diff --git a/altair/utils/schemapi.py b/altair/utils/schemapi.py
index 2dfdc8ee1..c6d37c096 100644
--- a/altair/utils/schemapi.py
+++ b/altair/utils/schemapi.py
@@ -4,6 +4,7 @@
 import contextlib
 import inspect
 import json
+from typing import Any
 
 import jsonschema
 import numpy as np
@@ -137,7 +138,14 @@ def __repr__(self):
         return "Undefined"
 
 
-Undefined = UndefinedType()
+# In the future Altair may implement a more complete set of type hints.
+# But for now, we'll add an annotation to indicate that the type checker
+# should permit any value passed to a function argument whose default
+# value is Undefined.
+UndefinedLike = Any
+
+
+Undefined: UndefinedLike = UndefinedType()
 
 
 class SchemaBase(object):
diff --git a/doc/user_guide/API.rst b/doc/user_guide/API.rst
index fcddd7f93..573a1f697 100644
--- a/doc/user_guide/API.rst
+++ b/doc/user_guide/API.rst
@@ -15,7 +15,6 @@ Top-Level Objects
 
 .. autosummary::
    :toctree: generated/toplevel/
-   :caption: Top-Level Objects
    :nosignatures:
 
    Chart
@@ -33,7 +32,6 @@ Encoding Channels
 
 .. autosummary::
    :toctree: generated/channels/
-   :caption: Encoding Channels
    :nosignatures:
 
    Angle
@@ -142,7 +140,6 @@ API Functions
 
 .. autosummary::
    :toctree: generated/api/
-   :caption: API Functions
    :nosignatures:
 
    binding
@@ -150,16 +147,18 @@ API Functions
    binding_radio
    binding_range
    binding_select
+   check_fields_and_encodings
    concat
    condition
    graticule
    hconcat
    layer
-   parameter
+   param
    repeat
    selection
    selection_interval
    selection_multi
+   selection_point
    selection_single
    sequence
    sphere
@@ -173,7 +172,6 @@ Low-Level Schema Wrappers
 
 .. autosummary::
    :toctree: generated/core/
-   :caption: Low-Level Schema Wrappers
    :nosignatures:
 
    Aggregate
@@ -286,6 +284,7 @@ Low-Level Schema Wrappers
    Day
    DensityTransform
    DerivedStream
+   Dict
    DictInlineDataset
    DictSelectionInit
    DictSelectionInitInterval
@@ -332,6 +331,7 @@ Low-Level Schema Wrappers
    FieldOrDatumDefWithConditionStringDatumDefText
    FieldOrDatumDefWithConditionStringFieldDefText
    FieldOrDatumDefWithConditionStringFieldDefstring
+   FieldRange
    FieldRangePredicate
    FieldValidPredicate
    FilterTransform
@@ -414,7 +414,6 @@ Low-Level Schema Wrappers
    Orientation
    OverlayMarkDef
    Padding
-   Parameter
    ParameterExtent
    ParameterName
    ParameterPredicate
diff --git a/tools/schemapi/schemapi.py b/tools/schemapi/schemapi.py
index 3ca87b991..e078f7881 100644
--- a/tools/schemapi/schemapi.py
+++ b/tools/schemapi/schemapi.py
@@ -2,6 +2,7 @@
 import contextlib
 import inspect
 import json
+from typing import Any
 
 import jsonschema
 import numpy as np
@@ -135,7 +136,14 @@ def __repr__(self):
         return "Undefined"
 
 
-Undefined = UndefinedType()
+# In the future Altair may implement a more complete set of type hints.
+# But for now, we'll add an annotation to indicate that the type checker
+# should permit any value passed to a function argument whose default
+# value is Undefined.
+UndefinedLike = Any
+
+
+Undefined: UndefinedLike = UndefinedType()
 
 
 class SchemaBase(object):