<a id="skfolio-preprocessing-csstandardscaler"></a>

# skfolio.preprocessing.CSStandardScaler

<a id="skfolio.preprocessing.CSStandardScaler"></a>

### *class* skfolio.preprocessing.CSStandardScaler(\*, min_group_size=8, atol=1e-12)

Cross-sectional standardization.

Standardizes each finite value within an observation’s cross-section to have
weighted mean zero and unit equal-weighted standard deviation over the estimation
universe.

When `cs_weights` is provided, weighted means and unbiased equal-weighted standard
deviations are estimated only on the estimation universe, defined by
`cs_weights > 0`. Assets outside that universe still receive standardized values
relative to the estimation universe. For this estimator, `cs_weights` is used to
define the estimation universe and to compute the cross-sectional mean, while the
standard deviation remains equal-weighted over the selected assets.

NaNs are treated as missing values. They are ignored when computing cross-sectional
statistics and are preserved in the output.

When `cs_groups` is `None`, standardization is performed globally within each
observation. For observation $t$, the standardized value $z_{t,i}$ is
defined by:

$$
z_{t,i} = \frac{x_{t,i} - \mu_t}{\sigma_t}
$$

where $\mu_t$ is the weighted mean,
$\sigma_t$ is the unbiased equal-weighted standard deviation,
$\mathcal{E}_t$ is the estimation universe, and
$N_{\mathcal{E}_t}$ is its number of assets:

$$
\mu_t = \frac{\sum_{i \in \mathcal{E}_t} w_{t,i} x_{t,i}}
             {\sum_{i \in \mathcal{E}_t} w_{t,i}},
\quad
\sigma_t = \sqrt{\frac{1}{N_{\mathcal{E}_t} - 1}
           \sum_{i \in \mathcal{E}_t} (x_{t,i} - \mu_t)^2}
$$

When `cs_groups` is provided, the same centering and scaling scheme is first applied
within each group. Groups with fewer than `min_group_size` estimation assets, and
missing groups (`cs_groups == -1`), fall back to global cross-sectional statistics.
The grouped result is then globally recentered to weighted mean zero and globally
rescaled to unit equal-weighted standard deviation over the estimation universe.

This transformer is stateless.

* **Parameters:**
  **min_group_size** *int, default=8*
  : Minimum number of estimation assets required in a group. Smaller groups fall
    back to global cross-sectional statistics.

  **atol** *float, default=1e-12*
  : Absolute tolerance below which the cross-sectional standard deviation is treated
    as zero. When `cs_groups` is `None`, this means that the observation has no
    measurable cross-sectional dispersion on its estimation universe, so finite
    outputs are set to zero rather than `NaN` and the row is treated as a neutral
    exposure. When `cs_groups` is provided, the same convention applies to the
    within-group standardization step and to the final global rescaling step.

### Methods

| [`fit`](#skfolio.preprocessing.CSStandardScaler.fit)(X[, y, cs_weights, cs_groups])                 | Fit the transformer.                                                                   |
|-----------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------|
| [`fit_transform`](#skfolio.preprocessing.CSStandardScaler.fit_transform)(X[, y, cs_weights, cs_groups])       | Fit to `X` and return the transformed values.                                          |
| [`get_feature_names_out`](#skfolio.preprocessing.CSStandardScaler.get_feature_names_out)([input_features])            | Get output feature names for transformation.                                           |
| [`get_metadata_routing`](#skfolio.preprocessing.CSStandardScaler.get_metadata_routing)()                             | Get metadata routing of this object.                                                   |
| [`get_params`](#skfolio.preprocessing.CSStandardScaler.get_params)([deep])                                 | Get parameters for this estimator.                                                     |
| [`set_fit_request`](#skfolio.preprocessing.CSStandardScaler.set_fit_request)(\*[, cs_groups, cs_weights])       | Configure whether metadata should be requested to be passed to the `fit` method.       |
| [`set_params`](#skfolio.preprocessing.CSStandardScaler.set_params)(\*\*params)                             | Set the parameters of this estimator.                                                  |
| [`set_transform_request`](#skfolio.preprocessing.CSStandardScaler.set_transform_request)(\*[, cs_groups, cs_weights]) | Configure whether metadata should be requested to be passed to the `transform` method. |
| [`transform`](#skfolio.preprocessing.CSStandardScaler.transform)(X[, cs_weights, cs_groups])              | Standardize each observation into cross-sectional z-scores.                            |

#### SEE ALSO
[`CSPercentileRankScaler`](https://skfolio.org/generated/skfolio.preprocessing.CSPercentileRankScaler.html.md#skfolio.preprocessing.CSPercentileRankScaler)

[`CSGaussianRankScaler`](https://skfolio.org/generated/skfolio.preprocessing.CSGaussianRankScaler.html.md#skfolio.preprocessing.CSGaussianRankScaler)

### Examples

```pycon
>>> import numpy as np
>>> from skfolio.preprocessing import CSStandardScaler
>>>
>>> X = np.array([[1.0, np.nan, 3.0, 4.0],
...               [4.0, 3.0, 2.0, 1.0],
...               [10.0, 20.0, np.nan, 40.0]])
>>>
>>> transformer = CSStandardScaler()
>>> transformer.fit_transform(X)
array([[-1.09108945,         nan,  0.21821789,  0.87287156],
       [ 1.161895  ,  0.38729833, -0.38729833, -1.161895  ],
       [-0.87287156, -0.21821789,         nan,  1.09108945]])
>>>
>>> # Use cs_weights for the estimation universe and weighted means, then standardize within groups.
>>> cs_weights = np.array([[3.0, 0.0, 1.0, 2.0],
...                        [4.0, 0.0, 2.0, 3.0],
...                        [2.0, 3.0, 0.0, 5.0]])
>>> cs_groups = np.array([[0, 0, 1, 1],
...                       [0, 0, 1, 1],
...                       [0, 0, 1, 1]])
>>>
>>> transformer = CSStandardScaler(min_group_size=2)
>>> transformer.fit_transform(X, cs_weights=cs_weights, cs_groups=cs_groups)
array([[-0.55454325,         nan, -0.62182063,  1.1427252 ],
       [ 0.62254586, -0.15324206,  0.5035012 , -1.16572861],
       [-1.33736075,  0.20821245,         nan,  0.41001683]])
```

<a id="skfolio.preprocessing.CSStandardScaler.fit"></a>

#### fit(X, y=None, cs_weights=None, cs_groups=None)

Fit the transformer.

Cross-sectional transformers are stateless and do not learn data-dependent
parameters. This method validates the estimator parameters, validates `X`, and
records `n_features_in_` for scikit-learn compatibility.

* **Parameters:**
  **X** *array-like of shape (n_observations, n_assets)*
  : Input matrix where each row is an observation and each column is an asset.

  **y** *Ignored*
  : Not used, present for API consistency by convention.

  **cs_weights** *array-like of shape (n_observations, n_assets), optional*
  : Optional cross-sectional weights accepted for API consistency with
    `transform`. They are ignored during fitting.

  **cs_groups** *array-like of shape (n_observations, n_assets), optional*
  : Optional cross-sectional group labels accepted for API consistency with
    `transform`. They are ignored during fitting.
* **Returns:**
  **self** *BaseCSTransformer*
  : Fitted estimator.

<a id="skfolio.preprocessing.CSStandardScaler.fit_transform"></a>

#### fit_transform(X, y=None, cs_weights=None, cs_groups=None)

Fit to `X` and return the transformed values.

* **Parameters:**
  **X** *array-like of shape (n_observations, n_assets)*
  : Input matrix where each row is an observation and each column is an asset.

  **y** *Ignored*
  : Not used, present for API consistency by convention.

  **cs_weights** *array-like of shape (n_observations, n_assets), optional*
  : Optional cross-sectional weights forwarded to `transform`.

  **cs_groups** *array-like of shape (n_observations, n_assets), optional*
  : Optional cross-sectional group labels forwarded to `transform`.
* **Returns:**
  **X_new** *ndarray of shape (n_observations, n_assets)*
  : Transformed array.

<a id="skfolio.preprocessing.CSStandardScaler.get_feature_names_out"></a>

#### get_feature_names_out(input_features=None)

Get output feature names for transformation.

* **Parameters:**
  **input_features** *array-like of str or None, default=None*
  : Input features.
    - If `input_features` is `None`, then `feature_names_in_` is
      used as feature names in. If `feature_names_in_` is not defined,
      then the following input feature names are generated:
      `["x0", "x1", ..., "x(n_features_in_ - 1)"]`.
    - If `input_features` is an array-like, then `input_features` must
      match `feature_names_in_` if `feature_names_in_` is defined.
* **Returns:**
  **feature_names_out** *ndarray of str objects*
  : Same as input features.

<a id="skfolio.preprocessing.CSStandardScaler.get_metadata_routing"></a>

#### get_metadata_routing()

Get metadata routing of this object.

Please check [User Guide](https://skfolio.org/user_guide/metadata_routing.html.md#metadata-routing) on how the routing
mechanism works.

* **Returns:**
  **routing** *MetadataRequest*
  : A `MetadataRequest` encapsulating
    routing information.

<a id="skfolio.preprocessing.CSStandardScaler.get_params"></a>

#### get_params(deep=True)

Get parameters for this estimator.

* **Parameters:**
  **deep** *bool, default=True*
  : If True, will return the parameters for this estimator and
    contained subobjects that are estimators.
* **Returns:**
  **params** *dict*
  : Parameter names mapped to their values.

<a id="skfolio.preprocessing.CSStandardScaler.set_fit_request"></a>

#### set_fit_request(\*, cs_groups='$UNCHANGED$', cs_weights='$UNCHANGED$')

Configure whether metadata should be requested to be passed to the `fit` method.

Note that this method is only relevant when this estimator is used as a
sub-estimator within a meta-estimator and metadata routing is enabled
with `enable_metadata_routing=True` (see `sklearn.set_config`).
Please check the [User Guide](https://skfolio.org/user_guide/metadata_routing.html.md#metadata-routing) on how the routing
mechanism works.

The options for each parameter are:

- `True`: metadata is requested, and passed to `fit` 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 `fit`.
- `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.

#### Versionadded
Added in version 1.3.

* **Parameters:**
  **cs_groups** *str, True, False, or None,                     default=sklearn.utils.metadata_routing.UNCHANGED*
  : Metadata routing for `cs_groups` parameter in `fit`.

  **cs_weights** *str, True, False, or None,                     default=sklearn.utils.metadata_routing.UNCHANGED*
  : Metadata routing for `cs_weights` parameter in `fit`.
* **Returns:**
  **self** *object*
  : The updated object.

<a id="skfolio.preprocessing.CSStandardScaler.set_params"></a>

#### 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:**
  **\*\*params** *dict*
  : Estimator parameters.
* **Returns:**
  **self** *estimator instance*
  : Estimator instance.

<a id="skfolio.preprocessing.CSStandardScaler.set_transform_request"></a>

#### set_transform_request(\*, cs_groups='$UNCHANGED$', cs_weights='$UNCHANGED$')

Configure whether metadata should be requested to be passed to the `transform` method.

Note that this method is only relevant when this estimator is used as a
sub-estimator within a meta-estimator and metadata routing is enabled
with `enable_metadata_routing=True` (see `sklearn.set_config`).
Please check the [User Guide](https://skfolio.org/user_guide/metadata_routing.html.md#metadata-routing) 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.

#### Versionadded
Added in version 1.3.

* **Parameters:**
  **cs_groups** *str, True, False, or None,                     default=sklearn.utils.metadata_routing.UNCHANGED*
  : Metadata routing for `cs_groups` parameter in `transform`.

  **cs_weights** *str, True, False, or None,                     default=sklearn.utils.metadata_routing.UNCHANGED*
  : Metadata routing for `cs_weights` parameter in `transform`.
* **Returns:**
  **self** *object*
  : The updated object.

<a id="skfolio.preprocessing.CSStandardScaler.transform"></a>

#### transform(X, cs_weights=None, cs_groups=None)

Standardize each observation into cross-sectional z-scores.

* **Parameters:**
  **X** *array-like of shape (n_observations, n_assets)*
  : Input matrix where each row represents an observation and
    each column represents an asset. NaNs are allowed and
    preserved.

  **cs_weights** *array-like of shape (n_observations, n_assets), optional*
  : Optional non-negative cross-sectional weights. Positive
    weights define the estimation universe and are used to
    compute weighted means. The standard deviation remains
    equal-weighted over the selected assets. If `None`, all
    finite assets are included in the estimation universe with
    unit weight.

  **cs_groups** *array-like of shape (n_observations, n_assets), optional*
  : Integer group labels >= -1. Missing groups (`-1`) and
    groups with fewer than `min_group_size` estimation assets
    fall back to global cross-sectional statistics. If `None`,
    standardization is performed globally within each
    observation.
* **Returns:**
  **Z** *ndarray of shape (n_observations, n_assets)*
  : Standardized values with weighted mean zero and unit
    equal-weighted standard deviation over the estimation
    universe.
* **Raises:**
  ValueError
  : If `min_group_size < 1`, `atol < 0`, `X` is not a non-empty
    2D array, `cs_weights` is invalid, or `cs_groups` is invalid.