How to write a custom estimator in sklearn and use cross-validation on it?

The answer also lies in sklearn’s documentation.

You need to define two things:

• an estimator that implements the fit(X, y) function, X being the matrix with inputs and y being the vector of outputs

• a scorer function, or callable object that can be used with: scorer(estimator, X, y) and returns the score of given model

Referring to your example: first of all, scorer shouldn’t be a method of the estimator, it’s a different notion. Just create a callable:

def scorer(estimator, X, y)
    return ?????  # compute whatever you want, it's up to you to define
                  # what does it mean that the given estimator is "good" or "bad"

Or even a more simple solution: you can pass a string 'mean_squared_error' or 'accuracy' (full list available in this part of the documentation) to cross_val_score function to use a predefined scorer.

Another possibility is to use make_scorer factory function.

As for the second thing, you can pass parameters to your model through the fit_params dict parameter of the cross_val_score function (as mentioned in the documentation). These parameters will be passed to the fit function.

class my_estimator():
    def fit(X, y, **kwargs):
        alpha = kwargs['alpha']
        beta=X[1,:]+alpha 
        return beta

After reading all the error messages, which provide quite clear idea of what’s missing, here is a simple example:

import numpy as np
from sklearn.cross_validation import cross_val_score

class RegularizedRegressor:
    def __init__(self, l = 0.01):
        self.l = l

    def combine(self, inputs):
        return sum([i*w for (i,w) in zip([1] + inputs, self.weights)])

    def predict(self, X):
        return [self.combine(x) for x in X]

    def classify(self, inputs):
        return sign(self.predict(inputs))

    def fit(self, X, y, **kwargs):
        self.l = kwargs['l']
        X = np.matrix(X)
        y = np.matrix(y)
        W = (X.transpose() * X).getI() * X.transpose() * y

        self.weights = [w[0] for w in W.tolist()]

    def get_params(self, deep = False):
        return {'l':self.l}

X = np.matrix([[0, 0], [1, 0], [0, 1], [1, 1]])
y = np.matrix([0, 1, 1, 0]).transpose()

print cross_val_score(RegularizedRegressor(),
                      X,
                      y, 
                      fit_params={'l':0.1},
                      scoring = 'mean_squared_error')