text: import logging
  import numpy as np
  from beartype import beartype
  import copy
  
  from UQpy.surrogates.polynomial_chaos.PolynomialChaosExpansion import PolynomialChaosExpansion
  from UQpy.surrogates.polynomial_chaos.polynomials.TotalDegreeBasis import PolynomialBasis
  from UQpy.surrogates.polynomial_chaos.regressions.baseclass.Regression import Regression
  from UQpy.surrogates.polynomial_chaos.regressions import LeastSquareRegression
  
  from sklearn import linear_model as regresion
  
  
  class LeastAngleRegression(Regression):
      @beartype
      def __init__(self, fit_intercept: bool = False, verbose: bool = False, n_nonzero_coefs: int = 1000,
                   normalize: bool = False):
          """
          Class to select the best model approximation and calculate the polynomial_chaos coefficients with the Least Angle 
          Regression method combined with ordinary least squares.
  
          :param n_nonzero_coefs: Maximum number of non-zero coefficients.
          :param fit_intercept: Whether to calculate the intercept for this model. Recommended false for PCE, since
           intercept is included in basis functions.
          :param verbose: Sets the verbosity amount.
          """
          self.fit_intercept = fit_intercept
          self.n_nonzero_coefs = n_nonzero_coefs
          self.normalize = normalize
          self.verbose = verbose
          self.logger = logging.getLogger(__name__)
  
      def run(self, x: np.ndarray, y: np.ndarray, design_matrix: np.ndarray):
          """
          Implements the LAR method to compute the polynomial_chaos coefficients. 
          Recommended only for model_selection algorithm.
  
          :param x: :class:`numpy.ndarray` containing the training points (samples).
          :param y: :class:`numpy.ndarray` containing the model evaluations (labels) at the training points.
          :param design_matrix: matrix containing the evaluation of the polynomials at the input points **x**.
          :return: Beta (polynomial_chaos coefficients)
          """
          polynomialbasis = design_matrix
          P = polynomialbasis.shape[1]
          n_samples, inputs_number = x.shape
  
          reg = regresion.Lars(fit_intercept=self.fit_intercept, verbose=self.verbose,
                               n_nonzero_coefs=self.n_nonzero_coefs, normalize=self.normalize)
          reg.fit(design_matrix, y)
  
          # LarsBeta = reg.coef_path_
          c_ = reg.coef_
  
          self.Beta_path = reg.coef_path_
  
          if c_.ndim == 1:
              c_ = c_.reshape(-1, 1)
  
          return c_, None, np.shape(c_)[1]
  
      @staticmethod
      def model_selection(pce_object: PolynomialChaosExpansion, target_error=1, check_overfitting=True):
          """
          LARS model selection algorithm for given TargetError of approximation
          measured by Cross validation: Leave-one-out error (1 is perfect approximation). Option to check overfitting by 
          empirical rule: if three steps in a row have a decreasing accuracy, stop the algorithm.
  
          :param PolynomialChaosExpansion: existing target PCE for model_selection
          :param target_error: Target error of an approximation (stoping criterion).
          :param check_overfitting: Whether to check over-fitting by empirical rule.
          :return: copy of input PolynomialChaosExpansion containing the best possible model for given data identified by LARs  
          """
  
          pce = copy.deepcopy(pce_object)
          x = pce.experimental_design_input
          y = pce.experimental_design_output
  
          pce.regression_method = LeastAngleRegression()
          pce.fit(x, y)
  
          LarsBeta = pce.regression_method.Beta_path
          P, steps = LarsBeta.shape
  
          polynomialbasis = pce.design_matrix
          multindex = pce.multi_index_set
  
          pce.regression_method = LeastSquareRegression()
  
          larsbasis = []
          OLSBetaList = []
          larsindex = []
  
          LarsError = []
          error = 0
          overfitting = False
          BestLarsError = 0
          step = 0
          
          if steps<3:
              raise Exception('LAR identified constant function! Check your data.')
  
          while BestLarsError < target_error and step < steps - 2 and overfitting == False:
  
              mask = LarsBeta[:, step + 2] != 0
              mask[0] = True
  
              larsindex.append(multindex[mask, :])
              larsbasis.append(list(np.array(pce_object.polynomial_basis.polynomials)[mask]))
  
              pce.polynomial_basis.polynomials_number = len(larsbasis[step])
              pce.polynomial_basis.polynomials = larsbasis[step]
              pce.multi_index_set = larsindex[step]
  
              pce.fit(x, y)
              coefficients = pce.coefficients
  
              LarsError.append(float(1 - pce.leaveoneout_error()))
  
              error = LarsError[step]
  
              if step == 0:
                  BestLarsMultindex = larsindex[step]
                  BestLarsBasis = larsbasis[step]
                  BestLarsError = LarsError[step]
  
              else:
                  if error > BestLarsError:
                      BestLarsMultindex = larsindex[step]
                      BestLarsBasis = larsbasis[step]
                      BestLarsError = LarsError[step]
  
              if (step > 3) and (check_overfitting == True):
                  if (BestLarsError > 0.6) and (error < LarsError[step - 1]) and (error < LarsError[step - 2]) and (
                          error < LarsError[step - 3]):
                      overfitting = True
  
              step += 1
  
          pce.polynomial_basis.polynomials_number = len(BestLarsBasis)
          pce.polynomial_basis.polynomials = BestLarsBasis
          pce.multi_index_set = BestLarsMultindex
  
          pce.fit(x, y)
  
          return pce
  