Counterfactual Explanations for Sustainable Tourism Indicators: Implementation in a Shiny Application

XLI Congreso Nacional de Estadística e Investigación Operativa

E. López Cano¹, J. Saugar¹, C. Lancho Martín¹, M. Cuesta², I. Martín de Diego¹, A. Amado³

(1) Data Science Laboratory, Universidad Rey Juan Carlos; (2) Universidad Carlos III; (3) Dephimáticas, S.L.

XML & Sustainable Tourism Indicators

Publication

Saugar, J., Lancho, C., Cuesta, M., Cano, E.L., de Diego, I.M., Amado, A. (2025). Counterfactual Explanations for Sustainable Tourism Indicators. In: Julian, V., et al. Intelligent Data Engineering and Automated Learning – IDEAL 2024. IDEAL 2024. Lecture Notes in Computer Science, vol 15346. Springer, Cham. https://doi.org/10.1007/978-3-031-77731-8_20

Explainable Machine Learning

provide simple explanations on complex Machine Learning (ML) models.

Counterfactuals

Through understandable “what if” scenarios, counterfactuals explore how changes in the input data affect the results of a model

Sustainable tourism indicators

Indicators such as “Average expense”, “Average stay”, “Percentage of tourism in GDP”, are classified into Dimensions.
Indicators are scaled using a given method (z-score, Min-Max, or distance to a reference value). Let \(x_j\) be such scaled indicators.
A composite indicator by dimension \(y\) is computed then as a weighted average:

\[y = \sum_{j=1}^{p} w_j x_j\]

The Global Sustainable Tourism Indicator (STI) is the weighted average of the dimensions indicators:

\[STI = \sum_{j=1}^{p} w_j x_j\]

Question to answer

What indicators does a destination need to change in order to improve the STI by a given amount?

Find the minimum and plausible changes \(\beta_j\) that can be made to the input variables \(x_j\) to achieve a desired change \(\varepsilon\) in the global indicator \(y\):

\[y' - y = \sum_{j=1}^{p} w_j (x_j + \beta_j) - \sum_{j=1}^{p} w_j x_j \geq \varepsilon\]

Model

\[\begin{align} \min \quad & \sum_{j=1}^{p} \beta_j + \lambda \sum_{j=1}^{p} \delta_j \label{f_obj} \\ \textrm{s.t.} \quad & y' - y = \sum_{j=1}^{p} w_j (x_j + \beta_j) - \sum_{j=1}^{p} w_j x_j \geq \varepsilon \label{y_epsilon} \\ %& \beta_j \leq a \cdot f_{std}(x_j), & \forall j = 1,\dots,p \label{beta_std} \\ & x_j + \beta_j \leq 1, & \forall j = 1,\dots,p \label{x_j_max1} \\ & \mu_{l} \leq \sum_{j=1}^{p} \delta_j \leq \mu_{u} \label{num_var_change} \\ &\beta_j \leq a f_{std}(x_j) \delta_j & \forall j=1,\dots,p \label{beta_binary} \\ % & \delta_j \leq \beta_j \leq m \delta_j & \forall j=1,\dots,p \label{beta_binary} \\ & \delta_j \in \{0,1\} & \forall j=1,\dots,p \label{delta_binary} \\ &\beta_0, \dots, \beta_p \geq 0, \ \beta_0, \dots, \beta_p \in \mathbb{R} \label{beta_0_real} \\ & \lambda \geq 0, \lambda \in \mathbb{R} \label{m_constant_large_enough} \end{align}\]

Model

The objective function \(\sum_{j=1}^{p} \beta_j + \lambda \sum_{j=1}^{p} \delta_j\) minimizes the changes made over the input variables (\(\beta_j\)), and the number of variables where a change is made (\(\delta_j\)).
Constraint \(y'-y \geq \varepsilon\) ensures that the new value \(y'\) of the indicator has increased in at least \(\varepsilon\), addressing the validity property.
To guarantee the plausibility property, constraint \(\beta_j \leq a f_{std}(x_j) \delta_j\) establishes the maximum change admitted in every variable \(x_j\) through a function \(f_{std}(\cdot)\) of its corresponding standard deviation. \(\delta_j \in \{0,1\}\) are binary variables controling which input variables some changes are made.
The actionability property is ensured with constraint \(x_j + \beta_j \leq 1\), which maintains each variable \(x_j\) within \([0,1]\).
Constraint \(\mu_{l} \leq \sum_{j=1}^{p} \delta_j \leq \mu_{u}\)controls the minimum and maximum number of \(x_j\) variables where a change is admitted.

The formulation of the problem involves different user-fixed parameters (\(\lambda\), \(\varepsilon\), \(f_{std}(\cdot)\), \(\mu_l\), \(\mu_u\) and \(a\)) that allow its adaptation to different scenarios, depending on the domain requirements.