Given label matrix L and labels Y, compute the covariance.

    Args:
        L: (np.array) [n, d] The augmented (indicator) label matrix
        Y: (np.array int) [n] The true labels in {1,...,k}

def compute_inv_covariance(L_aug, Y, k, p):
    """Given label matrix L and labels Y, compute the covariance.

    Args:
        L: (np.array) [n, d] The augmented (indicator) label matrix
        Y: (np.array int) [n] The true labels in {1,...,k}
    """
    return np.linalg.inv(compute_covariance(L_aug, Y, k, p))