TransformedTargetForecaster#

class TransformedTargetForecaster(steps)[source]#

Meta-estimator for forecasting transformed time series.

Pipeline functionality to apply transformers to the target series. The X data is not transformed. If you want to transform X, please use the ForecastingPipeline.

For a list t1, t2, …, tN, f, tp1, tp2, …, tpM

where t[i] and tp[i] are transformers (t to pre-, tp to post-process), and f is an sktime forecaster, the pipeline behaves as follows:

fit(y, X, fh) - changes state by running t1.fit_transform with X=y, y=X

then t2.fit_transform on X= the output of t1.fit_transform, y=X, etc sequentially, with t[i] receiving the output of t[i-1] as X, then running f.fit with y being the output of t[N], and X=X, then running tp1.fit_transform with X=y, y=X, then tp2.fit_transform on X= the output of tp1.fit_transform, etc sequentially, with tp[i] receiving the output of tp[i-1],

predict(X, fh) - result is of executing f.predict, with X=X, fh=fh,

then running tp1.inverse_transform with X= the output of f, y=X, then t2.inverse_transform on X= the output of t1.inverse_transform, etc sequentially, with t[i] receiving the output of t[i-1] as X, then running tp1.fit_transform with X= the output of t[N]s, y=X, then tp2.fit_transform on X= the output of tp1.fit_transform, etc sequentially, with tp[i] receiving the output of tp[i-1],

predict_interval(X, fh), predict_quantiles(X, fh) - as predict(X, fh),

with predict_interval or predict_quantiles substituted for predict

predict_var, predict_proba - uses base class default to obtain

crude estimates from predict_quantiles. Recommended to replace with better custom implementations if needed.

get_params, set_params uses sklearn compatible nesting interface

if list is unnamed, names are generated as names of classes if names are non-unique, f”_{str(i)}” is appended to each name string

where i is the total count of occurrence of a non-unique string inside the list of names leading up to it (inclusive)

TransformedTargetForecaster can also be created by using the magic multiplication

on any forecaster, i.e., if my_forecaster inherits from BaseForecaster,: and my_t1, my_t2, my_tp inherit from BaseTransformer, then, for instance, my_t1 * my_t2 * my_forecaster * my_tp will result in the same object as obtained from the constructor TransformedTargetForecaster([my_t1, my_t2, my_forecaster, my_tp])
magic multiplication can also be used with (str, transformer) pairs,: as long as one element in the chain is a transformer

Parameters

stepslist of sktime transformers and forecasters, or

list of tuples (str, estimator) of sktime transformers or forecasters: the list must contain exactly one forecaster
these are “blueprint” transformers resp forecasters,: forecaster/transformer states do not change when fit is called

Attributes

steps_list of tuples (str, estimator) of sktime transformers or forecasters: clones of estimators in steps which are fitted in the pipeline is always in (str, estimator) format, even if steps is just a list strings not passed in steps are replaced by unique generated strings i-th transformer in steps_ is clone of i-th in steps
forecaster_estimator, reference to the unique forecaster in steps_: Return reference to the forecaster in the pipeline.
transformers_pre_list of tuples (str, transformer) of sktime transformers: Return reference to the list of pre-forecast transformers.
transformers_ost_list of tuples (str, transformer) of sktime transformers: reference to pairs in steps_ that succeed forecaster_

Examples

>>> from sktime.datasets import load_airline
>>> from sktime.forecasting.naive import NaiveForecaster
>>> from sktime.forecasting.compose import TransformedTargetForecaster
>>> from sktime.transformations.series.impute import Imputer
>>> from sktime.transformations.series.detrend import Deseasonalizer
>>> from sktime.transformations.series.exponent import ExponentTransformer
>>> y = load_airline()

Example 1: string/estimator pairs >>> pipe = TransformedTargetForecaster(steps=[ … (“imputer”, Imputer(method=”mean”)), … (“detrender”, Deseasonalizer()), … (“forecaster”, NaiveForecaster(strategy=”drift”)), … ]) >>> pipe.fit(y) TransformedTargetForecaster(…) >>> y_pred = pipe.predict(fh=[1,2,3])

Example 2: without strings >>> pipe = TransformedTargetForecaster([ … Imputer(method=”mean”), … Deseasonalizer(), … NaiveForecaster(strategy=”drift”), … ExponentTransformer(), … ])

Example 3: using the dunder method >>> forecaster = NaiveForecaster(strategy=”drift”) >>> imputer = Imputer(method=”mean”) >>> pipe = imputer * Deseasonalizer() * forecaster * ExponentTransformer()

Methods

`check_is_fitted`()	Check if the estimator has been fitted.
`clone_tags`(estimator[, tag_names])	clone/mirror tags from another estimator as dynamic override.
`create_test_instance`([parameter_set])	Construct Estimator instance if possible.
`create_test_instances_and_names`([parameter_set])	Create list of all test instances and a list of names for them.
`fit`(y[, X, fh])	Fit forecaster to training data.
`fit_predict`(y[, X, fh])	Fit and forecast time series at future horizon.
`get_class_tag`(tag_name[, tag_value_default])	Get tag value from estimator class (only class tags).
`get_class_tags`()	Get class tags from estimator class and all its parent classes.
`get_fitted_params`()	Get fitted parameters.
`get_params`([deep])	Get parameters for this estimator.
`get_tag`(tag_name[, tag_value_default, …])	Get tag value from estimator class and dynamic tag overrides.
`get_tags`()	Get tags from estimator class and dynamic tag overrides.
`get_test_params`([parameter_set])	Return testing parameter settings for the estimator.
`inverse_transform`(Z[, X])	Reverse transformation on input series Z.
`is_composite`()	Check if the object is composite.
`predict`([fh, X])	Forecast time series at future horizon.
`predict_interval`([fh, X, coverage])	Compute/return prediction interval forecasts.
`predict_proba`([fh, X, marginal])	Compute/return fully probabilistic forecasts.
`predict_quantiles`([fh, X, alpha])	Compute/return quantile forecasts.
`predict_residuals`([y, X])	Return residuals of time series forecasts.
`predict_var`([fh, X, cov])	Compute/return variance forecasts.
`reset`()	Reset the object to a clean post-init state.
`score`(y[, X, fh])	Scores forecast against ground truth, using MAPE.
`set_params`(**kwargs)	Set the parameters of this estimator.
`set_tags`(**tag_dict)	Set dynamic tags to given values.
`transform`(Z[, X])	Return transformed version of input series Z.
`update`(y[, X, update_params])	Update cutoff value and, optionally, fitted parameters.
`update_predict`(y[, cv, X, update_params, …])	Make predictions and update model iteratively over the test set.
`update_predict_single`([y, fh, X, update_params])	Update model with new data and make forecasts.

property forecaster_[source]#

Return reference to the forecaster in the pipeline.

Returns

sktime forecaster: reference to unique forecaster in steps_ (without the name)

property transformers_pre_[source]#

Return reference to the list of pre-forecast transformers.

Returns

list of tuples (str, estimator) of sktime transformers: reference to tuples that come before the unique (str, forecaster) in steps_

property transformers_post_[source]#

Return reference to the list of post-forecast transformers.

Returns

list of tuples (str, estimator) of sktime transformers: reference to tuples that come after the unique (str, forecaster) in steps_

transform(Z, X=None)[source]#

Return transformed version of input series Z.

Parameters

Zpd.Series or pd.DataFrame: A time series to apply the transformation on.
Xpd.DataFrame, default=None: Exogenous data used in transformation.

Returns

Ztpd.Series or pd.DataFrame: Transformed version of input series Z.

inverse_transform(Z, X=None)[source]#

Reverse transformation on input series Z.

Parameters

Zpd.Series or pd.DataFrame: A time series to reverse the transformation on.
Xpd.DataFrame, default=None: Exogenous data used in transformation.

Returns

Z_invpd.Series or pd.DataFrame: The reconstructed timeseries after the transformation has been reversed.

check_is_fitted()[source]#

Check if the estimator has been fitted.

Raises

NotFittedError: If the estimator has not been fitted yet.

clone_tags(estimator, tag_names=None)[source]#

clone/mirror tags from another estimator as dynamic override.

Parameters

estimatorestimator inheriting from :class:BaseEstimator
tag_namesstr or list of str, default = None: Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns

Self: Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default')[source]#

Construct Estimator instance if possible.

Parameters

parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns

instanceinstance of the class with default parameters

Notes

get_test_params can return dict or list of dict. This function takes first or single dict that get_test_params returns, and constructs the object with that.

classmethod create_test_instances_and_names(parameter_set='default')[source]#

Create list of all test instances and a list of names for them.

Parameters

parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns

objslist of instances of cls: i-th instance is cls(**cls.get_test_params()[i])
nameslist of str, same length as objs: i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}
parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

property cutoff[source]#

Cut-off = “present time” state of forecaster.

Returns

cutoffpandas compatible index element

property fh[source]#: Forecasting horizon that was passed.

fit(y, X=None, fh=None)[source]#

Fit forecaster to training data.

State change:: Changes state to “fitted”.
Writes to self:: Sets self._is_fitted flag to True. Writes self._y and self._X with y and X, respectively. Sets self.cutoff and self._cutoff to last index seen in y. Sets fitted model attributes ending in “_”. Stores fh to self.fh if fh is passed.

Parameters

ytime series in sktime compatible data container format

Time series to which to fit the forecaster.

y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:

if self.get_tag(“scitype:y”)==”univariate”:: y must have a single column/variable
if self.get_tag(“scitype:y”)==”multivariate”:: y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

fhint, list, np.array or ForecastingHorizon, optional (default=None)

The forecasting horizon encoding the time stamps to forecast at. if self.get_tag(“requires-fh-in-fit”), must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y if self.get_tag(“X-y-must-have-same-index”), X.index must contain y.index there are no restrictions on number of columns (unlike for y)

Returns

selfReference to self.

fit_predict(y, X=None, fh=None)[source]#

Fit and forecast time series at future horizon.

State change:: Changes state to “fitted”.
Writes to self:: Sets is_fitted flag to True. Writes self._y and self._X with y and X, respectively. Sets self.cutoff and self._cutoff to last index seen in y. Sets fitted model attributes ending in “_”. Stores fh to self.fh.

Parameters

ytime series in sktime compatible data container format

Time series to which to fit the forecaster.

y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:

if self.get_tag(“scitype:y”)==”univariate”:: y must have a single column/variable
if self.get_tag(“scitype:y”)==”multivariate”:: y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

fhint, list, np.array or ForecastingHorizon (not optional)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”),

X.index must contain fh.index and y.index both

Returns

y_predtime series in sktime compatible data container format: Point forecasts at fh, with same index as fh y_pred has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)

classmethod get_class_tag(tag_name, tag_value_default=None)[source]#

Get tag value from estimator class (only class tags).

Parameters

tag_namestr: Name of tag value.
tag_value_defaultany type: Default/fallback value if tag is not found.

Returns

tag_value: Value of the tag_name tag in self. If not found, returns tag_value_default.

classmethod get_class_tags()[source]#

Get class tags from estimator class and all its parent classes.

Returns

collected_tagsdict: Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance. NOT overridden by dynamic tags set by set_tags or mirror_tags.

get_fitted_params()[source]#

Get fitted parameters.

State required:: Requires state to be “fitted”.

Returns

fitted_paramsdict

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters

deepboolean, optional, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsmapping of string to any: Parameter names mapped to their values.

get_tag(tag_name, tag_value_default=None, raise_error=True)[source]#

Get tag value from estimator class and dynamic tag overrides.

Parameters

tag_namestr: Name of tag to be retrieved
tag_value_defaultany type, optional; default=None: Default/fallback value if tag is not found
raise_errorbool: whether a ValueError is raised when the tag is not found

Returns

tag_value: Value of the tag_name tag in self. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises

ValueError if raise_error is True i.e. if tag_name is not in self.get_tags(
).keys()

get_tags()[source]#

Get tags from estimator class and dynamic tag overrides.

Returns

collected_tagsdict: Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance and then any overrides and new tags from _tags_dynamic object attribute.

classmethod get_test_params(parameter_set='default')[source]#

Return testing parameter settings for the estimator.

Parameters

parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns

paramsdict or list of 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

is_composite()[source]#

Check if the object is composite.

A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.

Returns

composite: bool, whether self contains a parameter which is BaseObject

property is_fitted[source]#: Whether fit has been called.

property named_steps[source]#: Map the steps to a dictionary.

predict(fh=None, X=None)[source]#

Forecast time series at future horizon.

State required:: Requires state to be “fitted”.
Accesses in self:: Fitted model attributes ending in “_”. self.cutoff, self._is_fitted
Writes to self:: Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters

fhint, list, np.array or ForecastingHorizon, optional (default=None): The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional
Xtime series in sktime compatible format, optional (default=None): Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), X.index must contain fh.index there are no restrictions on number of columns (unlike for y)

Returns

y_predtime series in sktime compatible data container format: Point forecasts at fh, with same index as fh y_pred has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)

predict_interval(fh=None, X=None, coverage=0.9)[source]#

Compute/return prediction interval forecasts.

If coverage is iterable, multiple intervals will be calculated.

State required:: Requires state to be “fitted”.
Accesses in self:: Fitted model attributes ending in “_”. self.cutoff, self._is_fitted
Writes to self:: Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters

fhint, list, np.array or ForecastingHorizon (not optional): The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional
Xtime series in sktime compatible format, optional (default=None): Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), must contain fh.index
coveragefloat or list of float of unique values, optional (default=0.90): nominal coverage(s) of predictive interval(s)

Returns

pred_intpd.DataFrame

Column has multi-index: first level is variable name from y in fit,

second level coverage fractions for which intervals were computed.: in the same order as in input coverage.

Third level is string “lower” or “upper”, for lower/upper interval end.

Row index is fh, with additional (upper) levels equal to instance levels,

from y seen in fit, if y seen in fit was Panel or Hierarchical.

Entries are forecasts of lower/upper interval end,

for var in col index, at nominal coverage in second col index, lower/upper depending on third col index, for the row index. Upper/lower interval end forecasts are equivalent to quantile forecasts at alpha = 0.5 - c/2, 0.5 + c/2 for c in coverage.

predict_proba(fh=None, X=None, marginal=True)[source]#

Compute/return fully probabilistic forecasts.

Note: currently only implemented for Series (non-panel, non-hierarchical) y.

State required:: Requires state to be “fitted”.
Accesses in self:: Fitted model attributes ending in “_”. self.cutoff, self._is_fitted
Writes to self:: Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters

fhint, list, np.array or ForecastingHorizon (not optional): The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional
Xtime series in sktime compatible format, optional (default=None): Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), must contain fh.index
marginalbool, optional (default=True): whether returned distribution is marginal by time index

Returns

pred_disttfp Distribution object

if marginal=True:: batch shape is 1D and same length as fh event shape is 1D, with length equal number of variables being forecast i-th (batch) distribution is forecast for i-th entry of fh j-th (event) index is j-th variable, order as y in fit/update
if marginal=False:: there is a single batch event shape is 2D, of shape (len(fh), no. variables) i-th (event dim 1) distribution is forecast for i-th entry of fh j-th (event dim 1) index is j-th variable, order as y in fit/update

predict_quantiles(fh=None, X=None, alpha=None)[source]#

Compute/return quantile forecasts.

If alpha is iterable, multiple quantiles will be calculated.

State required:: Requires state to be “fitted”.
Accesses in self:: Fitted model attributes ending in “_”. self.cutoff, self._is_fitted
Writes to self:: Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters

fhint, list, np.array or ForecastingHorizon (not optional): The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional
Xtime series in sktime compatible format, optional (default=None): Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), must contain fh.index
alphafloat or list of float of unique values, optional (default=[0.05, 0.95]): A probability or list of, at which quantile forecasts are computed.

Returns

quantilespd.DataFrame

Column has multi-index: first level is variable name from y in fit,: second level being the values of alpha passed to the function.
Row index is fh, with additional (upper) levels equal to instance levels,: from y seen in fit, if y seen in fit was Panel or Hierarchical.
Entries are quantile forecasts, for var in col index,: at quantile probability in second col index, for the row index.

predict_residuals(y=None, X=None)[source]#

Return residuals of time series forecasts.

Residuals will be computed for forecasts at y.index.

If fh must be passed in fit, must agree with y.index. If y is an np.ndarray, and no fh has been passed in fit, the residuals will be computed at a fh of range(len(y.shape[0]))

State required:: Requires state to be “fitted”. If fh has been set, must correspond to index of y (pandas or integer)
Accesses in self:: Fitted model attributes ending in “_”. self.cutoff, self._is_fitted
Writes to self:: Stores y.index to self.fh if has not been passed previously.

Parameters

ytime series in sktime compatible data container format: Time series with ground truth observations, to compute residuals to. Must have same type, dimension, and indices as expected return of predict. if None, the y seen so far (self._y) are used, in particular:

if preceded by a single fit call, then in-sample residuals are produced if fit requires fh, it must have pointed to index of y in fit
Xpd.DataFrame, or 2D np.ndarray, optional (default=None): Exogeneous time series to predict from if self.get_tag(“X-y-must-have-same-index”),

X.index must contain fh.index and y.index both

Returns

y_restime series in sktime compatible data container format: Forecast residuals at fh, with same index as fh y_res has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)

predict_var(fh=None, X=None, cov=False)[source]#

Compute/return variance forecasts.

State required:: Requires state to be “fitted”.
Accesses in self:: Fitted model attributes ending in “_”. self.cutoff, self._is_fitted
Writes to self:: Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters

fhint, list, np.array or ForecastingHorizon (not optional): The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional
Xtime series in sktime compatible format, optional (default=None): Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”),

X.index must contain fh.index and y.index both
covbool, optional (default=False): if True, computes covariance matrix forecast. if False, computes marginal variance forecasts.

Returns

pred_varpd.DataFrame, format dependent on cov variable

If cov=False:

Column names are exactly those of y passed in fit/update.: For nameless formats, column index will be a RangeIndex.
Row index is fh, with additional levels equal to instance levels,: from y seen in fit, if y seen in fit was Panel or Hierarchical.

Entries are variance forecasts, for var in col index. A variance forecast for given variable and fh index is a predicted

variance for that variable and index, given observed data.

If cov=True:

Column index is a multiindex: 1st level is variable names (as above): 2nd level is fh.
Row index is fh, with additional levels equal to instance levels,: from y seen in fit, if y seen in fit was Panel or Hierarchical.
Entries are (co-)variance forecasts, for var in col index, and: covariance between time index in row and col.

Note: no covariance forecasts are returned between different variables.

reset()[source]#

Reset the object to a clean post-init state.

Equivalent to sklearn.clone but overwrites self. After self.reset() call, self is equal in value to type(self)(**self.get_params(deep=False))

Detail behaviour: removes any object attributes, except:

hyper-parameters = arguments of __init__ object attributes containing double-underscores, i.e., the string “__”

runs __init__ with current values of hyper-parameters (result of get_params)

Not affected by the reset are: object attributes containing double-underscores class and object methods, class attributes

score(y, X=None, fh=None)[source]#

Scores forecast against ground truth, using MAPE.

Parameters

ypd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

Time series to score if self.get_tag(“scitype:y”)==”univariate”:

must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:: must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions apply

fhint, list, array-like or ForecastingHorizon, optional (default=None)

The forecasters horizon with the steps ahead to to predict.

Xpd.DataFrame, or 2D np.array, optional (default=None)

Exogeneous time series to score if self.get_tag(“X-y-must-have-same-index”), X.index must contain y.index

Returns

scorefloat: sMAPE loss of self.predict(fh, X) with respect to y_test.