我得到了由 X 和 Y 點組成的數(shù)據(jù)(x_1,...x_n; y1,...y_n)。我想使用兩個基函數(shù)將 X 擬合到 Y：max(x,mu_1)和min(x,mu_2)換句話說，我想估計以下等式：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上面的擬合是最好的。我的意思是這樣的mu_1和mu_2，這樣，當我適合y以平方剩余的X總和被最小化。或者我可以說我需要a_1, a_2, mu_1,mu_2以便最小化上述擬合的殘差平方和。我嘗試執(zhí)行以下操作：我創(chuàng)建了兩個參數(shù)的函數(shù)(mu_1 and mu_2)，返回 Y 到 X 的擬合質(zhì)量。然后我嘗試使用scipy.optimize.minimize. 這是代碼：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。我真的很感激任何幫助。
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守候你守候我
TA貢獻1802條經(jīng)驗 獲得超10個贊
這個圖形擬合器使用您的功能，它似乎可以滿足您的要求。
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)
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