Python 实现 3 种回归模型（Linear Regression，Lasso，Ridge）的示例

import numpy as np
from abc import ABCMeta, abstractmethod


class LinearModel(metaclass=ABCMeta):
  """
  Abstract base class of Linear Model.
  """

  def __init__(self):
    # Before fit or predict, please transform samples' mean to 0, var to 1.
    self.scaler = StandardScaler()

  @abstractmethod
  def fit(self, X, y):
    """fit func"""

  def predict(self, X):
    # before predict, you must run fit func.
    if not hasattr(self, 'coef_'):
      raise Exception('Please run `fit` before predict')

    X = self.scaler.transform(X)
    X = np.c_[np.ones(X.shape[0]), X]

    # `x @ y` == `np.dot(x, y)`
    return X @ self.coef_

class LinearRegression(LinearModel):
  """
  Linear Regression.
  """

  def __init__(self):
    super().__init__()

  def fit(self, X, y):
    """
    :param X_: shape = (n_samples + 1, n_features)
    :param y: shape = (n_samples])
    :return: self
    """
    self.scaler.fit(X)
    X = self.scaler.transform(X)
    X = np.c_[np.ones(X.shape[0]), X]
    self.coef_ = np.linalg.inv(X.T @ X) @ X.T @ y
    return self

class Lasso(LinearModel):
  """
  Lasso Regression, training by Coordinate Descent.
  cost = ||X @ coef_||^2 + alpha * ||coef_||_1
  """
  def __init__(self, alpha=1.0, n_iter=1000, e=0.1):
    self.alpha = alpha
    self.n_iter = n_iter
    self.e = e
    super().__init__()

  def fit(self, X, y):
    self.scaler.fit(X)
    X = self.scaler.transform(X)
    X = np.c_[np.ones(X.shape[0]), X]
    self.coef_ = np.zeros(X.shape[1])
    for _ in range(self.n_iter):
      z = np.sum(X * X, axis=0)
      tmp = np.zeros(X.shape[1])
      for k in range(X.shape[1]):
        wk = self.coef_[k]
        self.coef_[k] = 0
        p_k = X[:, k] @ (y - X @ self.coef_)
        if p_k < -self.alpha / 2:
          w_k = (p_k + self.alpha / 2) / z[k]
        elif p_k > self.alpha / 2:
          w_k = (p_k - self.alpha / 2) / z[k]
        else:
          w_k = 0
        tmp[k] = w_k
        self.coef_[k] = wk
      if np.linalg.norm(self.coef_ - tmp) < self.e:
        break
      self.coef_ = tmp
    return self

class Ridge(LinearModel):
  """
  Ridge Regression.
  """

  def __init__(self, alpha=1.0):
    self.alpha = alpha
    super().__init__()

  def fit(self, X, y):
    """
    :param X_: shape = (n_samples + 1, n_features)
    :param y: shape = (n_samples])
    :return: self
    """
    self.scaler.fit(X)
    X = self.scaler.transform(X)
    X = np.c_[np.ones(X.shape[0]), X]
    self.coef_ = np.linalg.inv(
      X.T @ X + self.alpha * np.eye(X.shape[1])) @ X.T @ y
    return self

import matplotlib.pyplot as plt
import numpy as np

def gen_reg_data():
  X = np.arange(0, 45, 0.1)
  X = X + np.random.random(size=X.shape[0]) * 20
  y = 2 * X + np.random.random(size=X.shape[0]) * 20 + 10
  return X, y

def test_linear_regression():
  clf = LinearRegression()
  X, y = gen_reg_data()
  clf.fit(X, y)
  plt.plot(X, y, '.')
  X_axis = np.arange(-5, 75, 0.1)
  plt.plot(X_axis, clf.predict(X_axis))
  plt.title("Linear Regression")
  plt.show()

def test_lasso():
  clf = Lasso()
  X, y = gen_reg_data()
  clf.fit(X, y)
  plt.plot(X, y, '.')
  X_axis = np.arange(-5, 75, 0.1)
  plt.plot(X_axis, clf.predict(X_axis))
  plt.title("Lasso")
  plt.show()

def test_ridge():
  clf = Ridge()
  X, y = gen_reg_data()
  clf.fit(X, y)
  plt.plot(X, y, '.')
  X_axis = np.arange(-5, 75, 0.1)
  plt.plot(X_axis, clf.predict(X_axis))
  plt.title("Ridge")
  plt.show()