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

公共的抽象基类

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_

Linear Regression

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

Lasso

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

Ridge

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

测试代码

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()

测试效果

更多机器学习代码，请访问 https://github.com/WiseDoge/plume

来源：https://www.jianshu.com/p/997e0ee1e010