Group Importances

In this notebook we show how to compute and interpret Overall Importances shown in InterpretML’s Global Explanations for EBMs. We also show how to compute importances of a group of features or terms.

Throughout the notebook we use term to denote both single features and interactions (pairs).

This notebook can be found in our examples folder on GitHub.

# install interpret if not already installed
try:
    import interpret
except ModuleNotFoundError:
    !pip install --quiet interpret pandas scikit-learn

Train an Explainable Boosting Machine (EBM) for a regression task

Let’s use the Boston dataset as a reference and train an EBM.

import numpy as np
import pandas as pd
from sklearn.datasets import load_diabetes
from interpret.glassbox import ExplainableBoostingRegressor

from interpret import set_visualize_provider
from interpret.provider import InlineProvider
set_visualize_provider(InlineProvider())

X, y = load_diabetes(return_X_y=True, as_frame=True)

ebm = ExplainableBoostingRegressor()
ebm.fit(X, y) 

ExplainableBoostingRegressor()

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Explain the Model

EBMs provide two different kinds of explanations: global explanations about the overall model behavior and local explanations about individual predictions from the model.

Global Explanation

Global Explanations are useful for understanding what a model finds important, as well as identifying potential flaws in its decision making or the training data. Let’s start by computing and displaying a global explanation:

from interpret import show
show(ebm.explain_global(name='EBM'))

The overall importance for each term is calculated as the average absolute contribution (score) a term (feature or pair) makes when predicting across the training dataset. This way of measuring term importance tends to favor terms which, on average, have large impact on predictions for many cases. The overall importance is not a measure of positive/negative – it is a measure of how important each term is in the scores. For regression, these scores are represented in the same units as the y-axis of the feature graphs. For classification, the scores would be in logits.

Going beyond overall term importances, because EBMs are additive models we can measure exactly how each term contributes to a prediction. Let’s take a look at the graph of the term, bp, by selecting it in the drop-down menu.

The way to interpret this is that if a new datapoint came in with bp = 0.1, the model adds about +33.1 to the final prediction. However, for a different datapoint with bp = 0.13, the model would now add approx. +36.7 to the prediction.

To make individual predictions, the model uses each term graph as a look up table, notes the contribution per term, and sums them together with the learned intercept to make a prediction. In regression, the intercept is the mean target (label) of the training set, and each term adds or subtracts to this mean. In classification, the intercept reflects the base rate of the positive class on a log scale. The gray above and below the graph shows the confidence of the model in that region of the graph.

Local Explanations

We can see the full breakdown of a prediction on a single sample with Local Explanations. Here’s how to compute the prediction breakdown for the first sample in our dataset:

from interpret import show
show(ebm.explain_local(X[:1], y[:1]), 0)

Let’s take a look at the prediction by selecting it in the drop-down menu.

The model prediction is 188.50. We can see that the intercept adds about +151.9, bp subtracts about 0.02, and age adds about 0.04. If we repeat this process for all the terms, we’ll arrive exactly at the model prediction of 188.50.

Viewing _all_ term importances

Due to space limitations in our graphs, the term importance summary only shows the top 15 terms. To view the overall importances of all terms of a trained EBM - the scores shown in the global explanation summary - we use term_importances():

importances = ebm.term_importances()
names = ebm.term_names_

for (term_name, importance) in zip(names, importances):
    print(f"Term {term_name} importance: {importance}")

Term age importance: 3.0428552990102853
Term sex importance: 10.361753402090136
Term bmi importance: 17.13419899366742
Term bp importance: 11.092578184688723
Term s1 importance: 1.3990182998139018
Term s2 importance: 3.131865292809736
Term s3 importance: 7.299987001298233
Term s4 importance: 6.0684231433566636
Term s5 importance: 16.839020450540122
Term s6 importance: 5.201952347510865
Term age & bp importance: 0.6591890660196494
Term age & s5 importance: 0.8364681711272833
Term bmi & bp importance: 0.601965132735232
Term bmi & s2 importance: 0.43002785599155113
Term bmi & s4 importance: 0.612248473444006
Term bmi & s5 importance: 0.7228824291396435
Term bmi & s6 importance: 0.6814893417376885
Term bp & s1 importance: 0.3514117284746946
Term s1 & s5 importance: 0.6446816758096351

Note that mean absolute contribution isn’t the only way of calculating term importances. Another metric our package provides is the min_max option, which computes the difference between the max (the highest score on the graph) and min (the lowest score on the graph) values for each term. Term importance measured with min_max is a measure of the maximum impact a term can have, even though it might have this amount of impact on very few cases, whereas avg_weight(the default parameter) is a measure of typical (average) contribution of a term across all cases.

importances = ebm.term_importances("min_max")
names = ebm.term_names_

for (term, importance) in zip(names, importances):
    print(f"Term {term} importance: {importance}")

Term age importance: 14.608798042461029
Term sex importance: 20.8070057729051
Term bmi importance: 99.12203537083795
Term bp importance: 68.70139770237145
Term s1 importance: 12.19079569434573
Term s2 importance: 18.862125035975495
Term s3 importance: 52.87606617269418
Term s4 importance: 29.062870674891435
Term s5 importance: 63.43222495243778
Term s6 importance: 37.15588430443918
Term age & bp importance: 6.322661867607936
Term age & s5 importance: 6.44895937277681
Term bmi & bp importance: 9.985891048693691
Term bmi & s2 importance: 5.910698624259576
Term bmi & s4 importance: 4.835665114361939
Term bmi & s5 importance: 7.306461271466229
Term bmi & s6 importance: 5.786089226654383
Term bp & s1 importance: 6.405297965552468
Term s1 & s5 importance: 7.5438758673073565

Feature/Term Group Importances

We provide utility functions to compute the importances of groups of features or terms and, optionally, append these importances to the global feature attribution bar graph. Note that shape function graphs are not generated for groups of features/terms, just their overall importance is shown on the Summary.

Grouping terms and then calculating and displaying their importance does not change the model and the predictions it makes in any way – group importances are just a method for computing the importance of groups of terms in addition to the importances of individual terms that are already calculated. As you’ll see in the examples below, it’s OK for features/terms to overlap in different groups.

Computing group importances

Let’s use the Adult dataset and train an EBM for a classification task.

import numpy as np
import pandas as pd
from interpret.glassbox import ExplainableBoostingClassifier

df = pd.read_csv(
    "https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data",
    header=None)
df.columns = [
    "Age", "WorkClass", "fnlwgt", "Education", "EducationNum",
    "MaritalStatus", "Occupation", "Relationship", "Race", "Gender",
    "CapitalGain", "CapitalLoss", "HoursPerWeek", "NativeCountry", "Income"
]
X = df.iloc[:, :-1]
y = df.iloc[:, -1]

adult_ebm = ExplainableBoostingClassifier()
adult_ebm.fit(X, y)

ExplainableBoostingClassifier()

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We then create a list of terms – single features or interactions – as our group and compute its importance:

from interpret.glassbox._ebm._research import *

social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
importance = compute_group_importance(social_feature_group, adult_ebm, X)
print(f"Group: {social_feature_group} - Importance: {importance}")

Group: ['MaritalStatus', 'Relationship', 'Race', 'Gender', 'NativeCountry'] - Importance: 1.3209614928944726

In this example we create a group with five terms and compute its importance. Similar to single feature importances, we interpret this score as the average absolute contribution this group of terms makes when predicting across the training dataset. Note that for each prediction, the contribution of each term in the group will be added before taking the absolute value.

We also have the option to create a global explanation containing the group importance or append it to an existing explanation:

my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
show(my_global_exp)

The importance of social_feature_group is about 1.30, which is higher than the importance of any individual feature/term:

We could make this type of comparison between different groups too:

education_feature_group = ["Education", "EducationNum"]
relationship_feature_group = ["MaritalStatus", "Relationship"]
social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
my_global_exp = append_group_importance(education_feature_group, adult_ebm, X, global_exp=my_global_exp)
my_global_exp = append_group_importance(relationship_feature_group, adult_ebm, X, global_exp=my_global_exp)
show(my_global_exp)

The importance of education_feature_group is about 0.52, higher than each of its individual terms but smaller than some individual terms such as Age. Remember, creating groups of features/terms does not, in any way, change the model and its predictions, it only allows you to estimate the importance of these groups.

This graph, for example, suggests that features related to relationships are more important than features reated to education.

We can also compare a group we are interested in (e.g. social_feature_group) with a group of all other reamining terms.

social_feature_group = ["MaritalStatus", "Relationship", "Race", "Gender", "NativeCountry"]
all_other_terms = [term for term in adult_ebm.term_names_ if term not in social_feature_group]

my_global_exp = append_group_importance(social_feature_group, adult_ebm, X)
my_global_exp = append_group_importance(all_other_terms, adult_ebm, X, group_name="all_other_terms", global_exp=my_global_exp)
show(my_global_exp)

Note that all_other_terms has the highest importance score, followed by social_feature_group.

It’s even possible to create a group with all terms.

all_terms_group = [term for term in adult_ebm.term_names_]
mew_global_exp = append_group_importance(all_terms_group, adult_ebm, X, group_name="all_terms")
show(mew_global_exp)

Finally, we also expose a function to compute the importances of a group of terms as well as all the model’s original terms.

my_dict = get_group_and_individual_importances([social_feature_group, education_feature_group], adult_ebm, X)
for key in my_dict:
    print(f"Term: {key} - Importance: {my_dict[key]}")

Term: MaritalStatus, Relationship, Race, Gender, NativeCountry - Importance: 1.3209614928944726
Term: Age - Importance: 0.8427255205615666
Term: CapitalGain - Importance: 0.7126959641552882
Term: MaritalStatus - Importance: 0.6041348630274861
Term: Relationship - Importance: 0.5414133175248781
Term: Education, EducationNum - Importance: 0.509093733650982
Term: Occupation - Importance: 0.41630572566327156
Term: Gender - Importance: 0.3714699357421156
Term: Education - Importance: 0.309210620451817
Term: HoursPerWeek - Importance: 0.29259463272680536
Term: EducationNum - Importance: 0.22331277141552638
Term: CapitalLoss - Importance: 0.1787631976741163
Term: fnlwgt - Importance: 0.12652119412529853
Term: WorkClass - Importance: 0.10952362116586717
Term: NativeCountry - Importance: 0.10228960307428704
Term: Age & HoursPerWeek - Importance: 0.09264315304937938
Term: MaritalStatus & HoursPerWeek - Importance: 0.06950172814814182
Term: Race - Importance: 0.0642426168614059
Term: Age & Education - Importance: 0.04965008754186661
Term: EducationNum & MaritalStatus - Importance: 0.049523840534962206
Term: Age & fnlwgt - Importance: 0.04542108128137932
Term: Age & Occupation - Importance: 0.03889271647262247
Term: Relationship & HoursPerWeek - Importance: 0.03302564969147786
Term: fnlwgt & Education - Importance: 0.030279790876389594
Term: Age & Race - Importance: 0.027021906307390955
Term: Age & EducationNum - Importance: 0.026529266416648854
Term: WorkClass & Relationship - Importance: 0.025907631368811756
Term: Age & Relationship - Importance: 0.018899977086990653
Term: WorkClass & Race - Importance: 0.012489460569585173