods for nuts sampling more robust by resampling values that lead to non-finite probabilities. A new optional argument `jitter-max-retries` can be passed to `pm.sample()` and `pm.init_nuts()` to control the maximum number of retries per chain. [4298](https://github.com/pymc-devs/pymc3/pull/4298)
 
 ### Documentation
 - Added a new notebook demonstrating how to incorporate sampling from a conjugate Dirichlet-multinomial posterior density in conjunction with other step methods (see [#4199](https://github.com/pymc-devs/pymc3/pull/4199)).

pymc3/sampling.py

@@ -60,7 +60,7 @@
     chains_and_samples,
 )
 from .vartypes import discrete_types
-from .exceptions import IncorrectArgumentsError
+from .exceptions import IncorrectArgumentsError, SamplingError
 from .parallel_sampling import _cpu_count, Draw
 from pymc3.step_methods.hmc import quadpotential
 import pymc3 as pm
@@ -246,6 +246,7 @@ def sample(
     discard_tuned_samples=True,
     compute_convergence_checks=True,
     callback=None,
+    jitter_max_retries=10,
     *,
     return_inferencedata=None,
     idata_kwargs: dict = None,
@@ -331,6 +332,10 @@ def sample(
         the ``draw.chain`` argument can be used to determine which of the active chains the sample
         is drawn from.
         Sampling can be interrupted by throwing a ``KeyboardInterrupt`` in the callback.
+    jitter_max_retries : int
+        Maximum number of repeated attempts (per chain) at creating an initial matrix with uniform jitter
+        that yields a finite probability. This applies to ``jitter+adapt_diag`` and ``jitter+adapt_full``
+        init methods.
     return_inferencedata : bool, default=False
         Whether to return the trace as an :class:`arviz:arviz.InferenceData` (True) object or a `MultiTrace` (False)
         Defaults to `False`, but we'll switch to `True` in an upcoming release.
@@ -490,6 +495,7 @@ def sample(
                 model=model,
                 random_seed=random_seed,
                 progressbar=progressbar,
+                jitter_max_retries=jitter_max_retries,
                 **kwargs,
             )
             if start is None:
@@ -1946,13 +1952,52 @@ def sample_prior_predictive(
     return prior
 
 
+def _init_jitter(model, chains, jitter_max_retries):
+    """Apply a uniform jitter in [-1, 1] to the test value as starting point in each chain.
+
+    pymc3.util.check_start_vals is used to test whether the jittered starting values produce
+    a finite log probability. Invalid values are resampled unless `jitter_max_retries` is achieved,
+    in which case the last sampled values are returned.
+
+    Parameters
+    ----------
+    model : Model
+    chains : int
+    jitter_max_retries : int
+        Maximum number of repeated attempts at initializing values (per chain).
+
+    Returns
+    -------
+    start : ``pymc3.model.Point``
+        Starting point for sampler
+    """
+    start = []
+    for _ in range(chains):
+        for i in range(jitter_max_retries + 1):
+            mean = {var: val.copy() for var, val in model.test_point.items()}
+            for val in mean.values():
+                val[...] += 2 * np.random.rand(*val.shape) - 1
+
+            if i < jitter_max_retries:
+                try:
+                    check_start_vals(mean, model)
+                except SamplingError:
+                    pass
+                else:
+                    break
+
+        start.append(mean)
+    return start
+
+
 def init_nuts(
     init="auto",
     chains=1,
     n_init=500000,
     model=None,
     random_seed=None,
     progressbar=True,
+    jitter_max_retries=10,
     **kwargs,
 ):
     """Set up the mass matrix initialization for NUTS.
@@ -1967,7 +2012,7 @@ def init_nuts(
         Initialization method to use.
 
         * auto: Choose a default initialization method automatically.
-          Currently, this is `'jitter+adapt_diag'`, but this can change in the future. If you
+          Currently, this is ``jitter+adapt_diag``, but this can change in the future. If you
           depend on the exact behaviour, choose an initialization method explicitly.
         * adapt_diag: Start with a identity mass matrix and then adapt a diagonal based on the
           variance of the tuning samples. All chains use the test value (usually the prior mean)
@@ -1994,6 +2039,10 @@ def init_nuts(
     model : Model (optional if in ``with`` context)
     progressbar : bool
         Whether or not to display a progressbar for advi sampling.
+    jitter_max_retries : int
+        Maximum number of repeated attempts (per chain) at creating an initial matrix with uniform jitter
+        that yields a finite probability. This applies to ``jitter+adapt_diag`` and ``jitter+adapt_full``
+        init methods.
     **kwargs : keyword arguments
         Extra keyword arguments are forwarded to pymc3.NUTS.
 
@@ -2038,12 +2087,7 @@ def init_nuts(
         var = np.ones_like(mean)
         potential = quadpotential.QuadPotentialDiagAdapt(model.ndim, mean, var, 10)
     elif init == "jitter+adapt_diag":
-        start = []
-        for _ in range(chains):
-            mean = {var: val.copy() for var, val in model.test_point.items()}
-            for val in mean.values():
-                val[...] += 2 * np.random.rand(*val.shape) - 1
-            start.append(mean)
+        start = _init_jitter(model, chains, jitter_max_retries)
         mean = np.mean([model.dict_to_array(vals) for vals in start], axis=0)
         var = np.ones_like(mean)
         potential = quadpotential.QuadPotentialDiagAdapt(model.ndim, mean, var, 10)
@@ -2125,12 +2169,7 @@ def init_nuts(
         cov = np.eye(model.ndim)
         potential = quadpotential.QuadPotentialFullAdapt(model.ndim, mean, cov, 10)
     elif init == "jitter+adapt_full":
-        start = []
-        for _ in range(chains):
-            mean = {var: val.copy() for var, val in model.test_point.items()}
-            for val in mean.values():
-                val[...] += 2 * np.random.rand(*val.shape) - 1
-            start.append(mean)
+        start = _init_jitter(model, chains, jitter_max_retries)
         mean = np.mean([model.dict_to_array(vals) for vals in start], axis=0)
         cov = np.eye(model.ndim)
         potential = quadpotential.QuadPotentialFullAdapt(model.ndim, mean, cov, 10)

pymc3/tests/test_sampling.py

@@ -815,6 +815,28 @@ def _mocked_init_nuts(*args, **kwargs):
             pm.sample(tune=1, draws=0, chains=1, init=init, start=start)
 
 
+@pytest.mark.parametrize(
+    "testval, jitter_max_retries, expectation",
+    [
+        (0, 0, pytest.raises(SamplingError)),
+        (0, 1, pytest.raises(SamplingError)),
+        (0, 4, does_not_raise()),
+        (0, 10, does_not_raise()),
+        (1, 0, does_not_raise()),
+    ],
+)
+def test_init_jitter(testval, jitter_max_retries, expectation):
+    with pm.Model() as m:
+        pm.HalfNormal("x", transform=None, testval=testval)
+
+    with expectation:
+        # Starting value is negative (invalid) when np.random.rand returns 0 (jitter = -1)
+        # and positive (valid) when it returns 1 (jitter = 1)
+        with mock.patch("numpy.random.rand", side_effect=[0, 0, 0, 1, 0]):
+            start = pm.sampling._init_jitter(m, chains=1, jitter_max_retries=jitter_max_retries)
+            pm.util.check_start_vals(start, m)
+
+
 @pytest.fixture(scope="class")
 def point_list_arg_bug_fixture() -> Tuple[pm.Model, pm.backends.base.MultiTrace]:
     with pm.Model() as pmodel: