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# `sklearn.linear_model`.ARDRegression

class sklearn.linear_model.ARDRegression(*, max_iter=None, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, threshold_lambda=10000.0, fit_intercept=True, copy_X=True, verbose=False, n_iter='deprecated')

  Bayesian ARD regression.

  Fit the weights of a regression model, using an ARD prior. The weights of the regression model are assumed to be in Gaussian distributions. Also estimate the parameters lambda (precisions of the distributions of the weights) and alpha (precision of the distribution of the noise). The estimation is done by an iterative procedures (Evidence Maximization)

  Read more in the User Guide.

  Parameters:
    max_iter int, default=None

      Maximum number of iterations. If `None`, it corresponds to `max_iter=300`.

      Changed in version 1.3.

    tol float, default=1e-3

      Stop the algorithm if w has converged.

    alpha_1 float, default=1e-6

      Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter.

    alpha_2 float, default=1e-6

      Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter.

    lambda_1 float, default=1e-6

      Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter.

    lambda_2 float, default=1e-6

      Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter.

    compute_score bool, default=False

      If True, compute the objective function at each step of the model.

    threshold_lambda float, default=10 000

      Threshold for removing (pruning) weights with high precision from the computation.

    fit_intercept bool, default=True

      Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).

    copy_X bool, default=True

      If True, X will be copied; else, it may be overwritten.

    verbose bool, default=False

      Verbose mode when fitting the model.

    n_iter int

      Maximum number of iterations.

      Deprecated since version 1.3: `n_iter` is deprecated in 1.3 and will be removed in 1.5. Use `max_iter` instead.

  Attributes:
    coef_array-like of shape (n_features,)

      Coefficients of the regression model (mean of distribution)

    alpha_float

      estimated precision of the noise.

    lambda_array-like of shape (n_features,)

      estimated precisions of the weights.

    sigma_array-like of shape (n_features, n_features)

      estimated variance-covariance matrix of the weights

    scores_float

      if computed, value of the objective function (to be maximized)

    n_iter_int

      The actual number of iterations to reach the stopping criterion.

      New in version 1.3.

    intercept_float

      Independent term in decision function. Set to 0.0 if `fit_intercept = False`.

    X_offset_float

      If `fit_intercept=True`, offset subtracted for centering data to a zero mean. Set to np.zeros(n_features) otherwise.

    X_scale_float

      Set to np.ones(n_features).

    n_features_in_int

      Number of features seen during fit.

      New in version 0.24.

    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.

      New in version 1.0.

  See also

  `BayesianRidge`

    Bayesian ridge regression.

  Notes

  For an example, see examples/linear_model/plot_ard.py.

  References

  D. J. C. MacKay, Bayesian nonlinear modeling for the prediction competition, ASHRAE Transactions, 1994.

  R. Salakhutdinov, Lecture notes on Statistical Machine Learning, http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15 Their beta is our `self.alpha_` Their alpha is our `self.lambda_` ARD is a little different than the slide: only dimensions/features for which `self.lambda_ < self.threshold_lambda` are kept and the rest are discarded.

  Examples

      >>> from sklearn import linear_model
      >>> clf = linear_model.ARDRegression()
      >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
      ARDRegression()
      >>> clf.predict([[1, 1]])
      array([1.])

  Methods

  `fit`(X, y) | Fit the model according to the given training data and parameters.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `predict`(X[, return_std]) | Predict using the linear model.
  `score`(X, y[, sample_weight]) | Return the coefficient of determination of the prediction.
  `set_params`(**params) | Set the parameters of this estimator.
  `set_predict_request`(*[, return_std]) | Request metadata passed to the `predict` method.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.

  fit(X, y)

    Fit the model according to the given training data and parameters.

    Iterative procedure to maximize the evidence

    Parameters:
      X array-like of shape (n_samples, n_features)

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

      y array-like of shape (n_samples,)

        Target values (integers). Will be cast to X’s dtype if necessary.

    Returns:
      self object

        Fitted estimator.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  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.

  predict(X, return_std=False)

    Predict using the linear model.

    In addition to the mean of the predictive distribution, also its standard deviation can be returned.

    Parameters:
      X{array-like, sparse matrix} of shape (n_samples, n_features)

        Samples.

      return_std bool, default=False

        Whether to return the standard deviation of posterior prediction.

    Returns:
      y_mean array-like of shape (n_samples,)

        Mean of predictive distribution of query points.

      y_std array-like of shape (n_samples,)

        Standard deviation of predictive distribution of query points.

  score(X, y, sample_weight=None)

    Return the coefficient of determination of the prediction.

    The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares `((y_true - y_pred)** 2).sum()` and \(v\) is the total sum of squares `((y_true - y_true.mean()) ** 2).sum()`. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of `y`, disregarding the input features, would get a \(R^2\) score of 0.0.

    Parameters:
      X array-like of shape (n_samples, n_features)

        Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape `(n_samples, n_samples_fitted)`, where `n_samples_fitted` is the number of samples used in the fitting for the estimator.

      y array-like of shape (n_samples,) or (n_samples, n_outputs)

        True values for `X`.

      sample_weight array-like of shape (n_samples,), default=None

        Sample weights.

    Returns:
      score float

        \(R^2\) of `self.predict(X)` w.r.t. `y`.

    Notes

    The \(R^2\) score used when calling `score` on a regressor uses `multioutput='uniform_average'` from version 0.23 to keep consistent with default value of `r2_score`. This influences the `score` method of all the multioutput regressors (except for `MultiOutputRegressor`).

  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.

  set_predict_request(*, return_std: bool | None | str = '$UNCHANGED$') → ARDRegression

    Request metadata passed to the `predict` 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 `predict` 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 `predict`.

    - `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`. Otherwise it has no effect.

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

        Metadata routing for `return_std` parameter in `predict`.

    Returns:
      self object

        The updated object.

  set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → ARDRegression

    Request metadata passed to the `score` 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 `score` 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 `score`.

    - `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`. Otherwise it has no effect.

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

        Metadata routing for `sample_weight` parameter in `score`.

    Returns:
      self object

        The updated object.

## Examples using `sklearn.linear_model.ARDRegression`

Comparing Linear Bayesian Regressors

Comparing Linear Bayesian Regressors

L1-based models for Sparse Signals

L1-based models for Sparse Signals