R optim vs.Scipy Minim公司

Question

我正在尝试用Python重新实现以下代码： http://www.wordfish.org/uploads/1/2/9/8/12985397/wordfish_1.3.r

然而，我正在努力移植优化（最大化）函数。 我设计了一个代码片段，并做了两个简单的例子，结果应该是一样的：

右侧：

omega = c(0)
y = c(18, 24, 23, 27, 24, 5, 7, 5, 4, 7, 64, 59, 66, 51, 50, 11, 17, 9, 13, 16)
b = c(-0.5047485, -0.6346391, -0.375262, -0.4550382, -0.4839501, 0.3181721, 0.4557756, 0.5618271, 0.3847818, 0.485241, -0.4500023, -0.4224367, -0.461969, -0.5605062, -0.4635604, 0.4995454, 0.5027968, 0.5656253, 0.5506545, 0.5368292 )
psi = c(2.653242, 2.687847, 2.564949, 2.61007, 2.694627, 2.533697, 2.60269, 2.564949, 2.60269, 2.631889, 3.65584, 3.632309, 3.591818, 3.572346, 3.605498, 3.580737, 3.54674, 3.569533, 3.624341, 3.538057)

llik_alpha_1 <- function(y,p,b,psi) { 
        omega <- p[1]
        lambda<-exp(psi+b*omega)     
        -sum(-lambda+log(lambda)*y)
    }

resa <- optim(p=omega,
              fn=llik_alpha_1,                        
              y=y,
              b=b,
              psi=psi,
              method=c("BFGS")
              )
resa

llik_alpha_1(y,omega,b,psi)

R的结果：

^{pr2}$

Python：

omega = np.array([0])
y = np.array([18, 24, 23, 27, 24, 5, 7, 5, 4, 7, 64, 59, 66, 51, 50, 11, 17, 9, 13, 16])
b = np.array([-0.5047485, -0.6346391, -0.375262, -0.4550382, -0.4839501, 0.3181721, 0.4557756, 0.5618271, 0.3847818, 0.485241, -0.4500023, -0.4224367, -0.461969, -0.5605062, -0.4635604, 0.4995454, 0.5027968, 0.5656253, 0.5506545, 0.5368292])
psi = np.array([2.653242, 2.687847, 2.564949, 2.61007, 2.694627, 2.533697, 2.60269, 2.564949, 2.60269, 2.631889, 3.65584, 3.632309, 3.591818, 3.572346, 3.605498, 3.580737, 3.54674, 3.569533, 3.624341, 3.538057])

def llik_alpha_1(y,p,b,psi):
    omega = p
    lambda_1 = np.exp(psi+b*omega)
    return -np.sum(-lambda_1+np.log(lambda_1)*y)

resa = minimize(fun=llik_alpha_1,
                args=(omega, b, psi),
                x0 = y,
                method='BFGS'
                )
print(resa)
llik_alpha_1(y, omega, b, psi)

Python的结果：

fun: -1269762128.486976
 hess_inv: array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])
      jac: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
       0., 0., 0.])
  message: 'Optimization terminated successfully.'
     nfev: 330
      nit: 1
     njev: 15
   status: 0
  success: True
        x: array([17066136.98700089, 17288740.69846503, 16498164.49306662,
       16788487.73050529, 17332318.02822256, 16297239.29934215,
       16740964.51518402, 16498244.64020571, 16740961.51518402,
       16928818.13940904, 23515038.90828061, 23363691.01979838,
       23103313.65978324, 22978062.91029989, 23191237.49641104,
       23032003.83680133, 22813239.86376185, 22959863.68956758,
       23312412.21319156, 22757393.14161763])
-1162.2877807382822

如您所见，两个优化函数都返回-1162.28778073828，但优化器的结果完全不同。在

• R： -1249.36539272541
• Python：-1269762128.486976

有人能解释一下我错在哪里吗？我想Python中的优化与R中的不同，但我不是专家。。。在

谢谢，并致以最诚挚的问候！在

迈克尔

编辑//解决方案： 万一有人感兴趣，我发现了我的错误 以下Python代码返回相同的结果：

omega = np.array([0])
y = np.array([18, 24, 23, 27, 24, 5, 7, 5, 4, 7, 64, 59, 66, 51, 50, 11, 17, 9, 13, 16])
b = np.array([-0.5047485, -0.6346391, -0.375262, -0.4550382, -0.4839501, 0.3181721, 0.4557756, 0.5618271, 0.3847818, 0.485241, -0.4500023, -0.4224367, -0.461969, -0.5605062, -0.4635604, 0.4995454, 0.5027968, 0.5656253, 0.5506545, 0.5368292])
psi = np.array([2.653242, 2.687847, 2.564949, 2.61007, 2.694627, 2.533697, 2.60269, 2.564949, 2.60269, 2.631889, 3.65584, 3.632309, 3.591818, 3.572346, 3.605498, 3.580737, 3.54674, 3.569533, 3.624341, 3.538057])

def llik_alpha_1(p,y,b,psi):
    lambda_1 = np.exp(psi+b*p)
    return -np.sum(-lambda_1+np.log(lambda_1)*y)

resa = minimize(fun=llik_alpha_1,
                args=(y, b, psi),
                x0 = omega,
                method='BFGS'
                )
print(resa)
llik_alpha_1(omega, y, b, psi)

问题是，我混淆了变量（ω和y）。x0是要优化的参数，在我的例子中是omega而不是y