@[TOC] 有约束条件的加权最小二乘的实现

加权最小二乘原理

详细见网址：加权最小二乘法

Python实现

import numpy as np
import pandas as pd
from scipy.optimize import minimize
class Constrained_regression:
def __init__(self, weight = None, intercept = True):
"""
默认选择最小二乘
"""
self.weight = weight
self.intercept = intercept
def weight_error(self, B, X_train, y_train):
# 加权最小二乘的损失函数
# 也是目标函数
# B表示beta，为待优化参数
data1 = np.dot(X_train, B)
data2 = y_train - data1
if self.weight is None: # 此时为普通最小二乘
self.weight = np.identity(self.sample_num)
weight_1 = np.linalg.pinv(self.weight)
temp3 = data2.transpose()
error1 = np.dot(temp3, weight_1)
error = np.dot(error1, data2)
return error
def cons(self):
# 创建约束条件
if self.intercept == True:
cons = ({'type': 'eq', 'fun': lambda x: np.sum(x[:-1])- 1})
else:
cons = ({'type': 'eq', 'fun': lambda x: np.sum(x)- 1})
bnds = []
for i in range(self.feature_num):
bnds.append((0, 1))
if self.intercept == True:
bnds.append((None, None))
bnds = tuple(bnds)
return cons, bnds
def fit(self, X, y):
# 模型训练
X_train = X
y_train = y
sample_num = X_train.shape[0]
feature_num = X_train.shape[1]
self.feature_num = feature_num
self.sample_num = sample_num
# 创造截距项
if self.intercept == True:
X_train['inter'] = 1
B_ini = list(np.zeros(feature_num) + 1/feature_num)
B_ini.append(0.5)
fun = lambda x: self.weight_error(B=x, X_train=X_train, y_train=y_train)
cons, bnds = self.cons()
res = minimize(fun, B_ini, method='SLSQP', constraints=cons, tol=1e-5, bounds = bnds)
return res.x
if __name__ == "__main__":
data = pd.read_csv('YFDdata.csv')
X_train = data[['bond', 'Conbond', 'Credebt']]
y_train = data['YFD']
model = Constrained_regression()
conf = model.fit(X_train, y_train)

第一次写CSDN，比较简单，下次会修正

最后

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