Why does Lime need training data to compute local explanations

Question

I am using Lime to compute local explanation, however I do not understand why do I have to pass training data X_train in the below line of code

explainer = lime_tabular.LimeTabularExplainer(X_train, mode="regression", feature_names= boston.feature_names)

Below is an excerpt around how Lime operates from this great book named Interpretable Machine Learning by Christoph Molnar around XAI -

The recipe for training local surrogate models:

• Select your instance of interest for which you want to have an explanation of its black box prediction.
• Perturb your dataset and get the black box predictions for these new points.
• Weight the new samples according to their proximity to the instance of interest.
• Train a weighted, interpretable model on the dataset with the variations.
• Explain the prediction by interpreting the local model.

If I understand correctly, Lime trains a weighted interpretable model for each instance of interest by sampling points from its neighbourhood. The weights assigned to the features in this model serve as the local explanation for that particular instance. And this is exactly what we do in the below lines of code -

exp = explainer.explain_instance(X_test.values[3], model.predict, num_features=6)

We pass an instance, using this instance it would compute the neighbours for which it would fit an interpretable model. So why did we pass X_train in the first line of code? How would Lime make use of it is what I don't understand.

Answer 1

LIME uses X_train to extract training data statistics and then, based on the LimeTabularExplainer initialization parameters, will use these statistics in different operations during its data sampling step.

For example, for continuous features it uses the extracted data statistics by sampling from a Normal distribution ~N(μ,σ) with σ the data standard deviation and μ either the data mean or the instance itself depending on the sample_around_instance argument.

Another example is the discretization of continuous features by LIME. The discretizers e.g. quartile, percentile etc. are based on these input training data in order for the discretization to be "data-aware".

The sampled instances are the ones that will be used on LIME's next steps and on these samples will be trained the final explanation model.