Bike-Sharing Dataset

This notebook analyzes the Capital Bikeshare system's rental data from 2011-2012. We'll explore how various factors influence bike rental patterns using advanced machine learning techniques. The Bike-Sharing Dataset contains: - 17,379 hourly records - 14 features including temporal and weather information - Target variable: hourly bike rental count

import effector
import numpy as np
import tensorflow as tf
from tensorflow import keras
import random

np.random.seed(42)
tf.random.set_seed(42)
random.seed(42)

2025-06-24 12:12:26.707704: I tensorflow/core/platform/cpu_feature_guard.cc:210] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

Preprocess the data

from ucimlrepo import fetch_ucirepo
bike_sharing_dataset = fetch_ucirepo(id=275)
X = bike_sharing_dataset.data.features
y = bike_sharing_dataset.data.targets

X = X.drop(["dteday", "atemp"], axis=1)

print("Design matrix shape: {}".format(X.shape))
print("---------------------------------")
for i, col_name in enumerate(X.columns):
    print("x_{} {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format(i, col_name, len(X[col_name].unique()), X[col_name].mean(), X[col_name].std(), X[col_name].min(), X[col_name].max()))

print("\nTarget shape: {}".format(y.shape))
print("---------------------------------")
for col_name in y.columns:
    print("Target: {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format(col_name, len(y[col_name].unique()), y[col_name].mean(), y[col_name].std(), y[col_name].min(), y[col_name].max()))

Design matrix shape: (17379, 11)
---------------------------------
x_0 season         , unique:    4, Mean:   2.50, Std:   1.11, Min:   1.00, Max:   4.00
x_1 yr             , unique:    2, Mean:   0.50, Std:   0.50, Min:   0.00, Max:   1.00
x_2 mnth           , unique:   12, Mean:   6.54, Std:   3.44, Min:   1.00, Max:  12.00
x_3 hr             , unique:   24, Mean:  11.55, Std:   6.91, Min:   0.00, Max:  23.00
x_4 holiday        , unique:    2, Mean:   0.03, Std:   0.17, Min:   0.00, Max:   1.00
x_5 weekday        , unique:    7, Mean:   3.00, Std:   2.01, Min:   0.00, Max:   6.00
x_6 workingday     , unique:    2, Mean:   0.68, Std:   0.47, Min:   0.00, Max:   1.00
x_7 weathersit     , unique:    4, Mean:   1.43, Std:   0.64, Min:   1.00, Max:   4.00
x_8 temp           , unique:   50, Mean:   0.50, Std:   0.19, Min:   0.02, Max:   1.00
x_9 hum            , unique:   89, Mean:   0.63, Std:   0.19, Min:   0.00, Max:   1.00
x_10 windspeed      , unique:   30, Mean:   0.19, Std:   0.12, Min:   0.00, Max:   0.85

Target shape: (17379, 1)
---------------------------------
Target: cnt            , unique:  869, Mean: 189.46, Std: 181.39, Min:   1.00, Max: 977.00

def preprocess(X, y):
    # Standarize X
    X_df = X
    x_mean = X_df.mean()
    x_std = X_df.std()
    X_df = (X_df - X_df.mean()) / X_df.std()

    # Standarize Y
    Y_df = y
    y_mean = Y_df.mean()
    y_std = Y_df.std()
    Y_df = (Y_df - Y_df.mean()) / Y_df.std()
    return X_df, Y_df, x_mean, x_std, y_mean, y_std

# shuffle and standarize all features
X_df, Y_df, x_mean, x_std, y_mean, y_std = preprocess(X, y)

def split(X_df, Y_df):
    # shuffle indices
    indices = X_df.index.tolist()
    np.random.shuffle(indices)

    # data split
    train_size = int(0.8 * len(X_df))

    X_train = X_df.iloc[indices[:train_size]]
    Y_train = Y_df.iloc[indices[:train_size]]
    X_test = X_df.iloc[indices[train_size:]]
    Y_test = Y_df.iloc[indices[train_size:]]

    return X_train, Y_train, X_test, Y_test

# train/test split
X_train, Y_train, X_test, Y_test = split(X_df, Y_df)

Fit a Neural Network

# Train - Evaluate - Explain a neural network
model = keras.Sequential([
    keras.layers.Dense(1024, activation="relu"),
    keras.layers.Dense(512, activation="relu"),
    keras.layers.Dense(256, activation="relu"),
    keras.layers.Dense(1)
])

optimizer = keras.optimizers.Adam(learning_rate=0.001)
model.compile(optimizer=optimizer, loss="mse", metrics=["mae", keras.metrics.RootMeanSquaredError()])
model.fit(X_train, Y_train, batch_size=512, epochs=20, verbose=1)
model.evaluate(X_train, Y_train, verbose=1)
model.evaluate(X_test, Y_test, verbose=1)

Epoch 1/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m1s[0m 11ms/step - loss: 0.6231 - mae: 0.5745 - root_mean_squared_error: 0.7853
Epoch 2/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 11ms/step - loss: 0.3870 - mae: 0.4506 - root_mean_squared_error: 0.6219
Epoch 3/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 13ms/step - loss: 0.2976 - mae: 0.3851 - root_mean_squared_error: 0.5454
Epoch 4/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 13ms/step - loss: 0.2237 - mae: 0.3326 - root_mean_squared_error: 0.4728
Epoch 5/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 12ms/step - loss: 0.1619 - mae: 0.2836 - root_mean_squared_error: 0.4023
Epoch 6/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 16ms/step - loss: 0.1193 - mae: 0.2386 - root_mean_squared_error: 0.3451
Epoch 7/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 15ms/step - loss: 0.0906 - mae: 0.2075 - root_mean_squared_error: 0.3009
Epoch 8/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 9ms/step - loss: 0.0753 - mae: 0.1895 - root_mean_squared_error: 0.2745
Epoch 9/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 8ms/step - loss: 0.0669 - mae: 0.1784 - root_mean_squared_error: 0.2586
Epoch 10/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 11ms/step - loss: 0.0610 - mae: 0.1703 - root_mean_squared_error: 0.2469
Epoch 11/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 13ms/step - loss: 0.0554 - mae: 0.1614 - root_mean_squared_error: 0.2353
Epoch 12/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 11ms/step - loss: 0.0500 - mae: 0.1524 - root_mean_squared_error: 0.2235
Epoch 13/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m1s[0m 19ms/step - loss: 0.0462 - mae: 0.1459 - root_mean_squared_error: 0.2149
Epoch 14/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 16ms/step - loss: 0.0431 - mae: 0.1407 - root_mean_squared_error: 0.2075
Epoch 15/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m1s[0m 29ms/step - loss: 0.0410 - mae: 0.1372 - root_mean_squared_error: 0.2026
Epoch 16/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m1s[0m 14ms/step - loss: 0.0399 - mae: 0.1360 - root_mean_squared_error: 0.1996
Epoch 17/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 15ms/step - loss: 0.0381 - mae: 0.1325 - root_mean_squared_error: 0.1952
Epoch 18/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 17ms/step - loss: 0.0378 - mae: 0.1323 - root_mean_squared_error: 0.1945
Epoch 19/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 14ms/step - loss: 0.0376 - mae: 0.1325 - root_mean_squared_error: 0.1940
Epoch 20/20
[1m28/28[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 13ms/step - loss: 0.0378 - mae: 0.1331 - root_mean_squared_error: 0.1944
[1m435/435[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m1s[0m 2ms/step - loss: 0.0420 - mae: 0.1422 - root_mean_squared_error: 0.2048
[1m109/109[0m [32m━━━━━━━━━━━━━━━━━━━━[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0701 - mae: 0.1725 - root_mean_squared_error: 0.2633





[0.06317276507616043, 0.16644978523254395, 0.25134193897247314]

We train a deep fully-connected Neural Network with 3 hidden layers for \(20\) epochs. The model achieves a root mean squared error on the test of about \(0.24\) units, that corresponds to approximately \(0.26 * 181 = 47\) counts.

Explain

def model_jac(x):
    x_tensor = tf.convert_to_tensor(x, dtype=tf.float32)
    with tf.GradientTape() as t:
        t.watch(x_tensor)
        pred = model(x_tensor)
        grads = t.gradient(pred, x_tensor)
    return grads.numpy()

def model_forward(x):
    return model(x).numpy().squeeze()

scale_y = {"mean": y_mean.iloc[0], "std": y_std.iloc[0]}
scale_x_list =[{"mean": x_mean.iloc[i], "std": x_std.iloc[i]} for i in range(len(x_mean))]
scale_x = scale_x_list[3]
feature_names = X_df.columns.to_list()
target_name = "bike-rentals"
y_limits=[-200, 800]
dy_limits = [-300, 300]

scale_x_list[8]["mean"] += 8
scale_x_list[8]["std"] *= 47

scale_x_list[9]["std"] *= 100
scale_x_list[10]["std"] *= 67

PDP - analyze all features

We start by examining all relevant features. Feature effect methods are generally more meaningful for numerical features, so we focus on them. Relevant features:

month
hr
weekday
workingday
temp
humidity
windspeed

pdp = effector.PDP(data=X_train.to_numpy(), model=model_forward, feature_names=feature_names, target_name=target_name, nof_instances=2000)
for i in [2, 3, 8, 9, 10]:
    pdp.plot(feature=i, centering=True, scale_x=scale_x_list[i], scale_y=scale_y, show_avg_output=True, nof_ice=200, y_limits=y_limits)

We observe that features: hour, temperature and humidity have an intersting structure. Out of them hour has by far the most influence on the output, so it makes sensce to focus on it further.

Feature `hour`

PDP - global

pdp = effector.PDP(data=X_train.to_numpy(), model=model_forward, feature_names=feature_names, target_name=target_name, nof_instances=5000)
pdp.plot(feature=3, centering=True, scale_x=scale_x, scale_y=scale_y, show_avg_output=True, nof_ice=200)

2025-06-24 12:12:58.719189: W external/local_xla/xla/tsl/framework/cpu_allocator_impl.cc:83] Allocation of 614400000 exceeds 10% of free system memory.
2025-06-24 12:12:58.843474: W external/local_xla/xla/tsl/framework/cpu_allocator_impl.cc:83] Allocation of 614400000 exceeds 10% of free system memory.
2025-06-24 12:12:58.937027: W external/local_xla/xla/tsl/framework/cpu_allocator_impl.cc:83] Allocation of 614400000 exceeds 10% of free system memory.
2025-06-24 12:12:59.827863: W external/local_xla/xla/tsl/framework/cpu_allocator_impl.cc:83] Allocation of 614400000 exceeds 10% of free system memory.
2025-06-24 12:12:59.939911: W external/local_xla/xla/tsl/framework/cpu_allocator_impl.cc:83] Allocation of 614400000 exceeds 10% of free system memory.

PDP - regional

regional_pdp = effector.RegionalPDP(data=X_train.to_numpy(), model=model_forward, feature_names=feature_names, nof_instances=5_000)
regional_pdp.summary(features=3, scale_x_list=scale_x_list)

100%|██████████| 1/1 [00:02<00:00,  2.26s/it]



Feature 3 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
hr 🔹 [id: 0 | heter: 0.24 | inst: 5000 | w: 1.00]
    workingday = 0.00 🔹 [id: 1 | heter: 0.13 | inst: 1548 | w: 0.31]
        temp ≤ 4.50 🔹 [id: 2 | heter: 0.06 | inst: 618 | w: 0.12]
        temp > 4.50 🔹 [id: 3 | heter: 0.10 | inst: 930 | w: 0.19]
    workingday ≠ 0.00 🔹 [id: 4 | heter: 0.12 | inst: 3452 | w: 0.69]
        yr = 0.00 🔹 [id: 5 | heter: 0.06 | inst: 1719 | w: 0.34]
        yr ≠ 0.00 🔹 [id: 6 | heter: 0.11 | inst: 1733 | w: 0.35]
--------------------------------------------------
Feature 3 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.24
    Level 1🔹heter: 0.13 | 🔻0.12 (48.45%)
        Level 2🔹heter: 0.08 | 🔻0.04 (32.86%)

for node_idx in [1, 4]:
    regional_pdp.plot(feature=3, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

for node_idx in [2, 3, 5, 6]:
    regional_pdp.plot(feature=3, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

RHALE - global

rhale = effector.RHALE(data=X_train.to_numpy(), model=model_forward, model_jac=model_jac, feature_names=feature_names, target_name=target_name)
rhale.plot(feature=3, heterogeneity="std", centering=True, scale_x=scale_x, scale_y=scale_y, show_avg_output=True)

RHALE - regional

regional_rhale = effector.RegionalRHALE(data=X_train.to_numpy(), model=model_forward, model_jac=model_jac, feature_names=feature_names, target_name=target_name)
regional_rhale.summary(features=3, scale_x_list=scale_x_list)

100%|██████████| 1/1 [00:03<00:00,  3.60s/it]



Feature 3 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
hr 🔹 [id: 0 | heter: 5.68 | inst: 13903 | w: 1.00]
    workingday = 0.00 🔹 [id: 1 | heter: 0.75 | inst: 4385 | w: 0.32]
        temp ≤ 6.81 🔹 [id: 2 | heter: 0.44 | inst: 2187 | w: 0.16]
        temp > 6.81 🔹 [id: 3 | heter: 0.60 | inst: 2198 | w: 0.16]
    workingday ≠ 0.00 🔹 [id: 4 | heter: 5.44 | inst: 9518 | w: 0.68]
--------------------------------------------------
Feature 3 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 5.68
    Level 1🔹heter: 3.96 | 🔻1.71 (30.22%)
        Level 2🔹heter: 0.16 | 🔻3.80 (95.84%)

for node_idx in [1, 4]:
    regional_rhale.plot(feature=3, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y)

for node_idx in [2, 3]:
    regional_rhale.plot(feature=3, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

SHAPDP - global

shap_dp = effector.ShapDP(data=X_train.to_numpy(), model=model_forward, feature_names=feature_names, target_name=target_name, nof_instances=500)
shap_dp.plot(feature=3, centering=True, scale_x=scale_x, scale_y=scale_y, show_avg_output=True)

PermutationExplainer explainer: 501it [02:43,  2.91it/s]

SHAPDP - regional

regional_shap_dp = effector.RegionalShapDP(data=X_train.to_numpy(), model=model_forward, feature_names=feature_names, nof_instances=500)
regional_shap_dp.summary(features=3, scale_x_list=scale_x_list)

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Feature 3 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
hr 🔹 [id: 0 | heter: 0.05 | inst: 500 | w: 1.00]
    workingday = 0.00 🔹 [id: 1 | heter: 0.02 | inst: 158 | w: 0.32]
        temp ≤ 9.11 🔹 [id: 2 | heter: 0.02 | inst: 92 | w: 0.18]
        temp > 9.11 🔹 [id: 3 | heter: 0.01 | inst: 66 | w: 0.13]
    workingday ≠ 0.00 🔹 [id: 4 | heter: 0.03 | inst: 342 | w: 0.68]
        yr = 0.00 🔹 [id: 5 | heter: 0.02 | inst: 169 | w: 0.34]
        yr ≠ 0.00 🔹 [id: 6 | heter: 0.02 | inst: 173 | w: 0.35]
--------------------------------------------------
Feature 3 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.05
    Level 1🔹heter: 0.03 | 🔻0.03 (51.02%)
        Level 2🔹heter: 0.02 | 🔻0.01 (30.09%)

for node_idx in [1, 4]:
    regional_shap_dp.plot(feature=3, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y)

for node_idx in [2, 3, 5, 6]:
    regional_shap_dp.plot(feature=3, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

/home/givasile/github/packages/effector/effector/global_effect_shap.py:469: RuntimeWarning: invalid value encountered in sqrt
  np.sqrt(self.feature_effect["feature_" + str(feature)]["spline_std"](x))

Conclusion

Global effect of hour All methods agree: hour has a strong influence on bike rentals, showing two clear peaks—around 8:00 and 17:00. This likely reflects commute times. But the exact shape of the effect varies between methods, hinting that local (regional) patterns could help explain these differences.

Regional effect of hour When we zoom in using regional methods, two patterns emerge:

On working days, the effect follows the global trend, with peaks at 8:00 and 17:00—again, probably due to commuting.
On non-working days, we see a single peak around 13:00, which makes sense if people are out enjoying leisure activities or sightseeing.

All methods agree up to this point.

Interactions Looking deeper, we see some interesting (but weaker) interactions. Most methods highlight either temperature or year (whether it’s the first or second year of data) as relevant.

For example, RHALE shows that on non-working days, the midday peak (12:00–14:00) becomes even stronger when the temperature is higher. That fits our intuition—people are more likely to rent bikes when it’s warm and sunny.