This paper discusses the connection between regularization and causality, resting on the simple problem of linear regression, using ridge regression and Lasso as illustrative cases study for their argument. The paper provides original insights on the link between both regularization and causality. For the final version, it would be nice if the authors could introduce a bit more context on do-calculation (two lines stating that this is a pivotal tool from the framework of causality) and give more practical insights on the consequences of their results.

This study introduces a novel approach that integrates agricultural census data with remotely sensed time series to develop precise predictive models for paddy rice yield across various regions of Peru. By utilizing sparse regression and Elastic-Net regularization techniques, the study identifies causal relationships between key remotely sensed variables-such as NDVI, precipitation, and temperature-and agricultural yield. To further enhance prediction accuracy, the first- and second-order dynamic transformations (velocity and acceleration) of these variables are applied, capturing non-linear patterns and delayed effects on yield. The findings highlight the improved predictive performance when combining regularization techniques with climatic and geospatial variables, enabling more precise forecasts of yield variability. The results confirm the existence of causal relationships in the Granger sense, emphasizing the value of this methodology for strategic agricultural management. This contributes to more efficient and sustainable production in paddy rice cultivation.