为了在逻辑回归中获取 Theta 的最优值，我使用了 optimize.minimize() 函数，我的函数 costFunction(X,y,theta) 根据给定的 X、y 和 theta 值返回成本和梯度。我已经用 theta 的初始值检查了我的函数 costFunction()，它运行正常。但是在 optimize.minimize() 中引用这个函数时，它报告了数值错误。
以下是我的 costFunction 代码以及我调用 optimize.minimize() 函数的地方：
def costFunction(X,y,theta): J = 0.0 m = Y.size J = -1/m * np.sum(((1-y)*np.log(1-sigmoid(np.dot(X,theta))))+((y)*np.log(sigmoid(np.dot(X,theta))))) grad = 1/m*np.dot(X.T,(sigmoid(np.dot(X,theta))-y)) return J, grad ```#To check the function :print(X[:,:3].shape)J,grad = costFunction(X[:,:3],Y,theta=[0,0,0])print(J)print( grad)#and this returns the following output:(1000, 3)0.6931471805599454[ 0. 17.25682 5.92721]#and here's where I call optimize.minimize() function:options = {'maxiter' : 400}initial_theta = np.zeros(3)x = X[:,:3]#res = optimize.minimize(computeCost,initial_theta,(X[:,:3],Y),jac = True,method = 'TNC',options = options)res = optimize.minimize(costFunction, initial_theta, (x, Y), jac=True, method='TNC', options=options)cost = res.funtheta = res.xprint("cost ".cost)print("theta ".theta)#and it returns the following error :ValueError Traceback (most recent call last)<ipython-input-69-55576d96c00a> in <module> 8 jac=True, 9 method='TNC',---> 10 options=options) 11 12 cost = res.fun~/anaconda3/lib/python3.7/site-packages/scipy/optimize/_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options) 604 elif meth == 'tnc': 605 return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,--> 606 **options) 607 elif meth == 'cobyla': 608 return _minimize_cobyla(fun, x0, args, constraints, **options)~/anaconda3/lib/python3.7/site-packages/scipy/optimize/tnc.py in _minimize_tnc(fun, x0, args, jac, bounds, eps, scale, offset, mesg_num, maxCGit, maxiter, eta, stepmx, accuracy, minfev, ftol, xtol, gtol, rescale, disp, callback, **unknown_options) 407 offset, messages, maxCGit, maxfun, 408 eta, stepmx, accuracy, fmin, ftol,--> 409 xtol, pgtol, rescale, callback) 410 411 funv, jacv = func_and_grad(x)~/anaconda3/lib/python3.7/site-packages/scipy/optimize/tnc.py in func_and_grad(x) 369 else: 370 def func_and_grad(x):--> 371 f = fun(x, *args) 372 g = jac(x, *args) 373 return f, g~/anaconda3/lib/python3.7/site-packages/scipy/optimize/optimize.py in __call__(self, x, *args) 61 def __call__(self, x, *args): 62 self.x = numpy.asarray(x).copy()---> 63 fg = self.fun(x, *args) 64 self.jac = fg[1] 65 return fg[0]<ipython-input-65-97115ec06e6e> in costFunction(X, y, theta) 2 J = 0.0 3 m = Y.size----> 4 J = -1/m * np.sum(((1-y)*np.log(1-sigmoid(np.dot(X,theta))))+((y)*np.log(sigmoid(np.dot(X,theta))))) 5 grad = 1/m*np.dot(X.T,(sigmoid(np.dot(X,theta))-y)) 6 return J, gradValueError: shapes (3,) and (1000,) not aligned: 3 (dim 0) != 1000 (dim 0)```回答：
看起来错误是由调用 optimizer.minimize() 时参数顺序引起的：
def costFunction(X,y,theta): J = 0.0 m = y.size print(y.shape) print(X.shape) print(theta.shape) J = -1/m * np.sum(((1-y)*np.log(1-sigmoid(np.dot(X,theta))))+((y)*np.log(sigmoid(np.dot(X,theta))))) grad = 1/m*np.dot(X.T, (sigmoid(np.dot(X, theta))-y)) return J, grad这将在明确测试和在 optimize.minimize() 中调用时打印不同的输出。原因是 scipy.optimize.minimize() 期望初始猜测 initial_theta 作为关键字参数，因此它必须在其他参数 x,Y 之前给出。由于您希望优化 theta，我建议您更改 costFunction() 中的参数顺序，并相应地更改 optimize.minimize() 的调用方式。以下是一个工作示例：
from scipy import optimizeimport numpy as npdef sigmoid(t): return 1./(1. + np.exp(t))X = np.random.random(size=(1000,3))Y = np.random.random(size=(1000))def costFunction(theta, x,y): J = 0.0 m = y.size J = -1/m * np.sum(((1-y)*np.log(1-sigmoid(np.dot(x,theta))))+((y)*np.log(sigmoid(np.dot(x,theta))))) grad = 1/m*np.dot(x.T, (sigmoid(np.dot(x, theta))-y)) return J, grad#To check the function :print(X[:,:3].shape)J,grad = costFunction(theta=np.asarray([0,0,0]), x=X[:,:3],y=Y)print(J)print( grad)options = {'maxiter' : 400}initial_theta = np.zeros(3)x = X[:,:3]res = optimize.minimize(costFunction, x0 = initial_theta, args=(x, Y), jac=True, method='TNC', options=options)cost = res.funthetaresult = res.xprint(cost)print(thetaresult)