diff --git a/tests/test_serialize_explanation.py b/tests/test_serialize_explanation.py
index 4da4187b..2efa9d61 100644
--- a/tests/test_serialize_explanation.py
+++ b/tests/test_serialize_explanation.py
@@ -90,8 +90,8 @@ def test_old_load_explanation_backcompat(self, iris, tabular_explainer, iris_svm
         explanation = explainer.explain_global(iris[DatasetConstants.X_TEST], include_local=False)
         loaded_explanation = load_explanation(os.path.join('.', 'tests', 'backcompat_explanation'))
         explanation._id = loaded_explanation._id
-        _assert_explanation_equivalence(explanation, loaded_explanation, rtol=1e-7)
-        _assert_numpy_explanation_types(explanation, loaded_explanation, rtol=1e-7)
+        _assert_explanation_equivalence(explanation, loaded_explanation, rtol=0.03, atol=0.002)
+        _assert_numpy_explanation_types(explanation, loaded_explanation, rtol=0.03, atol=0.002)
 
 
 def _generate_old_explanation(iris, tabular_explainer, iris_svm_model):
@@ -104,7 +104,7 @@ def _generate_old_explanation(iris, tabular_explainer, iris_svm_model):
     save_explanation(explanation, path, exist_ok=False)
 
 
-def _assert_explanation_equivalence(actual, expected, rtol=None):
+def _assert_explanation_equivalence(actual, expected, rtol=None, atol=None):
     # get the non-null properties in the expected explanation
     paramkeys = filter(lambda x, expected=expected: hasattr(expected, getattr(ExplainParams, x)),
                        list(ExplainParams.get_serializable()))
@@ -122,36 +122,36 @@ def _assert_explanation_equivalence(actual, expected, rtol=None):
             else:
                 expected_dataset = expected_value.original_dataset
             if issparse(actual_dataset) and issparse(expected_dataset):
-                _assert_sparse_data_equivalence(actual_dataset, expected_dataset, rtol=rtol)
+                _assert_sparse_data_equivalence(actual_dataset, expected_dataset, rtol=rtol, atol=atol)
             else:
-                _assert_allclose_or_eq(actual_dataset, expected_dataset, rtol=rtol)
+                _assert_allclose_or_eq(actual_dataset, expected_dataset, rtol=rtol, atol=atol)
         elif isinstance(actual_value, (np.ndarray, collections.abc.Sequence)):
-            _assert_allclose_or_eq(actual_value, expected_value, rtol=rtol)
+            _assert_allclose_or_eq(actual_value, expected_value, rtol=rtol, atol=atol)
         elif isinstance(actual_value, pd.DataFrame) and isinstance(expected_value, pd.DataFrame):
-            _assert_allclose_or_eq(actual_value.values, expected_value.values, rtol=rtol)
+            _assert_allclose_or_eq(actual_value.values, expected_value.values, rtol=rtol, atol=atol)
         elif issparse(actual_value) and issparse(expected_value):
-            _assert_sparse_data_equivalence(actual_value, expected_value, rtol=rtol)
+            _assert_sparse_data_equivalence(actual_value, expected_value, rtol=rtol, atol=atol)
         else:
             assert actual_value == expected_value
 
 
-def _assert_allclose_or_eq(actual, expected, rtol=None):
+def _assert_allclose_or_eq(actual, expected, rtol=None, atol=None):
     if rtol is not None:
         try:
-            return np.testing.assert_allclose(actual, expected, rtol=rtol)
+            return np.testing.assert_allclose(actual, expected, rtol=rtol, atol=atol)
         except TypeError:
             print("Caught type error, defaulting to regular compare")
     np.testing.assert_array_equal(actual, expected)
 
 
-def _assert_sparse_data_equivalence(actual, expected, rtol=None):
-    _assert_allclose_or_eq(actual.data, expected.data, rtol=rtol)
-    _assert_allclose_or_eq(actual.indices, expected.indices, rtol=rtol)
-    _assert_allclose_or_eq(actual.indptr, expected.indptr, rtol=rtol)
-    _assert_allclose_or_eq(actual.shape, expected.shape, rtol=rtol)
+def _assert_sparse_data_equivalence(actual, expected, rtol=None, atol=None):
+    _assert_allclose_or_eq(actual.data, expected.data, rtol=rtol, atol=atol)
+    _assert_allclose_or_eq(actual.indices, expected.indices, rtol=rtol, atol=atol)
+    _assert_allclose_or_eq(actual.indptr, expected.indptr, rtol=rtol, atol=atol)
+    _assert_allclose_or_eq(actual.shape, expected.shape, rtol=rtol, atol=atol)
 
 
-def _assert_numpy_explanation_types(actual, expected, rtol=None):
+def _assert_numpy_explanation_types(actual, expected, rtol=None, atol=None):
     # assert "_" variables equivalence
     if hasattr(actual, ExplainParams.get_private(ExplainParams.LOCAL_IMPORTANCE_VALUES)):
         assert(isinstance(actual._local_importance_values, np.ndarray))
@@ -161,14 +161,19 @@ def _assert_numpy_explanation_types(actual, expected, rtol=None):
                                           expected._local_importance_values)
         else:
             np.testing.assert_allclose(actual._local_importance_values,
-                                       expected._local_importance_values, rtol=rtol)
+                                       expected._local_importance_values,
+                                       rtol=rtol,
+                                       atol=atol)
     if hasattr(actual, ExplainParams.get_private(ExplainParams.EVAL_DATA)):
         assert(isinstance(actual._eval_data, np.ndarray))
         assert(isinstance(expected._eval_data, np.ndarray))
         if rtol is None:
             np.testing.assert_array_equal(actual._eval_data, expected._eval_data)
         else:
-            np.testing.assert_allclose(actual._eval_data, expected._eval_data, rtol=rtol)
+            np.testing.assert_allclose(actual._eval_data,
+                                       expected._eval_data,
+                                       rtol=rtol,
+                                       atol=atol)
 
 
 # performs serialization and de-serialization for any explanation