Checking running times and error for different parameters

This example shows how the running time and estimation error varies over a mock dataset while changing the coalition_size.

We will start by setting up the imports, environment variables and a basic score function that will be used to determine rankings.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.utils import check_random_state
from sharp import ShaRP
from sharp.utils import scores_to_ordering

import time
import pandas as pd


# Set up some environment variables
RNG_SEED = 42
N_SAMPLES = 500
N_EXPLAIN = 50
rng = check_random_state(RNG_SEED)


def score_function(X):
    return X.mean(axis=1)

We can now generate a simple mock dataset with 2 features, one sampled from a normal distribution, another from a bernoulli.

X = np.concatenate(
    [
        rng.normal(size=(N_SAMPLES, 1)),
        rng.normal(1, 0.5, size=(N_SAMPLES, 1)),
        rng.normal(0.3, 0.5, size=(N_SAMPLES, 1)),
        rng.normal(1, 0.75, size=(N_SAMPLES, 1)),
        rng.binomial(1, 0.5, size=(N_SAMPLES, 1)),
    ],
    axis=1,
)
y = score_function(X)
rank = scores_to_ordering(y)

x_explain = X[rng.choice(np.arange(X.shape[0]), size=N_EXPLAIN)]

# Calculate feature contributions using all coalitions
xai = ShaRP(
    qoi="rank",
    target_function=score_function,
    measure="shapley",
    sample_size=50,
    coalition_size=None,
    replace=False,
    random_state=RNG_SEED,
)
xai.fit(X)

start = time.time()
ftr_contrs_exact = xai.all(x_explain)
end = time.time()

Run ShaRP using different coalition sizes

# Calculate the approximations
cols = ["coalition_size", "time", "error"]
results = [["exact", (end - start) / N_EXPLAIN, 0]]

for coal_size in range(1, X.shape[-1]):
    xai = ShaRP(
        qoi="rank",
        target_function=score_function,
        measure="shapley",
        sample_size=50,
        coalition_size=coal_size,
        replace=False,
        random_state=RNG_SEED,
    )
    xai.fit(X)

    start = time.time()
    ftr_contrs_curr = xai.all(x_explain)
    end = time.time()

    data = [
        coal_size,
        (end - start) / N_EXPLAIN,
        np.mean(np.abs(ftr_contrs_curr - ftr_contrs_exact)),
    ]
    results.append(data)

results = pd.DataFrame(results, columns=cols)
results

	coalition_size	time	error
0	exact	0.162087	0.000000
1	1	0.051127	33.469881
2	2	0.110956	22.469133
3	3	0.151664	11.548757
4	4	0.160860	0.000000

Let’s visualize the results:

res_ = results[results["coalition_size"] != "exact"]

fig, ax1 = plt.subplots()

res_.plot.line("coalition_size", "time", color="red", marker="o", ax=ax1)
ax1.tick_params(axis="y", labelcolor="red")
ax1.set_ylabel("Avg. Time per Sample", color="red")
ax1.set_ylim(bottom=0)
ax1.get_legend().remove()

ax2 = ax1.twinx()
res_.plot.line("coalition_size", "error", color="blue", marker="o", ax=ax2)
ax2.tick_params(axis="y", labelcolor="blue")
ax2.set_ylabel("Avg. Error", color="blue")
ax2.set_ylim(bottom=0)
ax2.get_legend().remove()

plt.show()

Run ShaRP using different sample sizes

x_explain = X[rng.choice(np.arange(X.shape[0]), size=N_EXPLAIN)]

# Calculate feature contributions using all coalitions
xai = ShaRP(
    qoi="rank",
    target_function=score_function,
    measure="shapley",
    sample_size=50,
    coalition_size=None,
    replace=False,
    random_state=RNG_SEED,
)
xai.fit(X)

start = time.time()
ftr_contrs_exact = xai.all(x_explain)
end = time.time()

# Calculate the approximations
cols = ["sample_size", "time", "error"]
results = []

for sample_size in range(10, 51, 10):
    xai = ShaRP(
        qoi="rank",
        target_function=score_function,
        measure="shapley",
        sample_size=sample_size,
        coalition_size=None,
        replace=False,
        random_state=RNG_SEED,
    )
    xai.fit(X)

    start = time.time()
    ftr_contrs_curr = xai.all(x_explain)
    end = time.time()

    data = [
        sample_size,
        (end - start) / N_EXPLAIN,
        np.mean(np.abs(ftr_contrs_curr - ftr_contrs_exact)),
    ]
    results.append(data)

results = pd.DataFrame(results, columns=cols)
results

	sample_size	time	error
0	10	0.054590	4.480324
1	20	0.082827	2.637595
2	30	0.107321	1.867595
3	40	0.133917	1.137159
4	50	0.161328	0.000000

Let’s visualize the results:

res_ = results[results["sample_size"] != "exact"]

fig, ax1 = plt.subplots()

res_.plot.line("sample_size", "time", color="red", marker="o", ax=ax1)
ax1.tick_params(axis="y", labelcolor="red")
ax1.set_ylabel("Avg. Time per Sample", color="red")
ax1.set_ylim(bottom=0)
ax1.get_legend().remove()

ax2 = ax1.twinx()
res_.plot.line("sample_size", "error", color="blue", marker="o", ax=ax2)
ax2.tick_params(axis="y", labelcolor="blue")
ax2.set_ylabel("Avg. Error", color="blue")
ax2.set_ylim(bottom=0)
ax2.get_legend().remove()

plt.show()