Repository: sktime/sktime
Pull request: [ENH] `HierarchyEnsembleForecaster` parallelization backends
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Resolves #7947 

#### What does this implement/fix? Explain your changes.
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Replaces the for-loops in both fit and predict with the sktime parallelize function to allow for parallelization
#### Does your contribution introduce a new dependency? If yes, which one?
No.
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#### What should a reviewer concentrate their feedback on?
Maybe if the two fit functions (node_fit and level_fit) should be seperate as is or if they should be compressed into one function
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#### Did you add any tests for the change?
Two tests were added (test_hierarchy_ensemble_level_predict_parallel and test_hierarchy_ensemble_node_predict_parallel) that are basically identical to the already existing tests, except they now set joblib as the parallel config. This is to ensure identical results regardless of parallel or not. 

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Problem statement:
[ENH] Let HEF fit and predict in parallel
**Is your feature request related to a problem? Please describe.**
As it is the HierarchyEnsembleForecaster fits every model one at a time which may result in long training times if the hierarchy becomes sufficiently large. 

**Describe the solution you'd like**
Instead enable the option to use the sktime backend to let the forecasters be fit in parallel (also do that for the prediction since we are already at it) 

**Describe alternatives you've considered**
I suppose instead of creating the HEF with new forecasters one could use any already existing framework that allows us to train the forecasters in parallel and then skip the HEF training by setting 

HEF.fitted_list = [already trained forecasters]

**Additional context**
The idea to solve this is to replace the for-loops in both the by=level and by=node with something like this 

    fcstr_list = parallelize(
    node_fit,
    node_dict.items(),
    meta=meta,
    backend=backend,
    backend_params=backend_params,
    )
where node_fit would then just be a function to wrap around the forecasters.fit lines (since we cant parallelize over that directly). This could already look like 

      def node_fit(params, meta):
  
      key, node = params
      z = meta["z"]
      X = meta["X"]
  
      frcstr = meta["fcstr_dict"][key]
      df = z[z.index.droplevel(-1).isin(node)]
      if X is not None:
          X = X.loc[df.index]
      frcstr.fit(df, fh=meta["fh"], X=X)
      return frcstr, df

Hints from issue discussion:
@LHoelper 
Thanks for raising this issue!
This is one of the PRs I have raised which solves similar issue: https://github.com/sktime/sktime/pull/7683
And this could be a good reference point to start working on this forecaster.
Although it needs some insights from @fkiraly if it would align well with the forecaster architecture
Great suggestion, @LHoelper!

I think your approach makes most sense.

A PR would be much appreciated.

FYI @felipeangelimvieira - surprised that this feature did not already exist.

Commit message: Refactor: Rename function to _predict_one_forecaster to avoid confusion

Patch to review:
diff --git a/.all-contributorsrc b/.all-contributorsrc
index eb81ca53925..1d0c83e5be0 100644
--- a/.all-contributorsrc
+++ b/.all-contributorsrc
@@ -3413,6 +3413,15 @@
         "code"
       ]
     },
+    {
+      "login": "LHoelper",
+      "name": "Luca Hölper",
+      "avatar_url": "https://avatars.githubusercontent.com/LHoelper",
+      "profile": "https://github.com/LHoelper",
+      "contributions": [
+        "code"
+      ]
+    },
     {
       "login": "sky0walker99",
       "name": "Muhammed Haroon",
diff --git a/sktime/forecasting/compose/_hierarchy_ensemble.py b/sktime/forecasting/compose/_hierarchy_ensemble.py
index f4498bcfe22..bda4ba4e261 100644
--- a/sktime/forecasting/compose/_hierarchy_ensemble.py
+++ b/sktime/forecasting/compose/_hierarchy_ensemble.py
@@ -11,6 +11,7 @@
 from sktime.forecasting.base._base import BaseForecaster
 from sktime.forecasting.base._meta import _HeterogenousEnsembleForecaster
 from sktime.transformations.hierarchical.aggregate import _check_index_no_total
+from sktime.utils.parallel import parallelize
 from sktime.utils.warnings import warn
 
 
@@ -54,6 +55,39 @@ class HierarchyEnsembleForecaster(_HeterogenousEnsembleForecaster):
         if passed, applies ``default`` forecaster on the nodes/levels
         not mentioned in the ``forecaster`` argument.
 
+    backend : {"dask", "loky", "multiprocessing", "threading"}, by default None.
+        Runs parallel evaluate if specified and ``strategy`` is set as "refit".
+
+        - "None": executes loop sequentally, simple list comprehension
+        - "loky", "multiprocessing" and "threading": uses ``joblib.Parallel`` loops
+        - "joblib": custom and 3rd party ``joblib`` backends, e.g., ``spark``
+        - "dask": uses ``dask``, requires ``dask`` package in environment
+        - "dask_lazy": same as "dask",
+          but changes the return to (lazy) ``dask.dataframe.DataFrame``.
+
+        Recommendation: Use "dask" or "loky" for parallel evaluate.
+        "threading" is unlikely to see speed ups due to the GIL and the serialization
+        backend (``cloudpickle``) for "dask" and "loky" is generally more robust
+        than the standard ``pickle`` library used in "multiprocessing".
+    backend_params : dict, optional
+        additional parameters passed to the backend as config.
+        Directly passed to ``utils.parallel.parallelize``.
+        Valid keys depend on the value of ``backend``:
+
+        - "None": no additional parameters, ``backend_params`` is ignored
+        - "loky", "multiprocessing" and "threading": default ``joblib`` backends
+          any valid keys for ``joblib.Parallel`` can be passed here, e.g., ``n_jobs``,
+          with the exception of ``backend`` which is directly controlled by ``backend``.
+          If ``n_jobs`` is not passed, it will default to ``-1``, other parameters
+          will default to ``joblib`` defaults.
+        - "joblib": custom and 3rd party ``joblib`` backends, e.g., ``spark``.
+          any valid keys for ``joblib.Parallel`` can be passed here, e.g., ``n_jobs``,
+          ``backend`` must be passed as a key of ``backend_params`` in this case.
+          If ``n_jobs`` is not passed, it will default to ``-1``, other parameters
+          will default to ``joblib`` defaults.
+        - "dask": any valid keys for ``dask.compute`` can be passed,
+          e.g., ``scheduler``
+
     Examples
     --------
     >>> from sktime.forecasting.compose import HierarchyEnsembleForecaster
@@ -109,10 +143,20 @@ class HierarchyEnsembleForecaster(_HeterogenousEnsembleForecaster):
 
     _steps_attr = "_forecasters"
 
-    def __init__(self, forecasters, by="level", default=None):
+    def __init__(
+        self, forecasters, by="level", default=None, backend=None, backend_params=None
+    ):
         self.forecasters = forecasters
         self.by = by
         self.default = default
+        self.backend = backend
+        self.backend_params = backend_params
+        self.set_config(
+            **{
+                "backend:parallel": self.backend,
+                "backend:parallel:params": self.backend_params,
+            }
+        )
         super().__init__(forecasters=forecasters)
 
         if isinstance(forecasters, BaseForecaster):
@@ -219,31 +263,40 @@ def _fit(self, y, X, fh):
             self.fitted_list_.append([frcstr, y.index])
             return self
 
+        meta = {"X": x, "z": z, "fh": fh}
+
         if self.by == "level":
             hier_dict = self._get_hier_dict(z)
-            for _, forecaster, level in self.forecasters_:
-                if level in hier_dict.keys():
-                    frcstr = forecaster
-                    df = z[z.index.droplevel(-1).isin(hier_dict[level])]
-                    if X is not None:
-                        x = X.loc[df.index]
-                    frcstr.fit(df, fh=fh, X=x)
-                    self.fitted_list_.append([frcstr, df.index.droplevel(-1).unique()])
-                    self.forecasters_ = [
-                        (name, frcstr if f == forecaster else f, level)
-                        for name, f, level in self.forecasters_
-                    ]
+            meta["hier_dict"] = hier_dict
+
+            fcstr_list = parallelize(
+                _level_fit,
+                iter=self.forecasters_,
+                meta=meta,
+                backend=self.get_config()["backend:parallel"],
+                backend_params=self.get_config()["backend:parallel:params"],
+            )
 
+            for i in range(len(fcstr_list)):
+                self.fitted_list_.append(
+                    [fcstr_list[i][0], fcstr_list[i][1].index.droplevel(-1).unique()]
+                )
+                name, _, level = self.forecasters_[i]
+                self.forecasters_[i] = (name, fcstr_list[i][0], level)
         else:
             node_dict, frcstr_dict = self._get_node_dict(z)
-            for key, nodes in node_dict.items():
-                frcstr = frcstr_dict[key]
-                df = z[z.index.droplevel(-1).isin(nodes)]
-                if X is not None:
-                    x = X.loc[df.index]
-                frcstr.fit(df, fh=fh, X=x)
-                self.fitted_list_.append([frcstr, df.index.droplevel(-1).unique()])
+            meta["fcstr_dict"] = frcstr_dict
+
+            fcstr_list = parallelize(
+                _node_fit,
+                node_dict.items(),
+                meta=meta,
+                backend=self.get_config()["backend:parallel"],
+                backend_params=self.get_config()["backend:parallel:params"],
+            )
 
+            for fcstr, df in fcstr_list:
+                self.fitted_list_.append([fcstr, df.index.droplevel(-1).unique()])
         return self
 
     def _get_hier_dict(self, z):
@@ -404,18 +457,20 @@ def _predict(self, fh=None, X=None):
         y_pred : pd.Series
             Point predictions
         """
-        preds = []
-
         if X is not None:
             if _check_index_no_total(X):
                 X = self._aggregate(X)
         x = X
 
-        for forecaster, ind in self.fitted_list:
-            if X is not None and X.index.nlevels > 1:
-                x = X[X.index.droplevel(-1).isin(ind)]
-            pred = forecaster.predict(fh=fh, X=x)
-            preds.append(pred)
+        meta = {"x": x, "fh": fh}
+
+        preds = parallelize(
+            _predict_one_forecaster,
+            self.fitted_list,
+            meta,
+            backend=self.get_config()["backend:parallel"],
+            backend_params=self.get_config()["backend:parallel:params"],
+        )
 
         preds = pd.concat(preds, axis=0)
         preds.sort_index(inplace=True)
@@ -673,3 +728,98 @@ def get_test_params(cls):
         params3 = {"forecasters": NaiveForecaster()}
 
         return [params1, params2, params3]
+
+
+def _level_fit(params, meta):
+    """Fit a single forecaster.
+
+    Called from _fit if by=level was set to allow for parallelization.
+
+    Parameters
+    ----------
+    params: tuples
+        (str, estimator, int or list of tuple/s)
+        If called from the _fit function this will contain the self.forecasters_ list
+    meta: dict
+        Meta dictionary for parallelization. Needs to contain (at least)
+        the following keys:
+        z: pd.Series
+            The aggregated target time series
+        X: pd.DataFrame, None
+            The aggregated input data
+        hier_dict: dict
+            The level dictionary as created by the get_hier_dict function
+        fh : int, list or np.array, optional (default=None)
+            The forecasters horizon with the steps ahead to to predict.
+    """
+    _, forecaster, level = params
+    z = meta["z"]
+    X = meta["X"]
+    hier_dict = meta["hier_dict"]
+    if level in hier_dict.keys():
+        frcstr = forecaster
+        df = z[z.index.droplevel(-1).isin(hier_dict[level])]
+        if X is not None:
+            X = X.loc[df.index]
+        frcstr.fit(df, fh=meta["fh"], X=X)
+    return frcstr, df
+
+
+def _node_fit(params, meta):
+    """Fit a single forecaster.
+
+    Called from _fit if by=node was set to allow for parallelization.
+
+    Parameters
+    ----------
+    params: tuples
+        (str, estimator, int or list of tuple/s)
+        If called from the _fit function this will contain the node_dict from the
+        get_node_dict function
+    meta: dict
+        Meta dictionary for parallelization. Needs to contain (at least) the
+        following keys:
+        z: pd.Series
+            The aggregated target time series
+        X: pd.DataFrame, None
+            The aggregated input data
+        fcstr_dict: dict
+            The forecaster dictionary as created by the get_node_dict function
+        fh : int, list or np.array, optional (default=None)
+            The forecasters horizon with the steps ahead to to predict.
+    """
+    key, node = params
+    z = meta["z"]
+    X = meta["X"]
+    frcstr = meta["fcstr_dict"][key]
+    df = z[z.index.droplevel(-1).isin(node)]
+    if X is not None:
+        X = X.loc[df.index]
+    frcstr.fit(df, fh=meta["fh"], X=X)
+    return frcstr, df
+
+
+def _predict_one_forecaster(params, meta):
+    """Predict a single forecaster.
+
+    Called from _predict to allow for parallelization.
+
+    Parameters
+    ----------
+    params: tuples
+        (estimator, str)
+        If called from the _predict function this will contain the self.fitted list
+    meta: dict
+        Meta dictionary for parallelization. Needs to contain (at least)
+        the following keys:
+        X: pd.DataFrame, None
+            The aggregated input data
+        fh : int, list or np.array, optional (default=None)
+            The forecasters horizon with the steps ahead to to predict.
+    """
+    X = meta["x"]
+    fh = meta["fh"]
+    if X is not None and X.index.nlevels > 1:
+        X = X[X.index.droplevel(-1).isin(params[1])]
+    pred = params[0].predict(fh=fh, X=X)
+    return pred
diff --git a/sktime/forecasting/compose/tests/test_hierarchy_ensemble.py b/sktime/forecasting/compose/tests/test_hierarchy_ensemble.py
index 760818b6930..37464329793 100644
--- a/sktime/forecasting/compose/tests/test_hierarchy_ensemble.py
+++ b/sktime/forecasting/compose/tests/test_hierarchy_ensemble.py
@@ -63,6 +63,110 @@ def test_hierarchy_ensemble_level_predict(forecasters):
     assert np.all(actual_pred.loc[def_pred.index] == def_pred), msg
 
 
+@pytest.mark.skipif(
+    not run_test_for_class(HierarchyEnsembleForecaster),
+    reason="run test only if softdeps are present and incrementally (if requested)",
+)
+@pytest.mark.parametrize(
+    "forecasters",
+    [
+        [("ptf", PolynomialTrendForecaster(), 0), ("naive", NaiveForecaster(), 1)],
+        [("naive", NaiveForecaster(), 0)],
+    ],
+)
+def test_hierarchy_ensemble_level_predict_parallel(forecasters):
+    """Check the level predictions."""
+    agg = Aggregator()
+
+    y = _bottom_hier_datagen(
+        no_bottom_nodes=7,
+        no_levels=2,
+        random_seed=123,
+    )
+
+    parallel_config = {
+        "backend:parallel": "joblib",
+        "backend:parallel:params": {"backend": "loky", "n_jobs": -1},
+    }
+
+    forecaster = HierarchyEnsembleForecaster(
+        forecasters, default=forecasters[0][1].clone()
+    ).set_config(**parallel_config)
+
+    forecaster.fit(y, fh=[1, 2, 3])
+    actual_pred = forecaster.predict()
+
+    y = agg.fit_transform(y)
+
+    for i in range(len(forecasters)):
+        test_frcstr = forecasters[i][1].clone()
+        df = y[y.index.droplevel(-1).isin(forecaster.fitted_list[i][1])]
+        test_frcstr.fit(df, fh=[1, 2, 3])
+        test_pred = test_frcstr.predict()
+        msg = "Level predictions do not match"
+        assert np.all(actual_pred.loc[test_pred.index] == test_pred), msg
+
+    def_frcstr = forecasters[0][1].clone()
+    df = y[y.index.droplevel(-1).isin(forecaster.fitted_list[-1][1])]
+    def_frcstr.fit(df, fh=[1, 2, 3])
+    def_pred = def_frcstr.predict()
+    msg = "Level default predictions do not match"
+    assert np.all(actual_pred.loc[def_pred.index] == def_pred), msg
+
+
+@pytest.mark.skipif(
+    not run_test_for_class(HierarchyEnsembleForecaster),
+    reason="run test only if softdeps are present and incrementally (if requested)",
+)
+@pytest.mark.parametrize(
+    "forecasters",
+    [
+        [
+            ("ptf", PolynomialTrendForecaster(), [("__total", "__total")]),
+            ("naive", NaiveForecaster(), [("l2_node01", "__total")]),
+        ],
+        [("naive", NaiveForecaster(), [("l2_node01", "l1_node06")])],
+    ],
+)
+def test_hierarchy_ensemble_node_predict_parallel(forecasters):
+    """Check the node predictions."""
+    agg = Aggregator()
+
+    y = _bottom_hier_datagen(
+        no_bottom_nodes=7,
+        no_levels=2,
+        random_seed=123,
+    )
+    parallel_config = {
+        "backend:parallel": "joblib",
+        "backend:parallel:params": {"backend": "loky", "n_jobs": -1},
+    }
+
+    forecaster = HierarchyEnsembleForecaster(
+        forecasters, by="node", default=forecasters[0][1].clone()
+    ).set_config(**parallel_config)
+
+    forecaster.fit(y, fh=[1, 2, 3])
+    actual_pred = forecaster.predict()
+
+    y = agg.fit_transform(y)
+
+    for i in range(len(forecasters)):
+        test_frcstr = forecasters[i][1].clone()
+        df = y[y.index.droplevel(-1).isin(forecaster.fitted_list[i][1])]
+        test_frcstr.fit(df, fh=[1, 2, 3])
+        test_pred = test_frcstr.predict()
+        msg = "Node predictions do not match"
+        assert np.all(actual_pred.loc[test_pred.index] == test_pred), msg
+
+    def_frcstr = forecasters[0][1].clone()
+    df = y[y.index.droplevel(-1).isin(forecaster.fitted_list[-1][1])]
+    def_frcstr.fit(df, fh=[1, 2, 3])
+    def_pred = def_frcstr.predict()
+    msg = "Node default predictions do not match"
+    assert np.all(actual_pred.loc[def_pred.index] == def_pred), msg
+
+
 @pytest.mark.skipif(
     not run_test_for_class(HierarchyEnsembleForecaster),
     reason="run test only if softdeps are present and incrementally (if requested)",


Code review comments:
diff_hunk: @@ -109,10 +143,20 @@ class HierarchyEnsembleForecaster(_HeterogenousEnsembleForecaster):
 
     _steps_attr = "_forecasters"
 
-    def __init__(self, forecasters, by="level", default=None):
+    def __init__(
+        self, forecasters, by="level", default=None, backend=None, backend_params=None
+    ):
         self.forecasters = forecasters
         self.by = by
         self.default = default
+        self.backend = backend
+        self.backend_params = backend_params
+        self.set_config(
path: sktime/forecasting/compose/_hierarchy_ensemble.py
text: @user1:
I would remove the set_config from this - these will be inactive because the estimator does not broadcas.t