Using ShaRP to explain feature importance across a population

This example shows how sharp can be used to explain feature importance across a population. We will focus on analysing aggregate feature importance across the different strata of a ranking problem.

Each stratum is defined by a range (using percentiles) of a ranking problem. For each stratum, we will be able to understand which features have the highest impact (positive or negative) in each group’s ranking.

In this example, we will work with a sample of an ACS Income dataset.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import fetch_openml
from sklearn.preprocessing import MinMaxScaler

from sharp import ShaRP
from sharp.utils import check_inputs

# This will help make our visualizations look beautiful :)
plt.style.use("seaborn-v0_8-whitegrid")

X, y = fetch_openml(
    data_id=43141, parser="auto", return_X_y=True, read_csv_kwargs={"nrows": 150}
)

Change data types of categorical features and reduce the number of features in the dataset

numerical_cols = ["AGEP", "WKHP"]
ordinal_cols = ["SCHL"]

X = X.filter(items=numerical_cols + ordinal_cols)

X.describe()

	AGEP	WKHP	SCHL
count	150.000000	150.000000	150.000000
mean	27.933333	32.580000	16.833333
std	11.230750	13.937189	3.222023
min	18.000000	2.000000	1.000000
25%	19.000000	24.000000	16.000000
50%	21.000000	35.500000	18.000000
75%	36.000000	40.000000	19.000000
max	57.000000	75.000000	23.000000

We can also take a quick look at a few rows of our dataset:

X.head()

	AGEP	WKHP	SCHL
0	18.0	21.0	18.0
1	53.0	40.0	17.0
2	41.0	40.0	16.0
3	18.0	2.0	18.0
4	21.0	50.0	19.0

Checking the distributions of the features may also help us better understand the results for feature importance later on:

fig, axes = plt.subplots(1, 3, figsize=(19, 4.5))

for ax, col in zip(axes, X.columns):
    ax.hist(X[col], alpha=0.7, bins=10)
    ax.set_xlabel(col)

plt.show()

Suppose that a bank wants to rank individuals in this dataset who are are potentially high-earning to send them information about a loan opportunity. A team at the bank comes up with the following scoring function:

$$ Score = 20% ~cdot ~AGEP ~+ ~30%~cdot~WKHP ~+ ~50%~cdot~SCHL $$

A score is computed for each individual in the bank’s customer database, individuals are ranked on their score from higher to lower, and flyers to apply for the loan are sent to the best-ranked (i.e., highest-scoring) 50 individuals (the top-50).

Note: When building a ranker like this, it is often important to _standardize_ features. For example, if one of these features were income last year and the mode value was $50,000, it would orders of magnitude larger than the other features. Consider the ranker that was $Score = 10% ~cdot$ income last year $+ 90% ~cdot$ SCHL, all of $Score$ would be from income last year. We will do this below.

We’ll define the scoring function and calculate the scores of all individuals:

def score_function(X):
    X, _ = check_inputs(X)
    # AGEP, WKHP, SCHL
    return 0.2 * X[:, 0] + 0.3 * X[:, 1] + 0.5 * X[:, 2]


# Standardize X and calculate scores
scaler = MinMaxScaler()
X.iloc[:, :] = scaler.fit_transform(X)
y = score_function(X)

We can now set up our ShaRP object and calculate feature contributions across all individuals:

xai = ShaRP(
    qoi="rank",
    target_function=score_function,
    measure="shapley",
    sample_size=None,
    replace=False,
    random_state=42,
    n_jobs=-1,
)

xai.fit(X)

contributions = xai.all(X)

Let’s compare the aggregate feature contributions of the top-10 vs bottom-10 individuals, in terms of ranking:

# Indices for the 10 lowest-ranked individuals
bottom_idx = np.argpartition(y, 10)[:10]

# Indices for the 10 highest-ranked individuals
top_idx = np.argpartition(y, -10)[-10:]

# Set up the visualization
fig, axes = plt.subplots(1, 2, figsize=(13.5, 4.5), layout="constrained", sharey=True)
xai.plot.bar(contributions[top_idx].mean(0), ax=axes[0], alpha=0.7)
axes[0].set_xlabel("Top 10")
axes[0].set_ylabel("Aggregate Feature Importance")
xai.plot.bar(contributions[bottom_idx].mean(0), ax=axes[1], alpha=0.7)
axes[1].set_xlabel("Bottom 10")
axes[1].set_ylabel("")

plt.show()

We can also get a sense on how feature importance varies across strata:

xai.plot.strata_boxplot(X, y, contributions, n_strata=5, cmap="Pastel1")
plt.show()