Question

我是新手，在python上使用scipy和numpy。

我的问题：如何使用最佳alpha（水平平滑常数）最小化误差函数（平均绝对百分比误差，MAPE是否具体）？所以，我试图通过MAPE获得最佳alpha。

这是我的数学：

x = [ 3, 4, 5, 6]
y0 = x0
y1 = x0*alpha+ (1-alpha)*y0

MAPE = (y-x)/x [ This is an objective function and I am trying to solve for alpha here]

Constraints1: alpha<1
Constrants2 : alpha>0

Answer 1

这应该有效。我认为找到y比找到的递归循环有更好的方法。基本思想是你需要将你想要最小化的东西变成最小化参数（alpha）和其他任何东西（x）的函数。所以，这就是我所谓的mape。将alpha和额外参数（x）的初始猜测传递给最小化器。由于您的约束只是边界，因此使用method='SLSQP'时很容易。

import numpy as np
from scipy.optimize import minimize
from __future__ import division

def y(alpha, x):
    y = np.empty(len(x), float)
    y[0] = x[0]
    for i in xrange(1, len(x)):
        y[i] = x[i-1]*alpha + y[i-1]*(1-alpha)
    return y

def mape(alpha, x):
    diff = y(alpha, x) - x
    return np.mean(diff/x)

x = np.array([ 3, 4, 5, 6])
guess = .5
result = minimize(mape, guess, (x,), bounds=[(0,1)], method='SLSQP')

要获取您的信息，您可以：

print result
[alpha_opt] = result.x

请评论是否有任何混淆！

Answer 2

from __future__ import division
import numpy as np
from scipy.optimize import minimize



#coeffList[0] = alpha
#coeffList[1] = beta
#coeffList[2] =gamma

def mape(x, coeffList):
    diff = abs(y(x,coeffList)-x)
    print("np.mean(diff/x) : ", np.mean(diff/x))
    return np.mean(diff/x)


#Holt Winters-Multiplicative



def y(x, coeffList , debug=True):

    c =4 
    #Compute initial b and intercept using the first two complete c periods.
    xlen =len(x)
    #if xlen % c !=0:
    #    return None
    fc =float(c)
    xbar2 =sum([x[i] for i in range(c, 2 * c)])/ fc
    xbar1 =sum([x[i] for i in range(c)]) / fc
    b0 =(xbar2 - xbar1) / fc
    if debug: print ("b0 = ", b0)

    #Compute for the level estimate a0 using b0 above.
    tbar  =sum(i for i in range(1, c+1)) / fc
    print(tbar)
    a0 =xbar1  - b0 * tbar
    if debug: print ("a0 = ", a0)

    #Compute for initial indices
    I =[x[i] / (a0 + (i+1) * b0) for i in range(0, xlen)]
    if debug: print ("Initial indices = ", I)

    S=[0] * (xlen+ c)
    for i in range(c):
    S[i] =(I[i] + I[i+c]) / 2.0

    #Normalize so S[i] for i in [0, c)  will add to c.
    tS =c / sum([S[i] for i in range(c)])
    for i in range(c):
        S[i] *=tS
        if debug: print ("S[",i,"]=", S[i])

    # Holt - winters proper ...
    if debug: print( "Use Holt Winters formulae")


    At =a0
    Bt =b0
    #y =[0] * (xlen) 
    y = np.empty(len(x),float)
    for i in range(xlen):
        Atm1 =At
        Btm1 =Bt
        At =coeffList[0] * x[i] / S[i] + (1.0-coeffList[0]) * (Atm1 + Btm1)
        Bt =coeffList[1] * (At - Atm1) + (1- coeffList[1]) * Btm1
        S[i+c] =coeffList[2] * x[i] / At + (1.0 - coeffList[2]) * S[i]
        y[i]=(a0 + b0 * (i+1)) * S[i]

    return y


coeff = [0.2, 0.3, 0.4]

x =[146, 96, 59, 133, 192, 127, 79, 186, 272, 155, 98, 219]
test = y(x,coeff)
print("test : ",test)

result = minimize(mape, coeff, (x,), bounds =[(0,1),(0,1), (0,1)], method='SLSQP')

opt = result.x
print("opt : ", result.x)

最小化指数平滑中的alpha

2 个答案: