如何在python中为多维数据实现非线性最小二乘法？

Question

I have to implement least square fitting algorithm for this model function

Y = a_0 * e^(a_1*x_1+a_2*x_2+...+a_n*x_n)

The approach I found was to define function to calculate residuals and pass it to scipy.optimize.leastsq or lmfit. Yet i cannot make it to work with multidimensional data, when parameters are vector and not single values.

def residual(variables,X,y):
    a_0 = variables[0]
    a = variables[1]

    return (y - a_0 * np.exp(X.dot(a)))**2

X = np.random.randn(100,5)
y = np.random.randint(low=0,high=2,size=100)
a_0 = 1
a = np.random.randn(X.shape[1])

leastsq(residual,[a_0,a],args=(X,y))

I get this error.

ValueError: setting an array element with a sequence.

Can you point me the right course of action from here?

Answer 1

I think something like this should do the job :

def residual(variables,X,y):
    a_0 = variables[0]
    a = variables[1:]

    return (y - a_0 * np.exp(X.dot(a)))**2

X = np.random.randn(100,5)
y = np.random.randint(low=0,high=2,size=100)
a = np.random.randn(X.shape[1]+1)
a[0] = 1

res = scipy.optimize.leastsq(residual,a,args=(X,y))

Regards