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

1

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

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

2

Empirical Bayes for multiple sample sizes, from

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

3

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

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

4

Stein’s paradox and group rationality, from

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

5

Stein’s Paradox in Statistics, from

http://statweb.stanford.edu/~ckirby/brad/other/Article1977.pdf

Attributes
feature_names

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:

get_feature_names()

Returns the names of all transformed / added columns.

get_params([deep])

Get parameters for this estimator.

set_params(**params)

Set the parameters of this estimator.

transform(X[, y, override_return_df])

Perform the transformation to new categorical data.

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.

Attributes
feature_names

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:

get_feature_names()

Returns the names of all transformed / added columns.

get_params([deep])

Get parameters for this estimator.

set_params(**params)

Set the parameters of this estimator.

transform(X[, y, override_return_df])

Perform the transformation to new categorical data.

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() List[str]

Returns the names of all transformed / added columns.

Returns
feature_names: list

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

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_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.

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.