多项式回归没有给出我想要的

时间：2018-07-23 20:09:29

标签： python regression

我正在使用以下代码使多项式适合一组数据。它适用于简单的指数增长图，但是当它应该是正指数衰减时，这组数据会给出奇怪的结果和负值。附加的图像适合无用的数据。

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

# Importing the dataset
dataset = pd.read_csv('ML_mobility_6.csv')

X = dataset.iloc[:, 1:2].values
y = dataset.iloc[:, 2].values

# Fitting Ploynomial regression to the dataset
poly_reg = PolynomialFeatures(degree=4) #degree of polynomial
X_poly = poly_reg.fit_transform(X)
lin_reg_2 = LinearRegression()
lin_reg_2.fit(X_poly, y)
lin_reg_2.predict(poly_reg.fit_transform(X))
# Visulize Linear Regression Results

# Visualize Polynomial Regression Results
X_grid = np.arange(min(X),max(X), 10)
X_grid = X_grid.reshape((len(X_grid),1))

#original data
plt.scatter(X, y, color="red")
#xgrid is the values you want to predict in place of test data
plt.scatter(X_grid,lin_reg_2.predict(poly_reg.fit_transform(X_grid)),color="blue")

我正在使用的数据是：

30.04   1.97
30.43   1.92
30.84   1.86
31.26   1.81
31.7    1.76
32.15   1.72
32.62   1.67
33.11   1.62
33.61   1.57
34.13   1.52
34.67   1.47
35.23   1.43
35.8    1.38
36.4    1.33
37.02   1.29
37.66   1.24
38.32   1.2
39      1.16
41.99   0.985
45.43   0.835
49.37   0.7
53.89   0.583
57.72   0.504
61.97   0.433
66.68   0.37
71.91   0.315
77.7    0.267
84.13   0.225
91.26   0.189
99.17   0.157
114.3   0.116
128.5   0.0887
144.7   0.0675
163.4   0.0507
184.8   0.0375
209.4   0.0274
237.6   0.0197
270     0.014
307.2   0.00994
338.7   0.0075
373.6   0.00574
412.4   0.00433
455.3   0.00325
503 0.00243
555.9   0.00182
614.5   0.00136
679.5   0.00102
751.6   0.000749
831.7   0.000557
920.4   0.000413

非常感谢

enter image description here

1 个答案:

答案 0 :(得分：0)

您在评论中询问如何实现我建议的拟合方程，这是使用我的pyeq3拟合库（pip3 install pyeq3）的代码。由于方程对初始起始参数非常敏感，因此拟合库使用差分进化遗传算法确定初始参数估计值，从而获得良好的拟合度。

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
import pyeq3


##########################################################
# text data section
dataString = '''
30.04   1.97
30.43   1.92
30.84   1.86
31.26   1.81
31.7    1.76
32.15   1.72
32.62   1.67
33.11   1.62
33.61   1.57
34.13   1.52
34.67   1.47
35.23   1.43
35.8    1.38
36.4    1.33
37.02   1.29
37.66   1.24
38.32   1.2
39      1.16
41.99   0.985
45.43   0.835
49.37   0.7
53.89   0.583
57.72   0.504
61.97   0.433
66.68   0.37
71.91   0.315
77.7    0.267
84.13   0.225
91.26   0.189
99.17   0.157
114.3   0.116
128.5   0.0887
144.7   0.0675
163.4   0.0507
184.8   0.0375
209.4   0.0274
237.6   0.0197
270     0.014
307.2   0.00994
338.7   0.0075
373.6   0.00574
412.4   0.00433
455.3   0.00325
503 0.00243
555.9   0.00182
614.5   0.00136
679.5   0.00102
751.6   0.000749
831.7   0.000557
920.4   0.000413
'''


##########################################################
# pyeq3 fitting section

# this example fits to default lowest sum-of-squared errors
equation = pyeq3.Models_2D.Exponential.Hocket_Sherby('SSQABS')

# note that True is passed here to indicate weighted data, for unweighted pass False
pyeq3.dataConvertorService().ConvertAndSortColumnarASCII(dataString, equation, False)

print("Fitting data...")
equation.Solve()


##########################################################
# text output section for fitted parameter values

print("Equation:", equation.GetDisplayName(), str(equation.GetDimensionality()) + "D")
print("Fitting target of", equation.fittingTargetDictionary[equation.fittingTarget], '=', equation.CalculateAllDataFittingTarget(equation.solvedCoefficients))
print("Fitted Parameters:")
for i in range(len(equation.solvedCoefficients)):
    print("    %s = %-.16E" % (equation.GetCoefficientDesignators()[i], equation.solvedCoefficients[i]))
print()


##########################################################
# calculate absolute, relative, and percent errors from the fit
equation.CalculateModelErrors(equation.solvedCoefficients, equation.dataCache.allDataCacheDictionary)


##########################################################
# this section prints information on each individual data point
for i in range(len(equation.dataCache.allDataCacheDictionary['DependentData'])):
    print('X:', equation.dataCache.allDataCacheDictionary['IndependentData'][0][i],)
    print('Y:', equation.dataCache.allDataCacheDictionary['DependentData'][i],)
    print('Model:', equation.modelPredictions[i],)
    print('Abs. Error:', equation.modelAbsoluteError[i],)
    if not equation.dataCache.DependentDataContainsZeroFlag:
        print('Rel. Error:', equation.modelRelativeError[i],)
        print('Percent Error:', equation.modelPercentError[i])
    else:
        print()
print()


##########################################################
# overall fit and parameter statistics output section

equation.CalculateCoefficientAndFitStatistics()

if equation.upperCoefficientBounds or equation.lowerCoefficientBounds:
    print('You entered coefficient bounds. Parameter statistics may')
    print('not be valid for parameter values at or near the bounds.')
    print()

print('Degress of freedom error',  equation.df_e)
print('Degress of freedom regression',  equation.df_r)

if equation.rmse == None:
    print('Root Mean Squared Error (RMSE): n/a')
else:
    print('Root Mean Squared Error (RMSE):',  equation.rmse)

if equation.r2 == None:
    print('R-squared: n/a')
else:
    print('R-squared:',  equation.r2)

if equation.r2adj == None:
    print('R-squared adjusted: n/a')
else:
    print('R-squared adjusted:',  equation.r2adj)

if equation.Fstat == None:
    print('Model F-statistic: n/a')
else:
    print('Model F-statistic:',  equation.Fstat)

if equation.Fpv == None:
    print('Model F-statistic p-value: n/a')
else:
    print('Model F-statistic p-value:',  equation.Fpv)

if equation.ll == None:
    print('Model log-likelihood: n/a')
else:
    print('Model log-likelihood:',  equation.ll)

if equation.aic == None:
    print('Model AIC: n/a')
else:
    print('Model AIC:',  equation.aic)

if equation.bic == None:
    print('Model BIC: n/a')
else:
    print('Model BIC:',  equation.bic)


print()
print("Individual Parameter Statistics:")
for i in range(len(equation.solvedCoefficients)):
    if type(equation.tstat_beta) == type(None):
        tstat = 'n/a'
    else:
        tstat = '%-.5E' %  ( equation.tstat_beta[i])

    if type(equation.pstat_beta) == type(None):
        pstat = 'n/a'
    else:
        pstat = '%-.5E' %  ( equation.pstat_beta[i])

    if type(equation.sd_beta) != type(None):
        print("Coefficient %s = %-.16E, std error: %-.5E" % (equation.GetCoefficientDesignators()[i], equation.solvedCoefficients[i], equation.sd_beta[i]))
    else:
        print("Coefficient %s = %-.16E, std error: n/a" % (equation.GetCoefficientDesignators()[i], equation.solvedCoefficients[i]))
    print("          t-stat: %s, p-stat: %s, 95 percent confidence intervals: [%-.5E, %-.5E]" % (tstat,  pstat, equation.ci[i][0], equation.ci[i][1]))


print()
print("Coefficient Covariance Matrix:")
for i in  equation.cov_beta:
    print(i)


##########################################################
# graphics output section
def ModelScatterGraph(equation, graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)
    y_data = equation.dataCache.allDataCacheDictionary['DependentData']
    x_data = equation.dataCache.allDataCacheDictionary['IndependentData'][0]

    # first the raw data as a scatter plot
    axes.plot(x_data, y_data,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(x_data), max(x_data))

    tempcache = equation.dataCache # store the data cache
    equation.dataCache = pyeq3.dataCache()
    equation.dataCache.allDataCacheDictionary['IndependentData'] = numpy.array([xModel, xModel])
    equation.dataCache.FindOrCreateAllDataCache(equation)
    yModel = equation.CalculateModelPredictions(equation.solvedCoefficients, equation.dataCache.allDataCacheDictionary)
    equation.dataCache = tempcache # restore the original data cache

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_title(equation.GetDisplayName()) # add a title
    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
ModelScatterGraph(equation, graphWidth, graphHeight)
相关问题
最新问题