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python - Linear regression with positive coefficients for SOME of the features in Python

问题描述

I am trying to find a way to fit a linear regression. However I would like to force the coefficient of some drivers to be positive.

As far as I understood, scipy.optimize.nnls can do non-negative least squares but for all drivers.

Is there a way to do it automatically?

Thanks a lot.

标签： pythonscikit-learnlinear-regressioncoefficients

解决方案

这是一个图形拟合器，它在拟合函数中具有“砖墙”，它强制拟合参数之一为正。请注意，在此示例中，拟合度非常差 - 如果您移除“砖墙”，示例拟合度会大大提高。本例使用默认的 scipy curve_fit() 初始参数估计全部为 1.0，并且不使用 scipy 的遗传算法来帮助寻找初始参数估计。当使用这种技术时，初始参数估计必须在“砖墙”条件之外，以便非线性拟合器可以正常开始。

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

xData = numpy.array([19.1647, 18.0189, 16.9550, 15.7683, 14.7044, 13.6269, 12.6040, 11.4309, 10.2987, 9.23465, 8.18440, 7.89789, 7.62498, 7.36571, 7.01106, 6.71094, 6.46548, 6.27436, 6.16543, 6.05569, 5.91904, 5.78247, 5.53661, 4.85425, 4.29468, 3.74888, 3.16206, 2.58882, 1.93371, 1.52426, 1.14211, 0.719035, 0.377708, 0.0226971, -0.223181, -0.537231, -0.878491, -1.27484, -1.45266, -1.57583, -1.61717])
yData = numpy.array([0.644557, 0.641059, 0.637555, 0.634059, 0.634135, 0.631825, 0.631899, 0.627209, 0.622516, 0.617818, 0.616103, 0.613736, 0.610175, 0.606613, 0.605445, 0.603676, 0.604887, 0.600127, 0.604909, 0.588207, 0.581056, 0.576292, 0.566761, 0.555472, 0.545367, 0.538842, 0.529336, 0.518635, 0.506747, 0.499018, 0.491885, 0.484754, 0.475230, 0.464514, 0.454387, 0.444861, 0.437128, 0.415076, 0.401363, 0.390034, 0.378698])


def func(x, a, b, offset): #exponential curve fitting function
    # force a to be positive by using "brick wall" that
    # returns a large value, and therefore a large error,
    # if parameter a is not positive
    if a <= 0.0:
        return 1.0E10
    return a * numpy.exp(-b*x) + offset


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

print(fittedParameters)
print()

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()
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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