机器算法验证 - Python中的最大似然曲线/模型拟合 - 吾爱随笔录

我有一些我认为最适合 sigmoid 函数的二维数据。我可以使用以下 python 代码片段进行拟合。

from scipy.optimize import curve_fit
ydata = array([0.1,0.15,0.2,0.3,0.7,0.8,0.9, 0.9, 0.95])
xdata = array(range(0,len(ydata),1))

def sigmoid(x, x0, k):
    y = 1 / (1+ np.exp(-k*(x-x0)))
    return y

popt, pcov = curve_fit(sigmoid, xdata, ydata)

但是，我想使用最大似然方法，以便我可以报告可能性。我认为使用statsmodels包可以做到这一点，但我无法弄清楚。任何帮助，将不胜感激。

更新：

我认为该方法可能是重新定义似然函数，如此处所述：

http://statsmodels.sourceforge.net/devel/examples/generated/example_gmle.html

上述代码片段的绘图如下所示：

在此处输入图像描述

更新 2：

以下是如何在 R 中执行此操作：

require(bbmle)

# this sigmoid function is used to make some fake data
rsigmoid <- function(y1,y2,xi,xmid,w){
   y1+(y2-y1)/(1+exp((xmid-xi)/w))
}
counts <- round(rsigmoid(0, 1, 1:100+rnorm(100,0,3), 50, 10)*20,0)

# NOTE THAT THE SIGMOID FUNCTION IS REDEFINED AS AN R FORMULA
fit_sigmoid <- mle2(P1 ~ dbinom(prob=y1+(y2-y1)/(1+exp((xmid-xi)/w)), size=N), 
             start = list(xmid=50, w=10), 
             data=list(y1=0, y2=1, N=20, P1=counts, xi=1:100),
             method="L-BFGS-B", lower=c(xmid=1,w=1e-5), upper=c(xmid=100,w=100))

from scipy import stats import numpy as np from scipy.optimize import minimize import pylab as py ydata = np.array([0.1,0.15,0.2,0.3,0.7,0.8,0.9, 0.9, 0.95]) xdata = np.array(range(0,len(ydata),1)) def sigmoid(params): k = params[0] x0 = params[1] sd = params[2] yPred = 1 / (1+ np.exp(-k*(xdata-x0))) # Calculate negative log likelihood LL = -np.sum( stats.norm.logpdf(ydata, loc=yPred, scale=sd ) ) return(LL) initParams = [1, 1, 1] results = minimize(sigmoid, initParams, method='Nelder-Mead') print results.x estParms = results.x yOut = yPred = 1 / (1+ np.exp(-estParms[0]*(xdata-estParms[1]))) py.clf() py.plot(xdata,ydata, 'go') py.plot(xdata, yOut) py.show()