问题
I am trying to find the most valuable features by applying feature selection methods to my dataset. Im using the SelectKBest function for now. I can generate the score values and sort them as I want, but I don't understand exactly how this score value is calculated. I know that theoretically high score is more valuable, but I need a mathematical formula or an example to calculate the score for learning this deeply.
bestfeatures = SelectKBest(score_func=chi2, k=10)
fit = bestfeatures.fit(dataValues, dataTargetEncoded)
feat_importances = pd.Series(fit.scores_, index=dataValues.columns)
topFatures = feat_importances.nlargest(50).copy().index.values
print("TOP 50 Features (Best to worst) :\n")
print(topFatures)
Thank you in advance
回答1:
Say you have one feature and a target with 3 possible values
X = np.array([3.4, 3.4, 3. , 2.8, 2.7, 2.9, 3.3, 3. , 3.8, 2.5])
y = np.array([0, 0, 0, 1, 1, 1, 2, 2, 2, 2])
X y
0 3.4 0
1 3.4 0
2 3.0 0
3 2.8 1
4 2.7 1
5 2.9 1
6 3.3 2
7 3.0 2
8 3.8 2
9 2.5 2
First we binarize the target
y = LabelBinarizer().fit_transform(y)
X y1 y2 y3
0 3.4 1 0 0
1 3.4 1 0 0
2 3.0 1 0 0
3 2.8 0 1 0
4 2.7 0 1 0
5 2.9 0 1 0
6 3.3 0 0 1
7 3.0 0 0 1
8 3.8 0 0 1
9 2.5 0 0 1
Then perform a dot product between feature and target, i.e. sum all feature values by class value
observed = y.T.dot(X)
>>> observed
array([ 9.8, 8.4, 12.6])
Next take a sum of feature values and calculate class frequency
feature_count = X.sum(axis=0).reshape(1, -1)
class_prob = y.mean(axis=0).reshape(1, -1)
>>> class_prob, feature_count
(array([[0.3, 0.3, 0.4]]), array([[30.8]]))
Now as in the first step we take the dot product, and get expected and observed matrices
expected = np.dot(class_prob.T, feature_count)
>>> expected
array([[ 9.24],[ 9.24],[12.32]])
Finally we calculate a chi^2 value:
chi2 = ((observed.reshape(-1,1) - expected) ** 2 / expected).sum(axis=0)
>>> chi2
array([0.11666667])
We have a chi^2 value, now we need to judge how extreme it is. For that we use a chi^2 distribution with number of classes - 1 degrees of freedom and calculate the area from chi^2 to infinity to get the probability of chi^2 be the same or more extreme than we what we've got. This is a p-value. (using chi square survival function from scipy)
p = scipy.special.chdtrc(3 - 1, chi2)
>>> p
array([0.94333545])
Compare with SelectKBest:
s = SelectKBest(chi2, k=1)
s.fit(X.reshape(-1,1),y)
>>> s.scores_, s.pvalues_
(array([0.11666667]), [0.943335449873492])
来源：https://stackoverflow.com/questions/57273694/how-selectkbest-chi2-calculates-score