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: 3.2357671259109337
Term sex importance: 10.431907227185329
Term bmi importance: 17.34189713649959
Term bp importance: 11.393360813850238
Term s1 importance: 1.535831437239701
Term s2 importance: 3.172597989399135
Term s3 importance: 7.2821022176597054
Term s4 importance: 6.054837490610567
Term s5 importance: 17.198646537608173
Term s6 importance: 5.152081623321795
Term age & bp importance: 0.5536396223751048
Term age & s5 importance: 0.6984218945466711
Term bmi & bp importance: 0.5590693940335197
Term bmi & s4 importance: 0.6422460778583943
Term bmi & s5 importance: 0.6387171855892041
Term bmi & s6 importance: 0.5569204313150303
Term bp & s1 importance: 0.41429582648349744
Term s1 & s5 importance: 0.6854762194624874
Term s5 & s6 importance: 0.8994164799584223

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: 16.3031783304845
Term sex importance: 20.947878749427844
Term bmi importance: 99.88236502169572
Term bp importance: 70.5812655361787
Term s1 importance: 13.631773120507084
Term s2 importance: 19.631457279237022
Term s3 importance: 53.12806663213374
Term s4 importance: 28.821515052870232
Term s5 importance: 63.81503875799717
Term s6 importance: 36.767153432203166
Term age & bp importance: 5.711542514690193
Term age & s5 importance: 7.361992350063598
Term bmi & bp importance: 10.058669470849502
Term bmi & s4 importance: 4.093351889650322
Term bmi & s5 importance: 6.154372852444338
Term bmi & s6 importance: 5.333647095242265
Term bp & s1 importance: 6.524589504610913
Term s1 & s5 importance: 8.681891134556814
Term s5 & s6 importance: 10.999279605767754

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: 1.34025432582611

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: 1.34025432582611
Term: MaritalStatus - Importance: 0.9601033154733993
Term: Age - Importance: 0.9075504363031826
Term: CapitalGain - Importance: 0.7242090336171584
Term: Education, EducationNum - Importance: 0.513598199392493
Term: Occupation - Importance: 0.42065530988090966
Term: Gender - Importance: 0.39234898577594574
Term: Education - Importance: 0.3657090790264731
Term: HoursPerWeek - Importance: 0.295931834424345
Term: Relationship - Importance: 0.2697701281793175
Term: CapitalLoss - Importance: 0.17264993670426207
Term: EducationNum - Importance: 0.16219654512179993
Term: fnlwgt - Importance: 0.12630437546911447
Term: WorkClass - Importance: 0.11054790459401066
Term: NativeCountry - Importance: 0.10590814015759697
Term: Age & HoursPerWeek - Importance: 0.08705249809717623
Term: MaritalStatus & HoursPerWeek - Importance: 0.07200169386624186
Term: Race - Importance: 0.06401839354691273
Term: Age & Education - Importance: 0.05583959640954401
Term: Age & fnlwgt - Importance: 0.04083269718186386
Term: EducationNum & MaritalStatus - Importance: 0.03924505860470226
Term: Age & Occupation - Importance: 0.033552252065613485
Term: Relationship & HoursPerWeek - Importance: 0.027857079254725758
Term: fnlwgt & Education - Importance: 0.027766538995828705
Term: Age & EducationNum - Importance: 0.024768728763885493
Term: Age & Race - Importance: 0.020665493626763193
Term: Age & Relationship - Importance: 0.016400416447842223
Term: WorkClass & Relationship - Importance: 0.014481754580273691
Term: WorkClass & Race - Importance: 0.006825066959667514