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: 3.233104332124471
Term sex importance: 10.36930737699903
Term bmi importance: 17.29842718068298
Term bp importance: 11.356511214902474
Term s1 importance: 1.5035060542439667
Term s2 importance: 3.155428275864227
Term s3 importance: 7.298188744335262
Term s4 importance: 6.064825388009212
Term s5 importance: 17.1403440210491
Term s6 importance: 5.1359583567686915
Term age & bp importance: 0.6044700815558279
Term age & s5 importance: 0.7608377030339248
Term bmi & bp importance: 0.709414130288759
Term bmi & s4 importance: 0.790568233448765
Term bmi & s5 importance: 0.7175633370934789
Term bmi & s6 importance: 0.673097889385293
Term bp & s1 importance: 0.518849020375423
Term s1 & s5 importance: 0.767084723251186
Term s5 & s6 importance: 0.9371661451738582

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: 16.18162267147724
Term sex importance: 20.822174595539508
Term bmi importance: 99.22535290057229
Term bp importance: 70.32274534848557
Term s1 importance: 13.608435342064986
Term s2 importance: 19.16414120735687
Term s3 importance: 53.08588122672447
Term s4 importance: 28.924211103121845
Term s5 importance: 63.57952571061998
Term s6 importance: 36.60435719644536
Term age & bp importance: 5.7145805441065045
Term age & s5 importance: 7.588424923353074
Term bmi & bp importance: 11.575170359471262
Term bmi & s4 importance: 4.354823611662938
Term bmi & s5 importance: 7.257915272535968
Term bmi & s6 importance: 5.239844338987632
Term bp & s1 importance: 7.551983353606776
Term s1 & s5 importance: 9.082526359491439
Term s5 & s6 importance: 11.09425436876581

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: 1.2824565249385607

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: 1.2824565249385607
Term: Age - Importance: 0.8469191895473881
Term: CapitalGain - Importance: 0.7034245142205204
Term: Relationship - Importance: 0.6875446633479054
Term: Education, EducationNum - Importance: 0.5147785027281584
Term: MaritalStatus - Importance: 0.45282555550257103
Term: EducationNum - Importance: 0.4346090291658021
Term: Occupation - Importance: 0.3830888186899532
Term: Gender - Importance: 0.3142221983816183
Term: HoursPerWeek - Importance: 0.2977918783583298
Term: CapitalLoss - Importance: 0.1746348531038255
Term: fnlwgt - Importance: 0.12504237723645945
Term: Education - Importance: 0.10743813334651311
Term: WorkClass - Importance: 0.08940574810379932
Term: Age & HoursPerWeek - Importance: 0.08791797291095362
Term: MaritalStatus & HoursPerWeek - Importance: 0.06570371911045894
Term: NativeCountry - Importance: 0.05994082880207592
Term: Race - Importance: 0.05790311615220191
Term: Age & Education - Importance: 0.05305038639498749
Term: Age & fnlwgt - Importance: 0.04261505249706351
Term: Age & Occupation - Importance: 0.034874730439484865
Term: Relationship & HoursPerWeek - Importance: 0.03170647091380153
Term: Gender & HoursPerWeek - Importance: 0.03096085879256194
Term: fnlwgt & Education - Importance: 0.028029361672064424
Term: Age & Race - Importance: 0.02778381297576086
Term: Age & EducationNum - Importance: 0.027156472199630008
Term: WorkClass & Relationship - Importance: 0.025432202777688307
Term: Age & Relationship - Importance: 0.021039843589680307
Term: WorkClass & Race - Importance: 0.014217202114379135