使用附加变量进行回归以进行优化

Question

我得到了由 X 和 Y 点组成的数据(x_1,...x_n; y1,...y_n)。我想使用两个基函数将 X 拟合到 Y：max(x,mu_1)和min(x,mu_2)换句话说，我想估计以下等式：y_i = a_1*max(x_i,mu_1)+a_2*min(x_i,mu_2)我想找到 mu_1并且mu_2上面的拟合是最好的。我的意思是这样的mu_1和mu_2，这样，当我适合y以平方剩余的X总和被最小化。或者我可以说我需要a_1, a_2, mu_1,mu_2以便最小化上述拟合的残差平方和。我尝试执行以下操作：我创建了两个参数的函数(mu_1 and mu_2)，返回 Y 到 X 的拟合质量。然后我尝试使用scipy.optimize.minimize. 这是代码：import numpy as npfrom scipy.optimize import minimizefrom sklearn.linear_model import LinearRegression###Create X and YX = np.random.normal(10,1,size = 10000)Y = np.random.normal(20,1,size = 10000)###Create function that estimates quality of fitdef func(mu_1,mu_2):   ### basis functions   regressor_1 = np.maximum(X,mu_1).reshape(-1,1)   regressor_2 = np.minimum(X,mu_2).reshape(-1,1)   x_train = np.hstack((regressor_1,regressor_2))   model = LinearRegression().fit(x_train,Y)   ###I didnt find how to extract sum of squared residual, but I can get R    squared, so I thought that minimizing SSR is the same as maximizing R    squared and it is the same as minimizing -R^2   objective = model.score(x_train,Y)   return -1*objective### Now I want to find such mu_1 and mu_2 that minimize "func"minimum = minimize(func,0,0)minimum.x它不起作用。我真的很感激任何帮助。

Answer 1

这个图形拟合器使用您的功能，它似乎可以满足您的要求。

import numpy, scipy, matplotlib

import matplotlib.pyplot as plt

from scipy.optimize import curve_fit

import warnings

xData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.0, 6.6, 7.7])

yData = numpy.array([1.1, 20.2, 30.3, 60.4, 50.0, 60.6, 70.7])

def func(x, a_1, a_2, mu_1, mu_2):

    retArray = []

    for x_i in x: # process data points individually

        val = a_1*max(x_i,mu_1) + a_2*min(x_i,mu_2)

        retArray.append(val)

    return retArray

# turn off the curve_fit() "covariance estimation" warning

warnings.filterwarnings("ignore")

# these are the same as the scipy defaults

initialParameters = numpy.array([1.0, 1.0, 1.0, 1.0])

# curve fit the test data

fittedParameters, pcov = curve_fit(func, xData, yData, initialParameters)

modelPredictions = func(xData, *fittedParameters) 

absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors

MSE = numpy.mean(SE) # mean squared errors

RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE

Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))

print('Parameters:', fittedParameters)

print('RMSE:', RMSE)

print('R-squared:', Rsquared)

print()

##########################################################

# graphics output section

def ModelAndScatterPlot(graphWidth, graphHeight):

    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    axes = f.add_subplot(111)

    # first the raw data as a scatter plot

    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot

    xModel = numpy.linspace(min(xData), max(xData))

    yModel = func(xModel, *fittedParameters)

    # now the model as a line plot

    axes.plot(xModel, yModel)

    axes.set_xlabel('X Data') # X axis data label

    axes.set_ylabel('Y Data') # Y axis data label

    plt.show()

    plt.close('all') # clean up after using pyplot

graphWidth = 800

graphHeight = 600

ModelAndScatterPlot(graphWidth, graphHeight)