如何在 PyPlot 中的分類箱線圖上繪制擬合曲線？ 為什么結果與 Google Sheets 中的同一個圖不同？

Question

我有以下 csv 數據：

Dataset Size,MAPE,MAE,STD MAPE,STD MAE
35000,0.0715392337,23.38300578,0.9078698348,2.80407539
26250,0.06893431034,22.34732326,0.9833948236,1.926517044
17500,0.0756695622,26.0900766,0.6055443674,8.842862631
8750,0.07176532526,23.02646184,0.8284005282,2.190506033
4200,0.08661127364,29.89234607,0.9395831421,7.587818412
2100,0.08072315267,27.20110884,0.03956974712,4.948606892
1050,0.07505202908,27.04025924,0.841966778,4.550482956
700,0.07703248113,26.17923045,0.4468447145,1.523638508
350,0.08695408769,32.35331585,0.7891190087,4.18648457
200,0.09770903032,30.96197823,0.04648972591,3.892800694
170,0.1202382169,41.87828814,0.7257680584,6.70453713
150,0.1960949784,77.20321559,0.5661066006,21.57418682

根據上述數據，我想使用 matplotlib 或類似（seaborn、pandas 等）生成以下圖：

from pathlib import Path
from matplotlib import animation
import seaborn as sns
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy.optimize import curve_fit

nr_datapoints = 10
def exponenial_func(x, a, b, c):
    return a*np.exp(-b*x)+c
def myplot(data_file):
    df = pd.read_csv(data_file)
    print(df.head())

    fig, ax = plt.subplots()

    # Exponential line fit
    popt, pcov = curve_fit(exponenial_func, np.array([float(i) for i in range(len(df['Dataset Size']))]), df['MAPE'], p0=(0, 0.0145, 0.0823))
    xp = np.linspace(0,len(df['Dataset Size']), 100)  
    plt.plot(xp, exponenial_func(xp, *popt), color = 'g')
    # barplote with error bars
    ax.bar([str(s) for s in df['Dataset Size']], df['MAPE'], yerr=df['STD MAPE'])
    plt.title('Accuracy of Model vs. Dataset Size')
    plt.xlabel('Dataset Size')
    plt.ylabel('Mean Absolute Percentage Error')
    fig.tight_layout()
    plt.show()

我得到的情節如下：

盡管對數據擬合了指數函數，為什么我的代碼最終得到一條線而不是一條曲線？ （鑒於谷歌表格圖做同樣的事情，例如擬合數據的指數曲線）

Answer 1

嘗試了一些函數，我想我可以肯定地說，Google Sheets 指數函數的形式與此接近：

def sheetey_exponential_function(x, a, b, c):
    return a * b ** (x + c)

Answer 2

問題是水平軸不是線性的。 實際上它是逆線性的。 所以，如果你想你適合看起來像一個指數函數，你需要更換x與1/x ：

def exponenial_func(x, a, b, c):
    return a*np.exp(-b/x)+c

結果如下：