# James-Stein Encoder

class category_encoders.james_stein.JamesSteinEncoder(verbose=0, cols=None, drop_invariant=False, return_df=True, handle_unknown='value', handle_missing='value', model='independent', random_state=None, randomized=False, sigma=0.05)[source]

James-Stein estimator.

Supported targets: binomial and continuous. For polynomial target support, see PolynomialWrapper.

For feature value i, James-Stein estimator returns a weighted average of:

1. The mean target value for the observed feature value i.

2. The mean target value (regardless of the feature value).

This can be written as:

```JS_i = (1-B)*mean(y_i) + B*mean(y)
```

The question is, what should be the weight B? If we put too much weight on the conditional mean value, we will overfit. If we put too much weight on the global mean, we will underfit. The canonical solution in machine learning is to perform cross-validation. However, Charles Stein came with a closed-form solution to the problem. The intuition is: If the estimate of mean(y_i) is unreliable (y_i has high variance), we should put more weight on mean(y). Stein put it into an equation as:

```B = var(y_i) / (var(y_i)+var(y))
```

The only remaining issue is that we do not know var(y), let alone var(y_i). Hence, we have to estimate the variances. But how can we reliably estimate the variances, when we already struggle with the estimation of the mean values?! There are multiple solutions:

1. If we have the same count of observations for each feature value i and all y_i are close to each other, we can pretend that all var(y_i) are identical. This is called a pooled model. 2. If the observation counts are not equal, it makes sense to replace the variances with squared standard errors, which penalize small observation counts:

```SE^2 = var(y)/count(y)
```

This is called an independent model.

James-Stein estimator has, however, one practical limitation - it was defined only for normal distributions. If you want to apply it for binary classification, which allows only values {0, 1}, it is better to first convert the mean target value from the bound interval <0,1> into an unbounded interval by replacing mean(y) with log-odds ratio:

```log-odds_ratio_i = log(mean(y_i)/mean(y_not_i))
```

This is called binary model. The estimation of parameters of this model is, however, tricky and sometimes it fails fatally. In these situations, it is better to use beta model, which generally delivers slightly worse accuracy than binary model but does not suffer from fatal failures.

Parameters:
verbose: int

integer indicating verbosity of the output. 0 for none.

cols: list

a list of columns to encode, if None, all string columns will be encoded.

drop_invariant: bool

boolean for whether or not to drop encoded columns with 0 variance.

return_df: bool

boolean for whether to return a pandas DataFrame from transform (otherwise it will be a numpy array).

handle_missing: str

options are ‘return_nan’, ‘error’ and ‘value’, defaults to ‘value’, which returns the prior probability.

handle_unknown: str

options are ‘return_nan’, ‘error’ and ‘value’, defaults to ‘value’, which returns the prior probability.

model: str

options are ‘pooled’, ‘beta’, ‘binary’ and ‘independent’, defaults to ‘independent’.

randomized: bool,

adds normal (Gaussian) distribution noise into training data in order to decrease overfitting (testing data are untouched).

sigma: float

standard deviation (spread or “width”) of the normal distribution.

References



Parametric empirical Bayes inference: Theory and applications, equations 1.19 & 1.20, from

https://www.jstor.org/stable/2287098



Empirical Bayes for multiple sample sizes, from

http://chris-said.io/2017/05/03/empirical-bayes-for-multiple-sample-sizes/



Shrinkage Estimation of Log-odds Ratios for Comparing Mobility Tables, from

https://journals.sagepub.com/doi/abs/10.1177/0081175015570097



Stein’s paradox and group rationality, from

http://www.philos.rug.nl/~romeyn/presentation/2017_romeijn_-_Paris_Stein.pdf



Methods

 `fit`(X[, y]) Fits the encoder according to X and y. `fit_transform`(X[, y]) Encoders that utilize the target must make sure that the training data are transformed with: Returns the names of all input columns present when fitting. `get_feature_names_out`([input_features]) Returns the names of all transformed / added columns. Get metadata routing of this object. `get_params`([deep]) Get parameters for this estimator. `set_output`(*[, transform]) Set output container. `set_params`(**params) Set the parameters of this estimator. `set_transform_request`(*[, override_return_df]) Request metadata passed to the `transform` method. `transform`(X[, y, override_return_df]) Perform the transformation to new categorical data.
 get_feature_names
Parameters:
verbose: int

integer indicating verbosity of output. 0 for none.

cols: list

a list of columns to encode, if None, all string and categorical columns will be encoded.

drop_invariant: bool

boolean for whether or not to drop columns with 0 variance.

return_df: bool

boolean for whether to return a pandas DataFrame from transform and inverse transform (otherwise it will be a numpy array).

handle_missing: str

how to handle missing values at fit time. Options are ‘error’, ‘return_nan’, and ‘value’. Default ‘value’, which treat NaNs as a countable category at fit time.

handle_unknown: str, int or dict of {columnoption, …}.

how to handle unknown labels at transform time. Options are ‘error’ ‘return_nan’, ‘value’ and int. Defaults to None which uses NaN behaviour specified at fit time. Passing an int will fill with this int value.

kwargs: dict.

additional encoder specific parameters like regularisation.

Methods

 `fit`(X[, y]) Fits the encoder according to X and y. `fit_transform`(X[, y]) Encoders that utilize the target must make sure that the training data are transformed with: Returns the names of all input columns present when fitting. `get_feature_names_out`([input_features]) Returns the names of all transformed / added columns. Get metadata routing of this object. `get_params`([deep]) Get parameters for this estimator. `set_output`(*[, transform]) Set output container. `set_params`(**params) Set the parameters of this estimator. `set_transform_request`(*[, override_return_df]) Request metadata passed to the `transform` method. `transform`(X[, y, override_return_df]) Perform the transformation to new categorical data.
 get_feature_names
fit(X, y=None, **kwargs)

Fits the encoder according to X and y.

Parameters:
Xarray-like, shape = [n_samples, n_features]

Training vectors, where n_samples is the number of samples and n_features is the number of features.

yarray-like, shape = [n_samples]

Target values.

Returns:
selfencoder

Returns self.

fit_transform(X, y=None, **fit_params)
Encoders that utilize the target must make sure that the training data are transformed with:

transform(X, y)

and not with:

transform(X)

get_feature_names_in() List[str]

Returns the names of all input columns present when fitting. These columns are necessary for the transform step.

get_feature_names_out(input_features=None) ndarray

Returns the names of all transformed / added columns.

Note that in sklearn the get_feature_names_out function takes the feature_names_in as an argument and determines the output feature names using the input. A fit is usually not necessary and if so a NotFittedError is raised. We just require a fit all the time and return the fitted output columns.

Returns:
feature_names: np.ndarray

A numpy array with all feature names transformed or added. Note: potentially dropped features (because the feature is constant/invariant) are not included!

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

A `MetadataRequest` encapsulating routing information.

get_params(deep=True)

Get parameters for this estimator.

Parameters:
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:
paramsdict

Parameter names mapped to their values.

set_output(*, transform=None)

Set output container.

See sphx_glr_auto_examples_miscellaneous_plot_set_output.py for an example on how to use the API.

Parameters:
transform{“default”, “pandas”}, default=None

Configure output of transform and fit_transform.

• “default”: Default output format of a transformer

• “pandas”: DataFrame output

• None: Transform configuration is unchanged

Returns:
selfestimator instance

Estimator instance.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as `Pipeline`). The latter have parameters of the form `<component>__<parameter>` so that it’s possible to update each component of a nested object.

Parameters:
**paramsdict

Estimator parameters.

Returns:
selfestimator instance

Estimator instance.

set_transform_request(*, override_return_df: bool | None | str = '\$UNCHANGED\$')

Request metadata passed to the `transform` method.

Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config()`). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• `True`: metadata is requested, and passed to `transform` if provided. The request is ignored if metadata is not provided.

• `False`: metadata is not requested and the meta-estimator will not pass it to `transform`.

• `None`: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• `str`: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (`sklearn.utils.metadata_routing.UNCHANGED`) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `pipeline.Pipeline`. Otherwise it has no effect.

Parameters:
override_return_dfstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for `override_return_df` parameter in `transform`.

Returns:
selfobject

The updated object.

transform(X, y=None, override_return_df=False)

Perform the transformation to new categorical data.

Some encoders behave differently on whether y is given or not. This is mainly due to regularisation in order to avoid overfitting. On training data transform should be called with y, on test data without.

Parameters:
Xarray-like, shape = [n_samples, n_features]
yarray-like, shape = [n_samples] or None
override_return_dfbool

override self.return_df to force to return a data frame

Returns:
parray or DataFrame, shape = [n_samples, n_features_out]

Transformed values with encoding applied.