使用数据优化 Pandas 中的阶跃函数

Question

我有两个数据框 (df_1 & df_2) 和一些变量 (A,B,C):

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]})

我在下面有一个算法，它使用 A、B、C 来计算 df_2 中每一行的分数 (S)。它在 df_2 中找到得分最高 (S) 的行。它将 df_2 中得分最高的行与 df_1 进行比较，并计算 p_hat，这是衡量它们之间相似性的一种方法：

M_G = df_1.M
df_1 = df_1.set_index('O')
        
A = 1
B = 1
C = 1
 
# 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_M = df_1.M
df_1_M = df_1_M.sort_index()
df_1_R = df_1_M.reindex(M_Top.index)
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)

对于示例中 A、B、C 的值，它给出 p_hat = 0.333。我想找到 A、B、C 的值，它们给出 p_hat 的最大可能值。我想使用优化算法来确保我得到最大值。

图表适用于 C=2:

请问我怎样才能找到最大值p_hat？

Answer 1

我猜你可以使用 Optuna 包，它非常容易使用。您定义一个 objective 函数，在该函数中您可以以任何您想要的方式计算要优化的变量，为其创建一个 study 对象，Optuna 基本上完成其余的工作。

一个简单的二维函数的小例子：

import optuna

def optimize_me(trial):
    x = trial.suggest_uniform('x', -10, 10)
    y = trial.suggest_uniform('y', -10, 10)
    return ((y - 1) ** 2) + ((x + 2) ** 2)

study = optuna.create_study()
study.optimize(optimize_me, n_trials = 10)

您可以阅读有关 Optuna 的更多信息here

我主要用它来优化 RNN 的超参数，这是一个非常强大的包。

Answer 2

我找到了一种使用全局暴力优化的方法：

from scipy.optimize import brute

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]})



# 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)

# 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

# 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])

它给出：

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

Answer 3

或使用全局进化优化：（由@Aviv Yaniv 修复的代码）

from scipy.optimize import differential_evolution

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)
    
    print(z)
    return -p_hat[0]

# 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)

使用数据优化 Pandas 中的阶跃函数

Optimise a step function in Pandas using data

python

optimization

linear-algebra

pandas

scipy-optimize