An Explainable Framework Integrating Local Biplots and Gaussian Processes for Unemployment Rate Prediction in Colombia

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors' interesting and technically sound work integrates machine learning with explainability in unemployment forecasting. The paper demonstrates an innovative combination of UMAP-based local biplots and Gaussian Process regression, delivering high predictive accuracy and improved interpretability compared to traditional econometric models. The application to Colombia’s labor market, supported by long-term official datasets, provides a rich context for testing the framework.

However, several flaws limit the current version’s scientific clarity and practical impact. First, the paper lacks a formally stated objective, clear hypotheses, or a definition of the scientific problem. This weakens the logical structure and makes it difficult to assess the results in light of a testable research plan. Second, while Section 2.1 presents the dataset thoroughly, the practical economic relevance of using the unemployment rate as the primary outcome variable is underdeveloped. The authors should justify why monthly unemployment, often a methodologically smoothed and slowly varying indicator, is suitable for dynamic machine learning forecasting. Moreover, the applicability of the model to other indicators (e.g., inflation, interest rates, price levels), which are more volatile and commonly forecasted, should be discussed explicitly to clarify the broader value of the approach. Third, the model performance assessment lacks several critical elements: MAPE is not reported, no confidence intervals are presented, and it does not visualize the comparative forecasts (e.g., Figure 9) but only hyperparameter dynamics, omitting direct comparison plots between predicted and actual series. Finally, the conclusions do not clearly articulate the specific contribution of the authors or the practical utility of combining UMAP and Gaussian Processes for policymakers. The political values (for decision making) of predicted unemployment levels are briefly mentioned in the analysis but not substantiated in the conclusions.

The paper is potentially good, but it needs methodological refinement and a more explicit demonstration of its practical value for economic forecasting and decision-making support. Strengthening the structure, clarifying the dataset relevance, and completing the model validation would significantly improve its scientific soundness.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors address a classical and consistently relevant topic: the forecasting of macroeconomic variables. They compare various conventional time series methods with machine learning algorithms to predict unemployment rates and find that a supervised kernel-based relevance analysis, under the assumption of Gaussian processes, yields the best predictive performance. Additionally, the authors employ a biplot analysis using UMAP to illustrate the strength of the relationship between the explanatory variables and unemployment rates.

Overall, the paper is well-written and methodologically acceptable, which gives it potential to contribute to the literature. However, in my opinion, there are some concerns to be addressed by the authors:

1.In the tittle, better do not use acronyms.

2.Some statements, especially the economic ones, need improvement.

In the abstract, it is stated that “In Colombia, tackling unemployment is particularly vital for crafting impactful public policies (…).” Well, this applies to any country. The ability to forecast macroeconomic magnitudes is necessary in all countries.

It is not true that “Unemployment is not a deep-rooted problem around the world.” There are indeed countries where it is a relevant structural issue.

The authors state that “Unemployment forecasting is inherently challenged by the non-stationary and non-linear nature of economic data.” → This is a commonly held view, but it should be supported with a citation or tested for non-stationarity in their sample.

The authors claim that “Additionally, non-linearity reflects the fact that the relationships between unemployment and its driving factors are not constant but instead evolve in response to changing macroeconomic dynamics.” → It could still be linear, but with varying intensity.

The authors write that “In turn, traditional machine learning techniques, such as Support Vector Machines (SVM), Random Forest (RF), and Gaussian Processes (GP), have been extensively utilized in predictive modeling.” → There should be a review of applications of these techniques (or some of them) in the context relevant to the paper (macroeconomics/labor economics).

The selection of explanatory variables should be better justified (which variables were used by whom/in which work).

 3.Regarding the development of the application:

What is the data frequency? Are lagged variables used? Are predictions made on levels or first differences? What is the prediction horizon?

It would be useful to present descriptive statistics of the variables used over the analyzed time horizon.

In Section 3, a new subsection should be added to explain the validation strategies of the proposed methodology.

It should be clarified which explanatory variables are used in each of the competing methodologies. For example, in ARIMA, lags of the predicted time series are usually employed.

 4.There is a broad literature on forecasting in economics using non-econometric instruments.

For example, backpropagation neural networks have been used since the 1990s. With this, I mean that in the discussion section, the authors should relate their findings to other findings in the literature on the use of ML methods in forecasting unemployment/macroeconomic magnitudes. This connects with the previous query about the use of machine learning methods in the specific context employed by the authors.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1.  The author claims that the model has "explainability," but the whole article only discusses the visualization (such as UL-Biplot) and variable weights (such as the lengthscale parameter in GP) from the algorithmic dimension, without constructing any explicit economic model or hypothetical path about the mechanism of determining the unemployment rate. Macroeconomic theories (such as the theory of the natural rate of unemployment and the Phillips curve) are not combined to support the empirical framework. Therefore, the nature of so-called "interpretability" is limited to "vector visualization" at the mathematical level, which is significantly different from the "interdisciplinary semantic interpretation" increasingly emphasized by Computation or related interdisciplinary journals.
2. Among the seven variables integrated in this paper, "Real Salary" (RS), "General Participation Rate" (GPR), and "Economic Monitor Index" (EMI) are highly correlated and can all be regarded as approximate proxies for job market performance. However, the paper does not conduct any treatment or test on the collinearity or causal direction between variables. In addition, as the core driving factors of the predicted unemployment rate, variables such as government expenditure, foreign investment, and manufacturing employment are ignored, which makes the composition of input variables obviously incomplete and reduces the realistic explanatory power of the forecast results.
3. The authors compared the proposed GP model with ARIMA, SARIMA, Lasso, and others and concluded that "GP is better." However, the experimental part is obviously more adequate to the tuning of GP models, such as KerasTuner, sliding window verification, time lag variable construction, etc., while the traditional models such as ARIMA are only simply processed without standard steps such as seasonal difference, multi-order comparison, and residual white noise test. This comparison method is obviously biased towards deep models, which cannot form a truly fair model evaluation system, and also weakens the effectiveness of "improving prediction ability" claimed by this paper.
4. There are too many graphs in this paper; for example, Figures 4-8 show multiple UMAP clustering visualization graphs in succession, but the actual information content is highly repeated, and there is a lack of further analysis of these clustering structures and policy variables (such as government turnover and fiscal policy changes). In Figure 5, the stratification of political tenure is shown as the clustering basis, but the results show that there is "almost no difference."
5. Although this paper combines UMAP with Gaussian process on the technical route, the combination has been widely used in the field of machine learning, such as medical images, natural language processing, and social behavior prediction. This paper does not propose a new method, nor does it expand the existing theoretical boundary, and the so-called "innovation" is more reflected in method transfer than method breakthrough. In addition, the research object is limited to a single country, Colombia; the amount of data is small (228 records); the generalization ability and empirical value are limited; and it is difficult to support the "threshold of academic contribution" of high-level publication.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have substantially addressed the flaws previously identified in the revised manuscript. The manuscript has been structurally and scientifically enhanced, improving its clarity, depth, and practical relevance. The paper may be published

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Some of the comments have been more or less incorporated into the text. However, it still remains unclear which variables and how many lags are used as inputs in each method employed to predict the unemployment rate. As I already mentioned in the previous review, it is not clear whether the supposedly explanatory variables (such as real wages) are only used to analyze the biplots or whether they are also included, with lags, as inputs in the machine learning methods employed.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for your paper.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

None