python - 使用 Scipy.opt 进行 Andrew NG Logistic 回归中的形状误差

Question

我一直在尝试使用 python 和 Scipy.opt 编写 Andrew NG 的逻辑回归问题来优化函数。但是，我收到一个值错误，提示我的尺寸不匹配。我尝试将我的 theta 数组展平()，因为 scipy.opt 似乎不能很好地处理单列/行向量，但问题仍然存在。

请指出导致问题的原因以及如何避免问题的正确方向。

感谢一百万!

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as opt

dataset = pd.read_csv("Students Exam Dataset.txt", names=["Exam 1", "Exam 2", "Admitted"])
print(dataset.head())

positive = dataset[dataset["Admitted"] == 1]
negative = dataset[dataset["Admitted"] == 0]

#Visualizing Dataset
plt.scatter(positive["Exam 1"], positive["Exam 2"], color="blue", marker="o", label="Admitted")
plt.scatter(negative["Exam 1"], negative["Exam 2"], color="red", marker="x", label="Not Admitted")
plt.xlabel("Exam 1 Score")
plt.ylabel("Exam 2 Score")
plt.title("Admission Graph")
plt.legend()
#plt.show()

#Preprocessing Data
dataset.insert(0, "x0", 1)
col = len(dataset.columns)
x = dataset.iloc[:,0:col-1].values
y = dataset.iloc[:,col-1:col].values
b = np.zeros([1,col-1])
m = len(y)
print(f"X Shape: {x.shape}   Y Shape: {y.shape}   B Shape: {b.shape}")

#Defining Functions
def hypothesis(x, y, b):
    h = 1 / (1+np.exp(-x @ b.T))
    return h

def cost(x, y, b):
    first = (y.T @ np.log(hypothesis(x, y, b)))
    second = (1-y).T @ np.log(1 - hypothesis(x, y, b))
    j = (-1/m) * np.sum(first+second)
    return j

def gradient(x, y, b):
    grad_step = ((hypothesis(x, y, b) - y) @ x.T) / m
    return b

#Output
initial_cost = cost(x, y, b)
print(f"\nInitial Cost = {initial_cost}")
final_cost = opt.fmin_tnc(func=cost, x0=b.flatten() , fprime=gradient, args=(x,y))
print(f"Final Cost = {final_cost} \nTheta = {b}")

使用的数据集:ex2.txt

34.62365962451697,78.0246928153624,0
30.28671076822607,43.89499752400101,0
35.84740876993872,72.90219802708364,0
60.18259938620976,86.30855209546826,1
79.0327360507101,75.3443764369103,1
45.08327747668339,56.3163717815305,0
61.10666453684766,96.51142588489624,1
75.02474556738889,46.55401354116538,1
76.09878670226257,87.42056971926803,1
84.43281996120035,43.53339331072109,1
95.86155507093572,38.22527805795094,0
75.01365838958247,30.60326323428011,0
82.30705337399482,76.48196330235604,1
69.36458875970939,97.71869196188608,1
39.53833914367223,76.03681085115882,0
53.9710521485623,89.20735013750205,1
69.07014406283025,52.74046973016765,1
67.94685547711617,46.67857410673128,0
70.66150955499435,92.92713789364831,1
76.97878372747498,47.57596364975532,1
67.37202754570876,42.83843832029179,0
89.67677575072079,65.79936592745237,1
50.534788289883,48.85581152764205,0
34.21206097786789,44.20952859866288,0
77.9240914545704,68.9723599933059,1
62.27101367004632,69.95445795447587,1
80.1901807509566,44.82162893218353,1
93.114388797442,38.80067033713209,0
61.83020602312595,50.25610789244621,0
38.78580379679423,64.99568095539578,0
61.379289447425,72.80788731317097,1
85.40451939411645,57.05198397627122,1
52.10797973193984,63.12762376881715,0
52.04540476831827,69.43286012045222,1
40.23689373545111,71.16774802184875,0
54.63510555424817,52.21388588061123,0
33.91550010906887,98.86943574220611,0
64.17698887494485,80.90806058670817,1
74.78925295941542,41.57341522824434,0
34.1836400264419,75.2377203360134,0
83.90239366249155,56.30804621605327,1
51.54772026906181,46.85629026349976,0
94.44336776917852,65.56892160559052,1
82.36875375713919,40.61825515970618,0
51.04775177128865,45.82270145776001,0
62.22267576120188,52.06099194836679,0
77.19303492601364,70.45820000180959,1
97.77159928000232,86.7278223300282,1
62.07306379667647,96.76882412413983,1
91.56497449807442,88.69629254546599,1
79.94481794066932,74.16311935043758,1
99.2725269292572,60.99903099844988,1
90.54671411399852,43.39060180650027,1
34.52451385320009,60.39634245837173,0
50.2864961189907,49.80453881323059,0
49.58667721632031,59.80895099453265,0
97.64563396007767,68.86157272420604,1
32.57720016809309,95.59854761387875,0
74.24869136721598,69.82457122657193,1
71.79646205863379,78.45356224515052,1
75.3956114656803,85.75993667331619,1
35.28611281526193,47.02051394723416,0
56.25381749711624,39.26147251058019,0
30.05882244669796,49.59297386723685,0
44.66826172480893,66.45008614558913,0
66.56089447242954,41.09209807936973,0
40.45755098375164,97.53518548909936,1
49.07256321908844,51.88321182073966,0
80.27957401466998,92.11606081344084,1
66.74671856944039,60.99139402740988,1
32.72283304060323,43.30717306430063,0
64.0393204150601,78.03168802018232,1
72.34649422579923,96.22759296761404,1
60.45788573918959,73.09499809758037,1
58.84095621726802,75.85844831279042,1
99.82785779692128,72.36925193383885,1
47.26426910848174,88.47586499559782,1
50.45815980285988,75.80985952982456,1
60.45555629271532,42.50840943572217,0
82.22666157785568,42.71987853716458,0
88.9138964166533,69.80378889835472,1
94.83450672430196,45.69430680250754,1
67.31925746917527,66.58935317747915,1
57.23870631569862,59.51428198012956,1
80.36675600171273,90.96014789746954,1
68.46852178591112,85.59430710452014,1
42.0754545384731,78.84478600148043,0
75.47770200533905,90.42453899753964,1
78.63542434898018,96.64742716885644,1
52.34800398794107,60.76950525602592,0
94.09433112516793,77.15910509073893,1
90.44855097096364,87.50879176484702,1
55.48216114069585,35.57070347228866,0
74.49269241843041,84.84513684930135,1
89.84580670720979,45.35828361091658,1
83.48916274498238,48.38028579728175,1
42.2617008099817,87.10385094025457,1
99.31500880510394,68.77540947206617,1
55.34001756003703,64.9319380069486,1
74.77589300092767,89.52981289513276,1

Answer 1

好的!所以我在Github的深处搜索后自己找到了答案。值错误与数组的形状无关。首先，我必须将优化函数修改为:

from scipy.optimize import minimize
results = minimize(cost, b, args = (x,y),
                   method = 'CG', jac = compute_gradient, 
                   options = {"maxiter": 400, "disp" : True})

代码仍然无法工作，因为我的函数的参数的顺序是 (X,y,theta)。为了使函数正常工作，我必须将参数的顺序更改为 (theta, X, y)。这让我想知道这个顺序是否重要。因此，我将此更改应用到我的函数中，优化立即生效!

回想起来，我明白为什么 theta 必须是传递到成本和梯度函数的第一个参数。这是因为 scipy.optimize 中最小化函数的接口(interface)期望其 x0 参数是初始猜测，即。初始化的参数值。