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Interpretable forecasting models
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Introduction¶
Machine learning interpretability, also known as explainability, refers to the ability to understand, interpret, and explain the decisions or predictions made by machine learning models in a human-understandable way. It aims to shed light on how a model arrives at a particular result or decision.
Due to the complex nature of many modern machine learning models, such as ensemble methods, they often function as black boxes, making it difficult to understand why a particular prediction was made. Explanability techniques aim to demystify these models, providing insight into their inner workings and helping to build trust, improve transparency, and meet regulatory requirements in various domains. Improving model explainability not only helps to understand model behavior, but also helps to identify biases, improve model performance, and enable stakeholders to make more informed decisions based on machine learning insights.
The skforecast library is compatible with some of the most used interpretability methods: Shap values, Partial Dependency Plots and Model-specific methods.
Libraries¶
Libraries used in this document.
# Data manipulation
# ==============================================================================
import pandas as pd
import numpy as np
from skforecast.datasets import fetch_dataset
# Plotting
# ==============================================================================
import matplotlib.pyplot as plt
import shap
from skforecast.plot import set_dark_theme
# Modeling and forecasting
# ==============================================================================
import sklearn
import lightgbm
import skforecast
from sklearn.inspection import PartialDependenceDisplay
from lightgbm import LGBMRegressor
from skforecast.recursive import ForecasterRecursive
from skforecast.preprocessing import RollingFeatures
color = '\033[1m\033[38;5;208m'
print(f"{color}Version skforecast: {skforecast.__version__}")
print(f"{color}Version scikit-learn: {sklearn.__version__}")
print(f"{color}Version lightgbm: {lightgbm.__version__}")
print(f"{color}Version pandas: {pd.__version__}")
print(f"{color}Version numpy: {np.__version__}")
Data¶
# Download data
# ==============================================================================
data = fetch_dataset(name="vic_electricity")
data.head(3)
# Aggregation to daily frequency
# ==============================================================================
data = data.resample('D').agg({'Demand': 'sum', 'Temperature': 'mean'})
data.head(3)
# Create calendar variables
# ==============================================================================
data['day_of_week'] = data.index.dayofweek
data['month'] = data.index.month
data.head(3)
# Split train-test
# ==============================================================================
end_train = '2014-12-01 23:59:00'
data_train = data.loc[: end_train, :]
data_test = data.loc[end_train:, :]
print(f"Dates train : {data_train.index.min()} --- {data_train.index.max()} (n={len(data_train)})")
print(f"Dates test : {data_test.index.min()} --- {data_test.index.max()} (n={len(data_test)})")
Forecasting model¶
A forecasting model is created to predict the energy demand using the past 7 values (last week) and the temperature as an exogenous variable.
# Create a recursive multi-step forecaster (ForecasterAutoreg)
# ==============================================================================
window_features = RollingFeatures(stats=['mean'], window_sizes=24)
exog_features = ['Temperature', 'day_of_week', 'month']
forecaster = ForecasterRecursive(
regressor = LGBMRegressor(random_state=123, verbose=-1),
lags = 7,
window_features = window_features
)
forecaster.fit(
y = data_train['Demand'],
exog = data_train[exog_features],
)
forecaster
Model-specific feature importances¶
Feature importance in machine learning determines the relevance or importance of each feature (or variable) in a model's prediction. In other words, it measures how much each feature contributes to the model's output.
Feature importance can be used for several purposes, such as identifying the most relevant features for a given prediction, understanding the behavior of a model, and selecting the best set of features for a given task. It can also help to identify potential biases or errors in the data used to train the model. It is important to note that feature importance is not a definitive measure of causality. Just because a feature is identified as important does not necessarily mean that it caused the outcome. Other factors, such as confounding variables, may also be at play.
The method used to calculate feature importance may vary depending on the type of machine learning model used. Different models can have different assumptions and characteristics that affect the importance calculation. For example, decision tree-based models, such as Random Forest and Gradient Boosting, typically use methods that measure the reduction of impurities or the effect of permutations. Linear regression models typically use coefficients. The magnitude of the coefficient reflects the strength and direction of the relationship between the predictor and the target variable.
The importance of the predictors included in a forecaster can be obtained using the method get_feature_importances(). This method accesses the coef_ and feature_importances_ attributes of the internal regressor.
⚠ Warning
Theget_feature_importances() method will only return values if the forecaster's regressor has either the coef_ or feature_importances_ attribute, which is the default in scikit-learn.
# Extract feature importance
# ==============================================================================
importance = forecaster.get_feature_importances()
importance
Shap Values¶
SHAP (SHapley Additive exPlanations) values are a popular method for explaining machine learning models, as they help to understand how variables and values influence predictions visually and quantitatively.
It is possible to generate SHAP-values explanations from skforecast models with just two essential elements:
The internal regressor of the forecaster.
The training matrices created from the time series and used to fit the forecaster.
By leveraging these two components, users can create insightful and interpretable explanations for their skforecast models. These explanations can be used to verify the reliability of the model, identify the most significant factors that contribute to model predictions, and gain a deeper understanding of the underlying relationship between the input variables and the target variable.
Shap explainer and training matrices¶
# Training matrices used by the forecaster to fit the internal regressor
# ==============================================================================
X_train, y_train = forecaster.create_train_X_y(
y = data_train['Demand'],
exog = data_train[exog_features],
)
display(X_train.head(3))
# Create SHAP explainer (for three base models)
# ==============================================================================
explainer = shap.TreeExplainer(forecaster.regressor)
# Sample 50% of the data to speed up the calculation
rng = np.random.default_rng(seed=785412)
sample = rng.choice(X_train.index, size=int(len(X_train)*0.5), replace=False)
X_train_sample = X_train.loc[sample, :]
shap_values = explainer.shap_values(X_train_sample)
✎ Note
Shap library has several explainers, each designed for a different type of model. Theshap.TreeExplainer explainer is used for tree-based models, such as the LGBMRegressor used in this example. For more information, see the SHAP documentation.
SHAP Summary Plot¶
The SHAP summary plot typically displays the feature importance or contribution of each feature to the model's output across multiple data points. It shows how much each feature contributes to pushing the model's prediction away from a base value (often the model's average prediction). By examining a SHAP summary plot, one can gain insights into which features have the most significant impact on predictions, whether they positively or negatively influence the outcome, and how different feature values contribute to specific predictions.
# Shap summary plot (top 10)
# ==============================================================================
shap.initjs()
shap.summary_plot(shap_values, X_train_sample, max_display=10, show=False)
fig, ax = plt.gcf(), plt.gca()
ax.set_title("SHAP Summary plot")
ax.tick_params(labelsize=8)
fig.set_size_inches(6, 3)
shap.summary_plot(shap_values, X_train, plot_type="bar", plot_size=(6, 3))
Explain predictions in training data¶
A shap.force_plot is a specific type of visualization that provides an interactive and detailed view of how individual features contribute to a particular prediction made by a machine learning model. It's a local interpretation tool that helps understand why a model made a specific prediction for a given instance.
Visualize a single prediction
# Force plot for the first observation in the training set
# ==============================================================================
shap.force_plot(explainer.expected_value, shap_values[0,:], X_train_sample.iloc[0,:])
Visualize many predictions
# Force plot for the first 200 observations in the training set
# ==============================================================================
shap.force_plot(explainer.expected_value, shap_values[:200, :], X_train_sample.iloc[:200, :])
SHAP Dependence Plots¶
SHAP dependence plots are visualizations used to understand the relationship between a feature and the model output by displaying how the value of a single feature affects predictions made by the model while considering interactions with other features. These plots are particularly useful for examining how a certain feature impacts the model's predictions across its range of values while considering interactions with other variables.
# Dependence plot for Temperature
# ==============================================================================
fig, ax = plt.subplots(figsize=(6, 3))
shap.dependence_plot("Temperature", shap_values, X_train_sample, ax=ax)
Explain forecasted values¶
It is also possible to use SHAP values to explain the forecasted values. It helps to understand why the model made a specific prediction for a date in the future.
# Forecasting next 30 days
# ==============================================================================
predictions = forecaster.predict(steps=30, exog=data_test[exog_features])
predictions
# Plot predictions
# ==============================================================================
set_dark_theme()
fig, ax = plt.subplots(figsize=(6, 2.5))
data_test['Demand'].plot(ax=ax, label='Test')
predictions.plot(ax=ax, label='Predictions', linestyle='--')
ax.set_xlabel(None)
ax.legend();
The method create_predict_X is used to create the input matrix used internally by the forecaster's predict method. This matrix is then used to generate SHAP values for the forecasted values.
# Create input matrix used by the predict method
# ==============================================================================
X_predict = forecaster.create_predict_X(steps=30, exog=data_test[exog_features])
X_predict
# SHAP values for the predictions
# ==============================================================================
shap_values = explainer.shap_values(X_predict)
Visualize a single forecasted date
# Force plot for a specific forecasted date
# ==============================================================================
predicted_date = '2014-12-08'
iloc_predicted_date = X_predict.index.get_loc(predicted_date)
shap.force_plot(
explainer.expected_value,
shap_values[iloc_predicted_date,:],
X_predict.iloc[iloc_predicted_date,:]
)
Visualize many forecasted dates
# Force plot for all forecasted dates
# ==============================================================================
shap.force_plot(explainer.expected_value, shap_values, X_predict)
Scikit-learn partial dependence plots¶
Partial dependence plots (PDPs) are a useful tool for understanding the relationship between a feature and the target outcome in a machine learning model. In scikit-learn, you can create partial dependence plots using the plot_partial_dependence function. This function visualizes the effect of one or two features on the predicted outcome, while marginalizing the effect of all other features.
The resulting plots show how changes in the selected feature(s) affect the predicted outcome while holding other features constant on average. Remember that these plots should be interpreted in the context of your model and data. They provide insight into the relationship between specific features and the model's predictions.
A more detailed description of the Partial Dependency Plot can be found in Scikitlearn's User Guides.
# Scikit-learn partial dependence plots
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
pd.plots = PartialDependenceDisplay.from_estimator(
estimator = forecaster.regressor,
X = X_train,
features = ["Temperature", "lag_1"],
kind = 'both',
ax = ax,
)
ax.set_title("Partial Dependence Plot")
fig.tight_layout();
Session information¶
import session_info
session_info.show(html=False)
Citation¶
How to cite this document
If you use this document or any part of it, please acknowledge the source, thank you!
Interpretable forecasting models by Joaquín Amat Rodrigo and Javier Escobar Ortiz, available under a Attribution-NonCommercial-ShareAlike 4.0 International at https://www.cienciadedatos.net/documentos/py57-interpretable-forecasting-models.html
How to cite skforecast
If you use skforecast for a scientific publication, we would appreciate it if you cite the published software.
Zenodo:
Amat Rodrigo, Joaquin, & Escobar Ortiz, Javier. (2024). skforecast (v0.14.0). Zenodo. https://doi.org/10.5281/zenodo.8382788
APA:
Amat Rodrigo, J., & Escobar Ortiz, J. (2024). skforecast (Version 0.14.0) [Computer software]. https://doi.org/10.5281/zenodo.8382788
BibTeX:
@software{skforecast, author = {Amat Rodrigo, Joaquin and Escobar Ortiz, Javier}, title = {skforecast}, version = {0.14.0}, month = {11}, year = {2024}, license = {BSD-3-Clause}, url = {https://skforecast.org/}, doi = {10.5281/zenodo.8382788} }
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This work by Joaquín Amat Rodrigo and Javier Escobar Ortiz is licensed under a Attribution-NonCommercial-ShareAlike 4.0 International.