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# skfolio.distance.MutualInformation

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### *class* skfolio.distance.MutualInformation(n_bins_method=FREEDMAN, n_bins=None, normalize=True)

Mutual Information estimator.

In information theory, the mutual information is a measure of the mutual dependence
between variables.
The related distance metric is called the variation of information.

For two random variables X and Y, the mutual information I(X,Y) is defined as:

$$
I(X,Y) = H(X) + H(Y) - H(X,Y)

$$

with H(X) and H(Y) the marginal entropies and H(X,Y) the joint entropy.

The related distance metric known as the  variation of information is defined as:

$$
d(X,Y) = H(X,Y) - I(X,Y) =  H(X) + H(Y) - 2 \times I(X,Y)

$$

and its normalization as:

$$
D(X,Y) = \frac{d(X,Y)}{H(X,Y)} = \frac{H(X) + H(Y) - 2 \times I(X,Y)}{H(X) + H(Y) - I(X,Y)}

$$

* **Parameters:**
  **n_bins_method** *NBinsMethod, default=NBinsMethod.FREEDMAN*
  : Method to compute the number of bins for the contingency matrix estimation used
    for the computation of the mutual information.
    Possible values are:
    > * FREEDMAN (`default`)
    > * KNUTH

  **n_bins** *int, optional*
  : Instead of using `n_bins_method`, you can directly specify the number of bins
    with `n_bins`.

  **normalize** *bool, default=True*
  : If this is set to True, the variation of information is normalized.
    The default is `True`.
* **Attributes:**
  **codependence_** *ndarray of shape (n_assets, n_assets)*
  : Codependence matrix.

  **distance_** *ndarray of shape (n_assets, n_assets)*
  : Distance matrix.

  **n_features_in_** *int*
  : Number of assets seen during `fit`.

  **feature_names_in_** *ndarray of shape (`n_features_in_`,)*
  : Names of features seen during `fit`. Defined only when `X` has feature
    names that are all strings.

### Methods

| [`fit`](#skfolio.distance.MutualInformation.fit)(X[, y])            | Fit the Mutual Information estimator.   |
|-------------------------------------------------------------------------|-----------------------------------------|
| [`get_metadata_routing`](#skfolio.distance.MutualInformation.get_metadata_routing)() | Get metadata routing of this object.    |
| [`get_params`](#skfolio.distance.MutualInformation.get_params)([deep])     | Get parameters for this estimator.      |
| [`set_params`](#skfolio.distance.MutualInformation.set_params)(\*\*params) | Set the parameters of this estimator.   |

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

Fit the Mutual Information estimator.

* **Parameters:**
  **X** *array-like of shape (n_observations, n_assets)*
  : Price returns of the assets.

  **y** *Ignored*
  : Not used, present for API consistency by convention.
* **Returns:**
  **self** *MutualInformation*
  : Fitted estimator.

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#### 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.

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#### 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.

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#### 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.