algorithms.py 文件源码

def ridge_regression(data, labels, mu=0.0):
    r"""Implementation of the Regularized Least Squares solver.

    It solves the ridge regression problem with parameter ``mu`` on the
    `l2-norm`.

    Parameters
    ----------
    data : (N, P) ndarray
        Data matrix.
    labels : (N,)  or (N, 1) ndarray
        Labels vector.
    mu : float, optional (default is `0.0`)
        `l2-norm` penalty.

    Returns
    --------
    beta : (P, 1) ndarray
        Ridge regression solution.

    Examples
    --------
    >>> X = numpy.array([[0.1, 1.1, 0.3], [0.2, 1.2, 1.6], [0.3, 1.3, -0.6]])
    >>> beta = numpy.array([0.1, 0.1, 0.0])
    >>> Y = numpy.dot(X, beta)
    >>> beta = l1l2py.algorithms.ridge_regression(X, Y, 1e3).T
    >>> len(numpy.flatnonzero(beta))
    3

    """
    n, p = data.shape

    if n < p:
        tmp = np.dot(data, data.T)
        if mu:
            tmp += mu * n * np.eye(n)
        tmp = la.pinv(tmp)

        return np.dot(np.dot(data.T, tmp), labels.reshape(-1, 1))
    else:
        tmp = np.dot(data.T, data)
        if mu:
            tmp += mu * n * np.eye(p)
        tmp = la.pinv(tmp)

        return np.dot(tmp, np.dot(data.T, labels.reshape(-1, 1)))