Bike-Sharing Dataset
The Bike-Sharing Dataset contains the hourly and daily count of rental bikes between years 2011 and 2012 in Capital bikeshare system with the corresponding weather and seasonal information. The dataset contains 14 features with information about the day-type, e.g., month, hour, which day of the week, whether it is working-day, and the weather conditions, e.g., temperature, humidity, wind speed, etc. The target variable is the number of bike rentals per hour. The dataset contains 17,379 instances.
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)
Using `tqdm.autonotebook.tqdm` in notebook mode. Use `tqdm.tqdm` instead to force console mode (e.g. in jupyter console)
2024-03-28 17:24:36.392080: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-03-28 17:24:37.795745: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory
2024-03-28 17:24:37.795860: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory
2024-03-28 17:24:37.795868: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.
Preprocess the data
from ucimlrepo import fetch_ucirepo
# fetch dataset
bike_sharing_dataset = fetch_ucirepo(id=275)
# data (as pandas dataframes)
X = bike_sharing_dataset.data.features
y = bike_sharing_dataset.data.targets
# metadata
print(bike_sharing_dataset.metadata)
# variable information
print(bike_sharing_dataset.variables)
{'uci_id': 275, 'name': 'Bike Sharing', 'repository_url': 'https://archive.ics.uci.edu/dataset/275/bike+sharing+dataset', 'data_url': 'https://archive.ics.uci.edu/static/public/275/data.csv', 'abstract': 'This dataset contains the hourly and daily count of rental bikes between years 2011 and 2012 in Capital bikeshare system with the corresponding weather and seasonal information.', 'area': 'Social Science', 'tasks': ['Regression'], 'characteristics': ['Multivariate'], 'num_instances': 17389, 'num_features': 13, 'feature_types': ['Integer', 'Real'], 'demographics': [], 'target_col': ['cnt'], 'index_col': ['instant'], 'has_missing_values': 'no', 'missing_values_symbol': None, 'year_of_dataset_creation': 2013, 'last_updated': 'Sun Mar 10 2024', 'dataset_doi': '10.24432/C5W894', 'creators': ['Hadi Fanaee-T'], 'intro_paper': {'title': 'Event labeling combining ensemble detectors and background knowledge', 'authors': 'Hadi Fanaee-T, João Gama', 'published_in': 'Progress in Artificial Intelligence', 'year': 2013, 'url': 'https://www.semanticscholar.org/paper/bc42899f599d31a5d759f3e0a3ea8b52479d6423', 'doi': '10.1007/s13748-013-0040-3'}, 'additional_info': {'summary': 'Bike sharing systems are new generation of traditional bike rentals where whole process from membership, rental and return back has become automatic. Through these systems, user is able to easily rent a bike from a particular position and return back at another position. Currently, there are about over 500 bike-sharing programs around the world which is composed of over 500 thousands bicycles. Today, there exists great interest in these systems due to their important role in traffic, environmental and health issues. \r\n\r\nApart from interesting real world applications of bike sharing systems, the characteristics of data being generated by these systems make them attractive for the research. Opposed to other transport services such as bus or subway, the duration of travel, departure and arrival position is explicitly recorded in these systems. This feature turns bike sharing system into a virtual sensor network that can be used for sensing mobility in the city. Hence, it is expected that most of important events in the city could be detected via monitoring these data.', 'purpose': None, 'funded_by': None, 'instances_represent': None, 'recommended_data_splits': None, 'sensitive_data': None, 'preprocessing_description': None, 'variable_info': 'Both hour.csv and day.csv have the following fields, except hr which is not available in day.csv\r\n\t\r\n\t- instant: record index\r\n\t- dteday : date\r\n\t- season : season (1:winter, 2:spring, 3:summer, 4:fall)\r\n\t- yr : year (0: 2011, 1:2012)\r\n\t- mnth : month ( 1 to 12)\r\n\t- hr : hour (0 to 23)\r\n\t- holiday : weather day is holiday or not (extracted from http://dchr.dc.gov/page/holiday-schedule)\r\n\t- weekday : day of the week\r\n\t- workingday : if day is neither weekend nor holiday is 1, otherwise is 0.\r\n\t+ weathersit : \r\n\t\t- 1: Clear, Few clouds, Partly cloudy, Partly cloudy\r\n\t\t- 2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist\r\n\t\t- 3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds\r\n\t\t- 4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog\r\n\t- temp : Normalized temperature in Celsius. The values are derived via (t-t_min)/(t_max-t_min), t_min=-8, t_max=+39 (only in hourly scale)\r\n\t- atemp: Normalized feeling temperature in Celsius. The values are derived via (t-t_min)/(t_max-t_min), t_min=-16, t_max=+50 (only in hourly scale)\r\n\t- hum: Normalized humidity. The values are divided to 100 (max)\r\n\t- windspeed: Normalized wind speed. The values are divided to 67 (max)\r\n\t- casual: count of casual users\r\n\t- registered: count of registered users\r\n\t- cnt: count of total rental bikes including both casual and registered\r\n', 'citation': None}}
name role type demographic \
0 instant ID Integer None
1 dteday Feature Date None
2 season Feature Categorical None
3 yr Feature Categorical None
4 mnth Feature Categorical None
5 hr Feature Categorical None
6 holiday Feature Binary None
7 weekday Feature Categorical None
8 workingday Feature Binary None
9 weathersit Feature Categorical None
10 temp Feature Continuous None
11 atemp Feature Continuous None
12 hum Feature Continuous None
13 windspeed Feature Continuous None
14 casual Other Integer None
15 registered Other Integer None
16 cnt Target Integer None
description units missing_values
0 record index None no
1 date None no
2 1:winter, 2:spring, 3:summer, 4:fall None no
3 year (0: 2011, 1: 2012) None no
4 month (1 to 12) None no
5 hour (0 to 23) None no
6 weather day is holiday or not (extracted from ... None no
7 day of the week None no
8 if day is neither weekend nor holiday is 1, ot... None no
9 - 1: Clear, Few clouds, Partly cloudy, Partly ... None no
10 Normalized temperature in Celsius. The values ... C no
11 Normalized feeling temperature in Celsius. The... C no
12 Normalized humidity. The values are divided to... None no
13 Normalized wind speed. The values are divided ... None no
14 count of casual users None no
15 count of registered users None no
16 count of total rental bikes including both cas... None no
X = X.drop(["dteday", "atemp"], axis=1)
X.head()
| season | yr | mnth | hr | holiday | weekday | workingday | weathersit | temp | hum | windspeed | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 1 | 0 | 0 | 6 | 0 | 1 | 0.24 | 0.81 | 0.0 |
| 1 | 1 | 0 | 1 | 1 | 0 | 6 | 0 | 1 | 0.22 | 0.80 | 0.0 |
| 2 | 1 | 0 | 1 | 2 | 0 | 6 | 0 | 1 | 0.22 | 0.80 | 0.0 |
| 3 | 1 | 0 | 1 | 3 | 0 | 6 | 0 | 1 | 0.24 | 0.75 | 0.0 |
| 4 | 1 | 0 | 1 | 4 | 0 | 6 | 0 | 1 | 0.24 | 0.75 | 0.0 |
# load dataset
# df = pd.read_csv("./../data/Bike-Sharing-Dataset/hour.csv")
# drop columns
# df = df.drop(["instant", "dteday", "casual", "registered", "atemp"], axis=1)
print("Design matrix shape: {}".format(X.shape))
print("---------------------------------")
for col_name in X.columns:
print("Feature: {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format(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)
---------------------------------
Feature: season , unique: 4, Mean: 2.50, Std: 1.11, Min: 1.00, Max: 4.00
Feature: yr , unique: 2, Mean: 0.50, Std: 0.50, Min: 0.00, Max: 1.00
Feature: mnth , unique: 12, Mean: 6.54, Std: 3.44, Min: 1.00, Max: 12.00
Feature: hr , unique: 24, Mean: 11.55, Std: 6.91, Min: 0.00, Max: 23.00
Feature: holiday , unique: 2, Mean: 0.03, Std: 0.17, Min: 0.00, Max: 1.00
Feature: weekday , unique: 7, Mean: 3.00, Std: 2.01, Min: 0.00, Max: 6.00
Feature: workingday , unique: 2, Mean: 0.68, Std: 0.47, Min: 0.00, Max: 1.00
Feature: weathersit , unique: 4, Mean: 1.43, Std: 0.64, Min: 1.00, Max: 4.00
Feature: temp , unique: 50, Mean: 0.50, Std: 0.19, Min: 0.02, Max: 1.00
Feature: hum , unique: 89, Mean: 0.63, Std: 0.19, Min: 0.00, Max: 1.00
Feature: 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
Feature analysis:
| Feature | Description | Value Range |
|---|---|---|
| season | season | 1: winter, 2: spring, 3: summer, 4: fall |
| yr | year | 0: 2011, 1: 2012 |
| mnth | month | 1 to 12 |
| hr | hour | 0 to 23 |
| holiday | whether the day is a holiday or not | 0: no, 1: yes |
| weekday | day of the week | 0: Sunday, 1: Monday, …, 6: Saturday |
| workingday | whether the day is a working day or not | 0: no, 1: yes |
| weathersit | weather situation | 1: clear, 2: mist, 3: light rain, 4: heavy rain |
| temp | temperature | values in [0.02, 1.00], with mean: 0.50 and std: 0.19 |
| hum | humidity | values in [0.00, 1.00], with mean: 0.63 and std: 0.19 |
| windspeed | wind speed | values in [0.00, 0.85], with mean: 0.19 and std: 0.12 |
Target variable:
| Target | Description | Value Range |
|---|---|---|
| cnt | bike rentals per hour | values in [1, 977] with mean: 189.46 and std: 181.39 |
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)
2024-03-28 17:24:54.274872: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.429935: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.430254: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.431282: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-03-28 17:24:54.433073: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.433377: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.433601: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.511809: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.512287: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.512458: I tensorflow/compiler/xla/stream_executor/cuda/cuda_gpu_executor.cc:981] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-03-28 17:24:54.512848: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1613] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 2794 MB memory: -> device: 0, name: NVIDIA GeForce GTX 1650 Ti, pci bus id: 0000:01:00.0, compute capability: 7.5
Epoch 1/20
2024-03-28 17:24:55.960441: I tensorflow/compiler/xla/service/service.cc:173] XLA service 0x70a86c4aa520 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
2024-03-28 17:24:55.960460: I tensorflow/compiler/xla/service/service.cc:181] StreamExecutor device (0): NVIDIA GeForce GTX 1650 Ti, Compute Capability 7.5
2024-03-28 17:24:55.983708: I tensorflow/compiler/mlir/tensorflow/utils/dump_mlir_util.cc:268] disabling MLIR crash reproducer, set env var `MLIR_CRASH_REPRODUCER_DIRECTORY` to enable.
2024-03-28 17:24:56.214219: I tensorflow/tsl/platform/default/subprocess.cc:304] Start cannot spawn child process: No such file or directory
2024-03-28 17:24:56.298082: I tensorflow/compiler/jit/xla_compilation_cache.cc:477] Compiled cluster using XLA! This line is logged at most once for the lifetime of the process.
28/28 [==============================] - 3s 5ms/step - loss: 0.5113 - mae: 0.5164 - root_mean_squared_error: 0.7150
Epoch 2/20
28/28 [==============================] - 0s 4ms/step - loss: 0.3653 - mae: 0.4330 - root_mean_squared_error: 0.6044
Epoch 3/20
28/28 [==============================] - 0s 4ms/step - loss: 0.2810 - mae: 0.3716 - root_mean_squared_error: 0.5301
Epoch 4/20
28/28 [==============================] - 0s 4ms/step - loss: 0.2122 - mae: 0.3225 - root_mean_squared_error: 0.4606
Epoch 5/20
28/28 [==============================] - 0s 4ms/step - loss: 0.1509 - mae: 0.2682 - root_mean_squared_error: 0.3884
Epoch 6/20
28/28 [==============================] - 0s 4ms/step - loss: 0.1262 - mae: 0.2467 - root_mean_squared_error: 0.3553
Epoch 7/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0983 - mae: 0.2217 - root_mean_squared_error: 0.3135
Epoch 8/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0751 - mae: 0.1886 - root_mean_squared_error: 0.2740
Epoch 9/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0623 - mae: 0.1720 - root_mean_squared_error: 0.2495
Epoch 10/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0609 - mae: 0.1699 - root_mean_squared_error: 0.2467
Epoch 11/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0615 - mae: 0.1753 - root_mean_squared_error: 0.2480
Epoch 12/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0585 - mae: 0.1706 - root_mean_squared_error: 0.2418
Epoch 13/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0525 - mae: 0.1579 - root_mean_squared_error: 0.2292
Epoch 14/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0458 - mae: 0.1452 - root_mean_squared_error: 0.2139
Epoch 15/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0437 - mae: 0.1415 - root_mean_squared_error: 0.2092
Epoch 16/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0413 - mae: 0.1387 - root_mean_squared_error: 0.2031
Epoch 17/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0442 - mae: 0.1439 - root_mean_squared_error: 0.2103
Epoch 18/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0414 - mae: 0.1382 - root_mean_squared_error: 0.2035
Epoch 19/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0402 - mae: 0.1360 - root_mean_squared_error: 0.2005
Epoch 20/20
28/28 [==============================] - 0s 4ms/step - loss: 0.0489 - mae: 0.1513 - root_mean_squared_error: 0.2211
435/435 [==============================] - 1s 2ms/step - loss: 0.0457 - mae: 0.1488 - root_mean_squared_error: 0.2138
109/109 [==============================] - 0s 2ms/step - loss: 0.0652 - mae: 0.1726 - root_mean_squared_error: 0.2553
[0.06518784910440445, 0.17260313034057617, 0.25531911849975586]
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
We will focus on the feature temp (temperature) because its global effect is quite heterogeneous and the heterogeneity can be further explained using regional effects.
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_x = {"mean": x_mean.iloc[3], "std": x_std.iloc[3]}
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))]
feature_names = X_df.columns.to_list()
target_name = "bike-rentals"
Global Effect
We will first analyze the global effect of the feature hour on the target variable bike-rentals, using the PDP and RHALE methods.
PDP
pdp = effector.PDP(data=X_train.to_numpy(), model=model_forward, feature_names=feature_names, target_name=target_name, nof_instances=300)
pdp.plot(feature=3, centering=True, scale_x=scale_x, scale_y=scale_y, show_avg_output=True)
RHALE
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)
Degrees of freedom <= 0 for slice
invalid value encountered in true_divide
invalid value encountered in true_divide
Conclusion
The global effect of feature hour on the target variable bike-rentals shows two high peaks, one at around 8:00 and another at around 17:00, which probably corresponds to the morning and evening commute hours of the working days. However, the effect is quite heterogeneous. For this reason, we will analyze the regional effects which may explain the underlying heterogeneity.
Regional Effect
RegionalRHALE
# Regional RHALE
regional_rhale = effector.RegionalRHALE(
data=X_train.to_numpy(),
model=model_forward,
model_jac=model_jac,
cat_limit=10,
feature_names=feature_names,
nof_instances="all"
)
regional_rhale.fit(
features=3,
heter_small_enough=0.1,
heter_pcg_drop_thres=0.2,
binning_method=effector.binning_methods.Greedy(init_nof_bins=100, min_points_per_bin=100, discount=1., cat_limit=10),
max_depth=2,
nof_candidate_splits_for_numerical=10,
min_points_per_subregion=10,
candidate_conditioning_features="all",
split_categorical_features=True,
)
100%|██████████| 1/1 [00:09<00:00, 9.37s/it]
regional_rhale.show_partitioning(features=3, only_important=True, scale_x_list=scale_x_list)
Feature 3 - Full partition tree:
Node id: 0, name: hr, heter: 5.97 || nof_instances: 13903 || weight: 1.00
Node id: 1, name: hr | workingday == 0.0, heter: 2.41 || nof_instances: 4385 || weight: 0.32
Node id: 2, name: hr | workingday != 0.0, heter: 4.54 || nof_instances: 9518 || weight: 0.68
--------------------------------------------------
Feature 3 - Statistics per tree level:
Level 0, heter: 5.97
Level 1, heter: 3.86 || heter drop: 2.11 (35.31%)
regional_rhale.plot(feature=3, node_idx=1, heterogeneity=True, centering=True, scale_x_list=scale_x_list, scale_y=scale_y)
regional_rhale.plot(feature=3, node_idx=2, heterogeneity=True, centering=True, scale_x_list=scale_x_list, scale_y=scale_y)
RegionalPDP
regional_pdp = effector.RegionalPDP(
data=X_train.to_numpy(),
model=model_forward,
cat_limit=10,
feature_names=feature_names,
nof_instances="all"
)
regional_pdp.fit(
features=3,
heter_small_enough=0.1,
heter_pcg_drop_thres=0.1,
max_depth=2,
nof_candidate_splits_for_numerical=5,
min_points_per_subregion=10,
candidate_conditioning_features="all",
split_categorical_features=True,
nof_instances=1000
)
100%|██████████| 1/1 [00:04<00:00, 4.02s/it]
regional_pdp.show_partitioning(features=3, only_important=True, scale_x_list=scale_x_list)
Feature 3 - Full partition tree:
Node id: 0, name: hr, heter: 0.57 || nof_instances: 13903 || weight: 1.00
Node id: 1, name: hr | workingday == 1.0, heter: 0.43 || nof_instances: 9518 || weight: 0.68
Node id: 3, name: hr | workingday == 1.0 and yr == 1.0, heter: 0.39 || nof_instances: 4733 || weight: 0.34
Node id: 4, name: hr | workingday == 1.0 and yr != 1.0, heter: 0.31 || nof_instances: 4785 || weight: 0.34
Node id: 2, name: hr | workingday != 1.0, heter: 0.46 || nof_instances: 4385 || weight: 0.32
Node id: 5, name: hr | workingday != 1.0 and yr == 1.0, heter: 0.47 || nof_instances: 2202 || weight: 0.16
Node id: 6, name: hr | workingday != 1.0 and yr != 1.0, heter: 0.33 || nof_instances: 2183 || weight: 0.16
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Feature 3 - Statistics per tree level:
Level 0, heter: 0.57
Level 1, heter: 0.44 || heter drop: 0.13 (22.38%)
Level 2, heter: 0.37 || heter drop: 0.07 (16.57%)
regional_pdp.plot(feature=3, node_idx=1, heterogeneity="ice", centering=True, scale_x_list=scale_x_list, scale_y=scale_y)
regional_pdp.plot(feature=3, node_idx=2, heterogeneity="ice", centering=True, scale_x_list=scale_x_list, scale_y=scale_y)
Conclusion
The both PDP and RHALE regional effect reveal two distinct explanations; one for the working days and another for the non-working days. For the working days, the effect is quite similar to the global effect (unfortunately, working ways dominate our life), with two high peaks at around 8:00 and 17:00. However, for the non-working days, the effect is quite different, with a single high peak at around 13:00 which probably corresponds to sightseeing and leisure activities.