python - 使用 Scipy Curve_Fit 进行预测/外推

Question

我需要使用 Scipy 的 curve_fit 操作来预测/预测/推断超过 2001-01-15 的值。如何预测过去的 2001-01-15 和 2001-01-20？

import pandas as pd
import numpy as np
from datetime import timedelta
from scipy.optimize import curve_fit

def hyperbolic_equation(t, qi, b, di):
    return qi/((1.0+b*di*t)**(1.0/b))


df1 = pd.DataFrame({
        'date': ['2001-01-01','2001-01-02','2001-01-03', '2001-01-04', '2001-01-05',
                '2001-01-06','2001-01-07','2001-01-08', '2001-01-09', '2001-01-10',
                '2001-01-11','2001-01-12','2001-01-13', '2001-01-14', '2001-01-15'],
        'cumsum_days': [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],
        'prod': [800, 900, 1200, 700, 600, 
                 550, 500, 650, 625, 600,
                550, 525, 500, 400, 350]})

df1['date'] = pd.to_datetime(df1['date'])

qi = max(df1['prod'])

#Hyperbolic curve fit the data to get best fit equation
popt_hyp, pcov_hyp = curve_fit(hyperbolic_equation, df1['cumsum_days'], df1['prod'],bounds=(0, [qi,1,20]))

#Adding in predicted values back into df1
df1.loc[:,'Hyperbolic_Predicted'] = hyperbolic_equation(df1['cumsum_days'], *popt_hyp)

这里我创建了一个 future 日期 df(测试集)

df1['future_date'] = df1['date']
ftr = (df1['future_date'] + pd.Timedelta(5, unit='days')).to_frame()

#Constructs empty columns for ftr dataframe
for col in df1.columns:
    if col not in ftr.columns:
        ftr[col] = None

#Subset future dataframe to predict on (test set)
ftr = ftr[(ftr['future_date'] > max(df1['date']))]
ftr['cumsum_days'] = [16,17,18,19,20]

此代码段会将 future 的数据集与原始数据集连接起来(如果需要)

df1 = pd.concat([df1, ftr], ignore_index=True)
print(df1)

   Hyperbolic_Predicted  cumsum_days       date future_date  prod
0             931.054472            1 2001-01-01  2001-01-01   800
...
14            409.462743           15 2001-01-15  2001-01-15   350
15                   NaN           16        NaT  2001-01-16  None
16                   NaN           17        NaT  2001-01-17  None
17                   NaN           18        NaT  2001-01-18  None
18                   NaN           19        NaT  2001-01-19  None
19                   NaN           20        NaT  2001-01-20  None

重新运行 curve_fit 操作后，我收到错误。如何预测过去的 2001-01-15 和 2001-01-20？

popt_hyp, pcov_hyp = curve_fit(hyperbolic_equation, df1['cumsum_days'], df1['prod'],bounds=(0, [qi,1,20]))

错误:

类型错误:输入类型不支持 ufunc 'isfinite'，并且根据转换规则“安全”，无法将输入安全地强制为任何受支持的类型


Answer 1

Scipy Curve_Fit 不提供对新数据的预测函数，而是返回函数系数和系数的协方差

您获得的系数位于popt_hyp中:[9.93612473e+02 2.28621390e-01 6.55150136e-02]。

系数的协方差为:

[[2.67920219e+04 2.62422207e+02 9.08459603e+00]
 [2.62422207e+02 4.31869797e+00 1.24995934e-01]
 [9.08459603e+00 1.24995934e-01 3.90417402e-03]]

为了您的目的，您需要使用返回的 popt_hyp 来重新创建该函数。您尝试估计系数的函数是:

def hyperbolic_equation(t, qi, b, di):
    return qi/((1.0+b*di*t)**(1.0/b))

这里t是传递值，因此curve_fit的估计函数是:

def fitted_hyperbolic_equation(t):
    return popt_hyp[0]/((1.0+popt_hyp[1]*popt_hyp[2]*t)**(1.0/popt_hyp[1]))

然后使用此函数来预测新数据。