A Replication Study of Topological Data Analysis for Power-Grid Forecasting in Tanzania: Regularization and Cross-Validated Model Selection

Topological Data Analysis (TDA) has been increasingly applied in various fields due to its ability to capture complex structures and patterns in data. This study focuses on TDA for power-grid forecasting in Tanzania, specifically examining the impact of regularization techniques and cross-validated model selection. The purpose is to replicate a previous study's methodology to assess the effectiveness of different regularization methods and model selection strategies in improving the accuracy of power-grid forecasts. The objectives include validating the original findings, identifying potential improvements or limitations, and contributing new insights into TDA applications for energy systems. A replication study design was employed, involving a detailed reimplementation of the original methodology using the same dataset from Tanzania's power grid. Regularization techniques such as L1 and L2 regularization were applied, and cross-validation methods (k-fold) were used to select optimal models. The performance metrics included mean absolute error (MAE) and root mean squared error (RMSE). The findings indicate that L2 regularization generally outperformed L1 in reducing overfitting while maintaining a good balance between bias and variance, as evidenced by lower RMSE values during cross-validation. The model selection process using k-fold cross-validation significantly improved the robustness of the forecasting models. The study concludes that TDA, when combined with appropriate regularization methods and cross-validated model selection, can enhance the accuracy of power-grid forecasts in Tanzania. However, further research is needed to explore other potential improvements and generalizations. Recommendations include exploring more advanced regularization techniques and incorporating additional exogenous variables into the forecasting models for better performance. Future studies should also consider larger datasets and longer time horizons to validate the findings on a broader scale. Topological Data Analysis, Power-grid Forecasting, Regularization, Cross-Validation This study contributes new insights into the application of TDA for power-grid forecasting by demonstrating the effectiveness of L2 regularization in improving model accuracy through cross-validation.