如何使用 Symfit 或 curve_fit 对分段模型执行交叉验证？

问题描述

我正在尝试使用 Symfit 对分段模型执行交叉验证：

我的数据：

x_data = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],dtype=float)
y_data = np.array([1,10])

要使用交叉验证，我们需要创建一个估算器，所以我尝试将拟合打包在一个类中

from sklearn.model_selection import cross_validate,cross_val_score
class model:
    def __init__( self,a=None,b=None,c=None ):
        self.a = a
        self.b = b
        self.c = c 
        
    def _model_background(self,X,a,b,c):
        y1 = a*x + b-a*c
        y2 = b
        return Model({y: Piecewise((y1,x <= c),(y2,x > c))})

    def predict( self,X ):
        return self._model_background( X,self.a,self.b,self.c ) 

    def fit( self,y ):
        from symfit import parameters,variables,Fit,Piecewise,Model
        fit = Fit(self._model_background,x=x_data,y=y_data)
        fit_result = fit.execute()
        self.a = fit_result.value(a)
        self.b = fit_result.value(b)
        self.c = fit_result.value(c)
        return self

    def get_params( self,deep=False ):
        return { 'a':self.a,'b':self.b,'c':self.c }

    def set_params( self,**parameters ):
        for parameter,value in parameters.intems():
            setattr( self,parameter,value )
        return self

然后我执行交叉验证行

cross_validate( symfitmodel(),x_data,y_data,cv=5,scoring='neg_mean_squared_error' )

但似乎我没有按照应有的方式创建类错误信息：

C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py:548: FitFailedWarning: Estimator fit Failed. The score on this train-test partition for these parameters will be set to nan. Details: 
Traceback (most recent call last):
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\support.py",line 282,in __get__
    return getattr(obj,self.cache_attr)
AttributeError: 'Model' object has no attribute '_cached_connectivity_mapping'

During handling of the above exception,another exception occurred:
Traceback (most recent call last):
  File "C:\ProgramData\Anaconda3\lib\site-packages\sklearn\model_selection\_validation.py",line 531,in _fit_and_score
    estimator.fit(X_train,y_train,**fit_params)
  File "<ipython-input-3-db68eb82746d>",line 18,in fit
    fit = Fit(self._model_background,y=y_data)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\support.py",line 423,in wrapped_func
    return func(*bound_args.args,**bound_args.kwargs)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\fit.py",line 374,in __init__
    self.model = Model(model)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\models.py",line 875,in __init__
    super(HessianModel,self).__init__(*args,**kwargs)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\models.py",line 824,in __init__
    super(GradientModel,line 125,in __init__
    self._init_from_dict(model)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\models.py",line 651,in _init_from_dict
    super(BaseCallableModel,self)._init_from_dict(model_dict)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\models.py",line 309,in _init_from_dict
    ordered = list(toposort(self.connectivity_mapping))
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\support.py",line 285,in __get__
    setattr(obj,self.cache_attr,self.fget(obj))
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\models.py",line 383,in connectivity_mapping
    vars,params = seperate_symbols(expr)
  File "C:\ProgramData\Anaconda3\lib\site-packages\symfit\core\support.py",line 82,in seperate_symbols
    for symbol in func.free_symbols:
AttributeError: 'function' object has no attribute 'free_symbols'

  warnings.warn("Estimator fit Failed. The score on this train-test"

我用curve_fit尝试过，但没有成功：

class piecewise:    
    def __init__( self,x0=None,b=None ):
        self.x0 = x0
        self.a = a
        self.b = b 
        
    def _piecewise_background(self,x0,b):
        return np.piecewise(X,[X < x0],[lambda X:a*X + b-a*x0,lambda X:b])

    def predict( self,X ):
        return self._piecewise_background( X,self.x0,self.b ) 

    def fit( self,y ):
        from scipy.optimize import curve_fit
        popt,pcov = curve_fit( self._piecewise_background,y ) 
        self.x0 = popt[0]
        self.a = popt[1]
        self.b = popt[2]
        return self

    def get_params( self,deep=False ):
        return { 'x0':self.x0,'a':self.a,'b':self.b }

    def set_params( self,value )
        return self

有什么想法吗？

解决方法

这不是回答而是评论。

论文中显示了一种直接方法（非迭代，没有猜测的初始值）：https://fr.scribd.com/document/380941024/Regression-par-morceaux-Piecewise-Regression-pdf（本例中的第 8 页）。

当然，问题中给出的数据很少有人感兴趣，因为没有散点。所以不需要数值演算，结果是显而易见的。但这可以用来测试分段回归的方法。

散点数据示例

为了更具有代表性，以上数据进行了分散。下面的例子：

cross-validation curve-fitting piecewise python symfit