Understanding XGBoost for Geospatial Studies: Insights from Simulated Data and COVID-19 Forecasting in Germany
The eXtreme Gradient Boosting (XGBoost) algorithm is a popular machine learning method widely used in various fields, including COVID-19 research. As an ensemble learning method, XGBoost trains multiple submodels, such as decision trees, and consolidates their outputs to complete a task. Studies have shown that XGBoost often performs on par with deep learning models while maintaining the advantage of being interpretable. For comparative studies focused on simulation data and forecasting German daily COVID-19 infections, XGBoost is employed due to its shorter training time and fewer model parameters compared to deep learning models.
This study leverages controlled simulated experiments to separately analyze factors like sample size in different modeling approaches, while real data experiments offer insights into spatio-temporal variables in actual geospatial studies. It’s critical to note that this study does not aim for superior forecasting performance in general; hence, for global modeling, additional data like city traffic flow or advanced methods such as graph convolutional neural networks are not utilized.
Exploring Data Distributions and Sample Sizes with XGBoost
Data generated from linear, power, and trigonometric functions were used to evaluate the performance of XGBoost in global- and local modeling methods across aspects such as data distribution, sample size, and value range. All results presented are averaged over 100 independent simulations. Comparative performance analysis was conducted not only for the entire dataset but also for the subsets derived from different equations.
Table 1 showcases the average root mean squared error (RMSE) for global and local modeling of XGBoost using different data distributions—Normal and Pareto. Interestingly, data resampled with Pareto distribution yield better modeling results than those with Normal distribution due to the differences in their distribution characteristics. Local modeling generally outperforms global modeling with Normal distribution data, whereas global modeling fares better with Pareto distribution data. The preference between modeling approaches depends on data distribution, with global modeling often excelling, except in particular cases like a linear function with Normal distribution data.
Impact of Data Size and Value Range
For assessments based on different train data sizes, global and local modeling were examined under various equation combinations such as Linear+Power, Linear+Trigonometric, and Power+Trigonometric. Adequate data size proves to be crucial for enhanced model performance in both approaches. Local modeling shows better performance under Linear+Trigonometric combinations, while global modeling excels under Power+Trigonometric combinations. Global modeling is more sensitive to smaller data sizes, potentially losing focus on secondary samples, whereas local modeling remains stable across varying sizes as it achieves local optimization.
Varying data value ranges are also critical in assessing model performance. When experimenting with linear and power equations, any increase in maximum values correlates with increased RMSE for both modeling types. However, local modeling outperforms when the value range is significantly large. Moreover, applying log transformations to the data reinforces that simple value transformations cannot always improve model performance.
Geographical Applications in COVID-19 Forecasting
In implementing XGBoost for forecasting COVID-19 infections across Germany, four evaluation metrics—mean absolute error (MAE), mean squared error (MSE), RMSE, and Cosine similarity—were employed for performance comparison. Both global and local modeling achieved comparable results, with some differences in specific indicators. Temporal projections were examined in three regions: Berlin, Ansbach district, and Wittmund. Larger infected numbers yielded more accurate time series predictions, though both models noticed irregularities in regions with fewer cases.
Spatially, the analysis illustrated the relationship between true infected cases and RMSE—higher infected numbers resulted in higher absolute errors but lower relative errors. This pattern demonstrates how larger actual values can lead to a more significant deviation in absolute terms while aligning closer on a relative scale.
Conclusion and Insights
An important takeaway is that while both global and local modeling methods of XGBoost demonstrate similar efficacy in certain contexts, their application largely depends on specific conditions such as data balance, distribution, and range. This study highlights the necessity of comparing these methods in tasks like geospatial analysis, especially under varied data scenarios, such as unbalanced train samples and diverse value ranges.
Ultimately, the results emphasize that selecting the most suitable modeling approach is contingent upon the specificities of each geospatial study. Continued exploration and testing in real-world scenarios are crucial to refining these methods for optimal application in geospatial modeling and forecasting tasks, such as predicting COVID-19 infection trends in regions across Germany.
