# copyright: sktime developers, BSD-3-Clause License (see LICENSE file)
"""Implements hierarchical reconciliation transformers.
These reconcilers only depend on the structure of the hierarchy.
"""
__author__ = ["ciaran-g", "eenticott-shell", "k1m190r"]
import numpy as np
import pandas as pd
from numpy.linalg import inv
from sktime.transformations.base import BaseTransformer
from sktime.transformations.hierarchical.aggregate import _check_index_no_total
from sktime.utils.warnings import warn
# TODO: failing test which are escaped
[文档]class Reconciler(BaseTransformer):
"""Hierarchical reconciliation transformer.
Hierarchical reconciliation is a transformation which is used to make the
predictions in a hierarchy of time-series sum together appropriately.
The methods implemented in this class only require the structure of the
hierarchy or the forecasts values for reconciliation.
These functions are intended for transforming hierarchical forecasts, i.e.
after prediction. However they are general and can be used to transform
hierarchical time-series data.
Please refer to [1]_ for further information
Parameters
----------
method : {"bu", "ols", "wls_str", "td_fcst"}, default="bu"
The reconciliation approach applied to the forecasts
"bu" - bottom-up
"ols" - ordinary least squares
"wls_str" - weighted least squares (structural)
"td_fcst" - top down based on (forecast) proportions
See Also
--------
Aggregator
ReconcilerForecaster
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
Examples
--------
>>> from sktime.forecasting.trend import PolynomialTrendForecaster
>>> from sktime.transformations.hierarchical.reconcile import Reconciler
>>> from sktime.transformations.hierarchical.aggregate import Aggregator
>>> from sktime.utils._testing.hierarchical import _bottom_hier_datagen
>>> agg = Aggregator()
>>> y = _bottom_hier_datagen(
... no_bottom_nodes=3,
... no_levels=1,
... random_seed=123,
... )
>>> y = agg.fit_transform(y)
>>> forecaster = PolynomialTrendForecaster()
>>> forecaster.fit(y)
PolynomialTrendForecaster(...)
>>> prds = forecaster.predict(fh=[1])
>>> # reconcile forecasts
>>> reconciler = Reconciler(method="ols")
>>> prds_recon = reconciler.fit_transform(prds)
"""
_tags = {
# packaging info
# --------------
"authors": ["ciaran-g", "eenticott-shell", "k1m190r"],
"maintainers": "ciaran-g",
# estimator type
# --------------
"scitype:transform-input": "Series",
"scitype:transform-output": "Series",
"scitype:transform-labels": "None",
"scitype:instancewise": False, # is this an instance-wise transform?
"X_inner_mtype": [
"pd.DataFrame",
"pd.Series",
"pd-multiindex",
"pd_multiindex_hier",
],
"y_inner_mtype": "None", # which mtypes do _fit/_predict support for y?
"capability:inverse_transform": False,
"skip-inverse-transform": True, # is inverse-transform skipped when called?
"univariate-only": True, # can the transformer handle multivariate X?
"handles-missing-data": False, # can estimator handle missing data?
"X-y-must-have-same-index": False, # can estimator handle different X/y index?
"fit_is_empty": False, # is fit empty and can be skipped? Yes = True
"transform-returns-same-time-index": True,
}
METHOD_LIST = ["bu", "ols", "wls_str", "td_fcst"]
def __init__(self, method="bu"):
self.method = method
super().__init__()
def _add_totals(self, X):
"""Add total levels to X, using Aggregate."""
from sktime.transformations.hierarchical.aggregate import Aggregator
return Aggregator().fit_transform(X)
def _fit(self, X, y=None):
"""Fit transformer to X and y.
private _fit containing the core logic, called from fit
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Data to fit transform to
y : Ignored argument for interface compatibility.
Returns
-------
self: reference to self
"""
self._check_method()
# check the length of index
if X.index.nlevels < 2:
return self
# check index for no "__total", if not add totals to X
if _check_index_no_total(X):
X = self._add_totals(X)
# define reconciliation matrix
if self.method == "bu":
self.g_matrix = _get_g_matrix_bu(X)
elif self.method == "ols":
self.g_matrix = _get_g_matrix_ols(X)
elif self.method == "wls_str":
self.g_matrix = _get_g_matrix_wls_str(X)
elif self.method == "td_fcst":
self.g_matrix = _get_g_matrix_td_fcst(X)
else:
raise RuntimeError("unreachable condition, error in _check_method")
# now summation matrix
self.s_matrix = _get_s_matrix(X)
# parent child df
self.parent_child = _parent_child_df(self.s_matrix)
return self
def _transform(self, X, y=None):
"""Transform X and return a transformed version.
private _transform containing core logic, called from transform
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Data to be transformed
y : Ignored argument for interface compatibility.
Returns
-------
recon_preds : multi-indexed pd.DataFrame of Panel mtype pd_multiindex
"""
# check the length of index
if X.index.nlevels < 2:
warn(
"Reconciler is intended for use with X.index.nlevels > 1. "
"Returning X unchanged.",
obj=self,
)
return X
# check index for no "__total", if not add totals to X
if _check_index_no_total(X):
warn(
"No elements of the index of X named '__total' found. Adding "
"aggregate levels using the default Aggregator transformer "
"before reconciliation.",
obj=self,
)
X = self._add_totals(X)
# check here that index of X matches the self.s_matrix
al_inds = X.droplevel(level=-1).index.unique()
chk_newindx = np.all(self.s_matrix.index == al_inds)
if not chk_newindx:
raise ValueError(
"Check unique indexes of X.droplevel(level=-1) matches "
"the data used in Reconciler().fit(X)."
)
X = X.groupby(level=-1)
# could use X.transform() with np.dot, v. marginally faster in my tests
# - loop can use index matching via df.dot() which is probably worth it
recon_preds = []
gmat = self.g_matrix
for _name, group in X:
if self.method == "td_fcst":
gmat = _update_td_fcst(
g_matrix=gmat, x_sf=group.droplevel(-1), conn_df=self.parent_child
)
# reconcile via SGy
fcst = self.s_matrix.dot(gmat.dot(group.droplevel(-1)))
# add back in time index
fcst.index = group.index
recon_preds.append(fcst)
recon_preds = pd.concat(recon_preds, axis=0)
recon_preds = recon_preds.sort_index()
return recon_preds
def _check_method(self):
"""Raise warning if method is not defined correctly."""
if not np.isin(self.method, self.METHOD_LIST):
raise ValueError(f"""method must be one of {self.METHOD_LIST}.""")
else:
pass
[文档] @classmethod
def get_test_params(cls):
"""Return testing parameter settings for the estimator.
Returns
-------
params : dict, default = {}
Parameters to create testing instances of the class
Each dict are parameters to construct an "interesting" test instance, i.e.,
``MyClass(**params)`` or ``MyClass(**params[i])`` creates a valid test
instance.
``create_test_instance`` uses the first (or only) dictionary in ``params``
"""
return [{"method": x} for x in cls.METHOD_LIST]
def _get_s_matrix(X):
"""Determine the summation "S" matrix.
Reconciliation methods require the S matrix, which is defined by the
structure of the hierarchy only. The S matrix is inferred from the input
multi-index of the forecasts and is used to sum bottom-level forecasts
appropriately.
Please refer to [1]_ for further information.
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Returns
-------
s_matrix : pd.DataFrame with rows equal to the number of unique nodes in
the hierarchy, and columns equal to the number of bottom level nodes only,
i.e. with no aggregate nodes. The matrix indexes is inherited from the
input data, with the time level removed.
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
"""
# get bottom level indexes
bl_inds = (
X.loc[~(X.index.get_level_values(level=-2).isin(["__total"]))]
.index.droplevel(level=-1)
.unique()
)
# get all level indexes
al_inds = X.droplevel(level=-1).index.unique()
# set up matrix
s_matrix = pd.DataFrame(
[[0.0 for i in range(len(bl_inds))] for i in range(len(al_inds))],
index=al_inds,
)
s_matrix.columns = bl_inds
# now insert indicator for bottom level
for i in s_matrix.columns:
s_matrix.loc[s_matrix.index == i, i] = 1.0
# now for each unique column add aggregate indicator
for i in s_matrix.columns:
if s_matrix.index.nlevels > 1:
# replace index with totals -> ("nodeA", "__total")
agg_ind = list(i)[::-1]
for j in range(len(agg_ind)):
agg_ind[j] = "__total"
# insert indicator
s_matrix.loc[tuple(agg_ind[::-1]), i] = 1.0
else:
s_matrix.loc["__total", i] = 1.0
# drop new levels not present in original matrix
s_matrix = s_matrix.loc[s_matrix.index.isin(al_inds)]
return s_matrix
def _get_g_matrix_bu(X):
"""Determine the reconciliation "G" matrix for the bottom up method.
Reconciliation methods require the G matrix. The G matrix is used to redefine
base forecasts for the entire hierarchy to the bottom-level only before
summation using the S matrix.
Please refer to [1]_ for further information.
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Returns
-------
g_matrix : pd.DataFrame with rows equal to the number of bottom level nodes
only, i.e. with no aggregate nodes, and columns equal to the number of
unique nodes in the hierarchy. The matrix indexes is inherited from the
input data, with the time level removed.
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
"""
# get bottom level indexes
bl_inds = (
X.loc[~(X.index.get_level_values(level=-2).isin(["__total"]))]
.index.droplevel(level=-1)
.unique()
)
# get all level indexes
al_inds = X.droplevel(level=-1).index.unique()
g_matrix = pd.DataFrame(
[[0.0 for i in range(len(bl_inds))] for i in range(len(al_inds))],
index=al_inds,
)
g_matrix.columns = bl_inds
# now insert indicator for bottom level
for i in g_matrix.columns:
g_matrix.loc[g_matrix.index == i, i] = 1.0
return g_matrix.transpose()
def _get_g_matrix_ols(X):
"""Determine the reconciliation "G" matrix for the ordinary least squares method.
Reconciliation methods require the G matrix. The G matrix is used to redefine
base forecasts for the entire hierarchy to the bottom-level only before
summation using the S matrix.
Please refer to [1]_ for further information.
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Returns
-------
g_ols : pd.DataFrame with rows equal to the number of bottom level nodes
only, i.e. with no aggregate nodes, and columns equal to the number of
unique nodes in the hierarchy. The matrix indexes is inherited from the
summation matrix.
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
"""
# get s matrix
smat = _get_s_matrix(X)
# get g
g_ols = pd.DataFrame(
np.dot(inv(np.dot(np.transpose(smat), smat)), np.transpose(smat))
)
# set indexes of matrix
g_ols = g_ols.transpose()
g_ols = g_ols.set_index(smat.index)
g_ols.columns = smat.columns
g_ols = g_ols.transpose()
return g_ols
def _get_g_matrix_wls_str(X):
"""Reconciliation "G" matrix for the weighted least squares (structural) method.
Reconciliation methods require the G matrix. The G matrix is used to re-define
base forecasts for the entire hierarchy to the bottom-level only before
summation using the S matrix.
Please refer to [1]_ for further information.
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Returns
-------
g_wls_str : pd.DataFrame with rows equal to the number of bottom level nodes
only, i.e. with no aggregate nodes, and columns equal to the number of
unique nodes in the hierarchy. The matrix indexes is inherited from the
summation matrix.
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
"""
# this is similar to the ols except we have a new matrix W
smat = _get_s_matrix(X)
diag_data = np.diag(smat.sum(axis=1).values)
w_mat = pd.DataFrame(diag_data, index=smat.index, columns=smat.index)
g_wls_str = pd.DataFrame(
np.dot(
inv(np.dot(np.transpose(smat), np.dot(w_mat, smat))),
np.dot(np.transpose(smat), w_mat),
)
)
# set indexes of matrix
g_wls_str = g_wls_str.transpose()
g_wls_str = g_wls_str.set_index(smat.index)
g_wls_str.columns = smat.columns
g_wls_str = g_wls_str.transpose()
return g_wls_str
def _get_g_matrix_td_fcst(X):
"""Determine the "G" matrix for the top down forecast proportions method.
Reconciliation methods require the G matrix. The G matrix is used to redefine
base forecasts for the entire hierarchy to the bottom-level only before
summation using the S matrix.
Note that the G matrix for this method changes for each forecast. This
is just a template G matrix which is updated at each iteration.
Please refer to [1]_ for further information.
Parameters
----------
X : Panel of mtype pd_multiindex_hier
Returns
-------
g_matrix : pd.DataFrame with rows equal to the number of bottom level nodes
only, i.e. with no aggregate nodes, and columns equal to the number of
unique nodes in the hierarchy. The matrix indexes is inherited from the
input data, with the time level removed.
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
"""
g_matrix = _get_g_matrix_bu(X)
g_matrix = g_matrix.replace(to_replace=1, value=0)
return g_matrix
def _update_td_fcst(g_matrix, x_sf, conn_df):
"""Update the "G" matrix for the top down forecast proportions method.
Reconciliation methods require the G matrix. The G matrix is used to redefine
base forecasts for the entire hierarchy to the bottom-level only before
summation using the S matrix.
This takes the gmatrix template from _get_g_matrix_td_fcst() and updates
it based on a single forecast.
Please refer to [1]_ for further information.
Parameters
----------
g_matrix : pd.DataFrame reconciliation matrix template from
_get_g_matrix_td_fcst()
x_sf : pd.Series which contains a hierarchy forecast for a single timepoint
conn_df : A look up table containing the child and parent of each connection
in a hierarchy
Returns
-------
g_matrix : pd.DataFrame with rows equal to the number of bottom level nodes
only, i.e. with no aggregate nodes, and columns equal to the number of
unique nodes in the hierarchy. The matrix indexes is inherited from the
input data, with the time level removed.
References
----------
.. [1] https://otexts.com/fpp3/hierarchical.html
"""
for i in g_matrix.index:
# start from each bottom index
child = i
props = []
# if the bottom level are single strings, integers, or whatever
if not isinstance(child, tuple):
child_chk = (child,)
else:
child_chk = child
while sum([j == "__total" for j in list(child_chk)]) < len(child_chk):
# find the parent of the child
parent = conn_df.loc[conn_df["child"] == child, "parent"].values[0]
# now need to find nodes directly connected to the parent
children = conn_df.loc[conn_df["parent"] == parent, "child"].unique()
# calculate proportions
props.append((x_sf.loc[child] / x_sf.loc[children].sum()).values[0])
# move up the chain
child = parent
if not isinstance(child, tuple):
child_chk = (child,)
else:
child_chk = child
g_matrix.loc[i, "__total"] = np.prod(props)
return g_matrix
def _parent_child_df(s_matrix):
"""Extract the parent and child connections in a hierarchy.
This function takes the summation S matrix for a given hierarchy and
returns a dataframe containing a the parent and child node id for each
connection in a hierarchy.
Parameters
----------
s_matrix : The summation matrix for a given hierarchy from the function
_get_s_matrix().
Returns
-------
df : A two column pd.DataFrame with rows equal to the number of
connections in a hierarchy.
"""
parent_child = []
total_count = s_matrix.index.to_frame()
total_count = (total_count == "__total").sum(axis=1)
# for each bottom node
for i in s_matrix.columns:
# get all connections
connected_nodes = s_matrix[(s_matrix[i] == 1)].sum(axis=1)
# for non-flattened hierarchies make sure "__totals" are above
connected_nodes = (connected_nodes + total_count).dropna()
connected_nodes = connected_nodes.sort_values(ascending=False)
# starting from top add list of [parent, child]
for j in range(len(connected_nodes.index) - 1):
parent_child.append(
[connected_nodes.index[j], connected_nodes.index[j + 1]]
)
df = pd.DataFrame(parent_child)
df.columns = ["parent", "child"]
df = df.drop_duplicates().sort_values(["parent", "child"]).reset_index(drop=True)
return df
