Scipy 中的差异进化与数据

Question

我有两个数据框（df_1、df_2）：

df_1 = pd.DataFrame({'O' : [1,2,3], 'M' : [2,8,3]})

df_2 = pd.DataFrame({'O' : [1,1,1, 2,2,2, 3,3,3],
                     'M' : [9,2,4, 6,7,8, 5,3,4],
                     'X' : [2,4,6, 4,8,7, 3,1,9],
                     'Y' : [3,6,1, 4,6,5, 1,0,7],
                     'Z' : [2,4,8, 3,5,4, 7,5,1]})

还有一个功能（好玩）：

# Index
df_1 = df_1.set_index('O')
df_1_M = df_1.M
df_1_M = df_1_M.sort_index()

# Fun
def fun(z, *params):
    A,B,C = z
        
    # Score
    df_2['S'] = df_2['X']*A + df_2['Y']*B + df_2['Z']*C
    
    # Top score
    df_Sort = df_2.sort_values(['S', 'X', 'M'], ascending=[False, True, True])
    df_O    = df_Sort.set_index('O')
    M_Top   = df_O[~df_O.index.duplicated(keep='first')].M
    M_Top   = M_Top.sort_index()
        
    # Compare the top scoring row for each O to df_1
    df_1_R = df_1_M.reindex(M_Top.index) # Nan
    T_N_T  = M_Top == df_1_R

    # Record the results for the given values of A,B,C
    df_Res = pd.DataFrame({'it_is':T_N_T}) # is this row of df_1 the same as this row of M_Top?
        
    # p_hat =         TP / (TP + FP)
    p_hat = df_Res.sum() / len(df_Res.index)
        
    return -p_hat

我可以使用蛮力对其进行优化：

from scipy.optimize import brute

# Range
min_ = -2
max_ = 2
step = .5
ran_ge = slice(min_, max_+step, step)
ranges = (ran_ge,ran_ge,ran_ge)

# Params
params = (df_1, df_2)

# Brute
resbrute = brute(fun,ranges,args=params,full_output=True,finish=None)

print('Global maximum ',                   resbrute[0])
print('Function value at global maximum ',-resbrute[1])

这给出了：

Global maximum  [-2.   0.5  1.5]
Function value at global maximum  0.6666666666666666

但是当维度和分辨率增加时，这需要很长时间。为了节省时间，我想通过差分进化（DE）来优化它。我试过了：

from scipy.optimize import differential_evolution

# Bounds
min_ = -2
max_ = 2
ran_ge = (min_, max_)
bounds = [ran_ge,ran_ge,ran_ge]

# Params
params = (df_1, df_2)

# DE
DE = differential_evolution(fun,bounds,args=params)

但我得到了：

ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or a.all().

任何想法为什么它通过蛮力而不是通过差异进化起作用？如何通过差异进化使其工作？

Answer 1

看代码，fun(z, *params)函数返回一个序列，differential_evolution不知道怎么处理。

# pandas.core.series.Series
type(p_hat)

将fun(z, *params)的返回值改为：

return -p_hat[0]

我们得到正确答案：

# Function value at global maximum  0.6666666666666666
print('Function value at global maximum ',-DE.fun)

代码修复：

import pandas as pd

df_1 = pd.DataFrame({'O' : [1,2,3], 'M' : [2,8,3]})

df_2 = pd.DataFrame({'O' : [1,1,1, 2,2,2, 3,3,3],
                     'M' : [9,2,4, 6,7,8, 5,3,4],
                     'X' : [2,4,6, 4,8,7, 3,1,9],
                     'Y' : [3,6,1, 4,6,5, 1,0,7],
                     'Z' : [2,4,8, 3,5,4, 7,5,1]})

# Index
df_1 = df_1.set_index('O')
df_1_M = df_1.M
df_1_M = df_1_M.sort_index()


# Fun
def fun(z, *params):
    A, B, C = z

    # Score
    df_2['S'] = df_2['X'] * A + df_2['Y'] * B + df_2['Z'] * C

    # Top score
    df_Sort = df_2.sort_values(['S', 'X', 'M'], ascending=[False, True, True])
    df_O = df_Sort.set_index('O')
    M_Top = df_O[~df_O.index.duplicated(keep='first')].M
    M_Top = M_Top.sort_index()

    # Compare the top scoring row for each O to df_1
    df_1_R = df_1_M.reindex(M_Top.index)  # Nan
    T_N_T = M_Top == df_1_R

    # Record the results for the given values of A,B,C
    df_Res = pd.DataFrame({'it_is': T_N_T})  # is this row of df_1 the same as this row of M_Top?

    # p_hat =         TP / (TP + FP)
    p_hat = df_Res.sum() / len(df_Res.index)

    return -p_hat[0]

from scipy.optimize import differential_evolution

# Bounds
min_ = -2
max_ = 2
ran_ge = (min_, max_)
bounds = [ran_ge,ran_ge,ran_ge]

# Params
params = (df_1, df_2)

# DE
DE = differential_evolution(fun,bounds,args=params)

print('Function value at global maximum ',-DE.fun)