LIME is a recent method that claims to help explaining individual predictions from classifiers agnostically. See e.g. arxiv or its implementation on github for details.
I am trying to understand what exactly it outputs. For that, I am using a trivial example: logistic regression.
Consider the following set of events:
data =  for t in range(100000): a = 1 - 2*numpy.random.random() # U(-1, 1) b = 1 - 2*numpy.random.random() # U(-1, 1) noise = numpy.random.logistic() c = int(a + b + noise > 0) # the target data.append([a, b, c]) data = numpy.array(data) x = data[:, :-1] y = data[:, -1]
This is a latent logistic process with parameters $a_0 = 0$, $a_1 = a_2 = 1$, of which logistic regression assymptotically fits.
Let us fit the data using logistic regression:
classifier = sklearn.linear_model.LogisticRegression(C=1e10) # C=inf => no regularization classifier.fit(x, y) print(classifier.coef_) # [[ 0.99092809 1.00551462]]
Now, lets apply LIME to it:
explainer = lime.lime_tabular.LimeTabularExplainer(x, feature_names=['a', 'b']) instance = numpy.array([1, 1]) explanation = explainer.explain_instance(instance, classifier.predict_proba, num_samples=100000) print(explanation.as_list())
The result I get is something like this:
[ ('a > 0.50', 0.2216), ('b > 0.50', 0.2170) ]
the question is: what is this supposed to mean?
In the code implementaion repo you linked there's an example code which claims that explains, see cell 8
Note that LIME has discretized the features in the explanation. This is because we let discretize_continuous=True in the constructor (this is the default).
If you modify the constructor to
explainer = lime.lime_tabular.LimeTabularExplainer(x, feature_names=['a', 'b'],discretize_continuous=False)
then the output is something like
[('b', 0.11223168027269199), ('a', 0.11110292313683988)]
I understood that both instances – discretized or not – are supposed to approximate a linear model in the vicinity of the feature example [1,1].
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