Energy poverty is a persistent global issue where households lack access to adequate energy services. Research often focuses on contemporaneous factors, overlooking the predictive power of long-term socioeconomic trajectories. This study addresses two questions: How do past socioeconomic conditions afect future energy poverty? And what are the minimal interventions that could prevent a household from becoming energy-poor? We aim to shift the focus from reactive mitigation to proactive prevention by developing a framework that forecasts risk and identifies actionable pathways to avoid it. Using seven years of Australian longitudinal data, we train a machine learning classifier to predict energy poverty in the following year. We then apply counterfactual analysis to identify minimal, interpretable changes that alter the predicted outcome. The model successfully predicts future energy poverty with a ROC AUC of 70.01%. The counterfactual analysis consistently reveals that modest increases in household income, often less than 5%, are the most efective single intervention. Other factors, such as decreases in energy prices and reductions in unemployment, also contribute to preventing energy poverty, often in combination with income gains. “What-if” scenarios suggest that external shocks, like a sudden rise in energy prices or job loss, can be ofset by small, timely income adjustments. The efectiveness of these changes, whether recent or past, highlights the importance of long-term financial stability. Also, it enables proactive policy by identifying at-risk households a year in advance and suggesting targeted interventions as a more eficient alternative to broad measures.
Energy poverty remains a pressing global challenge, afecting the quality of life for millions of people. It
refers to a situation where households cannot access or aford adequate, reliable, and clean energy
services for their daily needs. Despite international eforts to address this issue, approximately 750 million
people still do not have access to electricity, and over 2 billion lack access to clean cooking fuels [
The consequences of energy poverty extend far beyond basic comfort. Limited access to energy
reduces educational opportunities, restricts access to jobs [
Many factors contribute to energy poverty. These include rising energy prices, economic instability,
and the presence of ineficient or poor-quality housing [
Besides identifying households at risk, it is equally important to consider what actions can help prevent energy poverty. In other words, if a household is predicted to become energy-poor, what actions could be taken, or could have been taken, to prevent this outcome? Ideally, these actions should require minimal intervention but provide the greatest benefit in terms of prevention.
Our work addresses these two gaps in the existing research: First (Contribution 1), we explore how past factors, such as income, energy prices, regional circumstances, and other socioeconomic variables, afect future energy poverty outcomes. We apply a machine learning algorithm that uses household-level data from seven previous years to predict energy poverty status in the following year. Second (Contribution 2), we use counterfactual analysis on the model developed in Contribution 1 to identify specific, minimal, and human-interpretable changes that could help a household shift from being energy-poor to non-energy-poor. These changes might result from personal actions or targeted policies. We refer to these as chains of minimal changes. We also present “what-if” scenarios that identify shocks which increase poverty risk and the minimal counterfactual response required to mitigate that risk.
Contribution 1 and Contribution 2 are complementary, and allow us to move from reacting to energy poverty after it occurs to taking proactive measures to prevent it. Our approach identifies households at risk one year in advance and provides practical suggestions for actions that require the least efort but have the greatest impact on preventing energy poverty. In this way, we bridge the gap between prediction and real-life intervention, providing practical guidance for policymakers, community organizations, and individuals seeking to reduce the long-term efects of energy poverty.
To conduct our analysis, we use the Household, Income and Labour Dynamics in Australia (HILDA)
Survey1, which is a nationally representative, long-term study that tracks the same individuals and
households in Australia from 2007 to 2021. The survey collects data on income, jobs, education, health,
and family life, providing a strong foundation to study how energy poverty changes over time. For
measuring “energy-poverty”, we employ the Multidimensional Energy Poverty Index (MEPI) [
Energy poverty can be defined as a household’s inability to aford or access energy services needed to
support adequate living conditions and human development. While conceptual definitions of energy
poverty have been the subject of extensive discussion in the literature (for an overview see Sy and
Mokaddem [
Based on the literature, energy poverty is a complex phenomenon stemming from a wide range
of factors. These include macroeconomic conditions like GDP, governance, and a country’s energy
mix [
Given the multi-layered nature of these determinants, a recent body of literature has introduced
machine learning techniques to predict energy poverty outcomes. Evidence based on a Extreme Gradient
Boosting (XGBoost) framework to predict the risk of experiencing energy poverty in the Netherlands
identifies income, house value, and house ownership as the main drivers of energy poverty [
While the previous studies are based on a single energy poverty indicator, other studies define a
multidimensional energy poverty index similar to ours [
We use the HILDA Survey, a comprehensive, nationally representative longitudinal study that examines the economic, social, and demographic dynamics of Australian households. Initiated in 2001 and conducted annually, it tracks individuals and households over time, providing important information on income, labor market activities, health, education, and family relationships, among other factors. The original 2001 sample included approximately 7,600 households and 13,000 individuals, with periodic updates to account for attrition.
The variables used to model energy poverty are described in Table 3 (Section C), and include labor market indicators (such as part-time employment rate, unemployment rate, and labor force participation), economic measures (GSP per capita and energy prices), and household characteristics (income, household size, and region). We also include individual information such as age, years of education, marital status, employment, health, and the presence of children in the household.
In this study, we approach energy poverty as a classification problem. Let ⊆ R be the feature
space, and denote an element (feature vector) by x ∈ . We employ a machine learning model
: → [
Outcome—The MEPI Indicator: The MEPI variable captures both expenditure-based and subjective dimensions. The expenditure-based measures include the 2M, TPR, and LIHC indicators. The subjective dimension is reflected by two self-assessed indicators: the household’s inability to pay for heating due to a lack of money (Heat), and the inability to pay electricity, gas, or telephone bills on time (Arrears).
The MEPI index is calculated as follows: Let = {1, . . . , } be the set of = 5 poverty indicators.
Let ℐ be a set of individuals, with element , ∈ ℐ, and be a set of time periods, ∈ , representing
a specific moment when the survey was conducted. Let denote the status of the -th individual in
the -th indicator during period . If an individual is poor under indicator in the period , then EP
takes the value of one, and zero otherwise. Following the family of indexes typically described in the
literature on material deprivation [
Although it is common to give the same importance () to each indicator, we focus more on the
indicators where deprivation is rare. This method is known as the Frequency-Based Weighting
Approach [
In the context of this work, an individual is regarded as energy poor if MEPI > 0 [
Variables and Data Preparation: We model energy poverty at time = 8 as a function of
socioeconomic and demographic characteristics observed in periods − 1, . . . , − 7 . We exclude the period
to ensure that our forecasting relies entirely on historical data. Our focus is on the role of past factors.
Including contemporaneous variables could potentially mask the efects of lagged factors, especially
if there is autocorrelation in the data. More importantly, the inclusion of contemporaneous variables
may introduce reverse causality between energy poverty and socio-demographic characteristics such
as health and education [
To capture the temporal dynamics of the variables, we created lagged features, which serve as the input to the predictive models. Generically, for each original feature, we obtained new features representing its values from each of the previous years.
We then split the dataset into training, validation, and test subsets to facilitate model development and evaluation. Out of the 7,977 participants in our dataset, 6,382 (80%) were randomly selected for training and validating the predictive models, while the remaining 1,595 participants (20%) were included in the test set. The test set was held out and used exclusively to evaluate the final performance of the models, providing a fair estimate of their forecasting accuracy. Moreover, the dataset is split by individual to prevent data leakage.
Before training the model, we standardized the data to ensure consistency and reliability in our
modeling process. The standardization parameters were estimated solely from the training set to avoid
information leakage. Specifically, we removed the median and scaled the data using the interquartile
range, as described in [
Model Development: We treat the energy poverty forecasting task as a classification problem. Specifically, households are classified as energy-poor depending on whether their MEPI is greater than 0 (cut-of point). To model the relationship between the socioeconomic and demographic factors and the MEPI indicator, we used a balanced bagging classifier.
A balanced bagging classifier [
We optimized the hyperparameters of our classifier using a grid search. For details on the specific hyperparameters and grid configurations, see Section A. We employed 5-fold cross-validation on the training dataset to ensure the robustness of the hyperparameters across diferent data splits, selecting the best set based on the highest Receiver Operating Characteristic - Area Under Curve (ROC AUC) score.
The final model was trained on the complete training set using the identified optimal hyperparameters and subsequently evaluated on a held-out test set of 1,595 participants.
In addition to the balanced bagging classifier, we tested two other class-imbalance ensembles. Namely,
we benchmarked the random under-sampling boosting [
Counterfactual Explanations: Counterfactuals are a post-hoc means to understand and explain the
model predictions [
Our focus is on minimal changes in order to ensure that the counterfactual recommendations remain practical and actionable, allowing individuals to make small adjustments that could have a meaningful impact on their future energy poverty risk. The minimal changes align with the concept of proximity, where the suggested profile modifications are as close as possible to the individual’s original state. Besides proximity, another relevant aspect is diversity, meaning that multiple plausible pathways out of energy poverty profiles should be considered.
In this work, counterfactual explanations are formulated as a constrained optimization problem, as
proposed by Mothilal et al. [
Formally, if is the total number of counterfactual examples to be generated, then the set of counterfactuals {x′}=1 is obtained by solving the following optimization problem: ⎧
{x′}=1 = arg min ⎨ ∑︁ ∑︁ · ( , ′, )
x′ ⎩ =1 ∈ℱ + 1 ∑︁ ℓ( (x′), 0) − ({x =1 ′}=1) }︃ , with
(︀ {x′}=1︀) = ∑︁ ∑︁
Δ(x′, x′), =1 =+1 Δ(x, x′) = ∑︁ ( , ′ ), ∈ℱ where the first term measures the weighted distance between the original instance x and each counterfactual x′. The per-feature distance (, , ′, ) measures the change for feature ∈ ℱ . The term is a binary mask, where = 1 if feature is mutable and = 0 otherwise. The weight reflects the dificulty of changing feature and is defined as the inverse of the median absolute deviation (MAD).
The second term is a hinge-style loss on the logit of the predicted probability: ℓ︀( (x′), 0︀) = max(︀ 0, 1 + logit(︀ (x′))︀ , where logit() = ln
1 − .
This penalizes any counterfactual x′ whose predicted probability (x′) is not confidently below the decision boundary for class 0.
The third term promotes diversity among the generated counterfactuals by maximizing their pairwise
distances. To avoid overloading notation, we distinguish between a per-feature distance (·, ·) and a
vector-level distance Δ(·, ·):
(3)
(4)
(5)
(6)
and, following Mothilal et al. [
That is, corresponds to the 1 change for continuous features, while categorical feature
modifications are penalized uniformly to discourage unnecessary changes [
The parameters and control the trade-of between proximity, classification change, and diversity. In our analysis, we set = 5
and = 2.5 . We used a genetic algorithm to solve Equation (3) and generated = 50 counterfactuals for each of the prototype profiles described below.
In our analysis, we set = 5 and = 2.5 , based on preliminary tests with alternative parameter values. These tests indicated that a lower resulted in counterfactuals needing larger changes in features, making them unrealistic for households. On the other hand, higher values limited proximity too much. Similarly, varying showed that values that were too small limited diversity, and values that were too large reduced interpretability. The selected values ofered the best trade-of between minimal, realistic changes and suficient diversity. the set of immutable features. We impose the following constraints, for all = 1, . . . , : To encode immutability explicitly, let ℳ ⊆ ℱ
denote the set of mutable features and ℐ = ℱ ∖ ℳ ′, = , ∀ ∈ ℐ. within a ±5% ∈ ℱcont. ∩ ℳ,
To ensure realism and actionability, we also restrict changes in continuous mutable features to lie band around their original values. Let = 0.05 . Then, for all = 1, . . . , and all (1 − ) ≤ ′, ≤ (1 + ) .
We note here that counterfactual explanations are closely related to, and often considered a form
of, contrastive explanations [47]. The literature, however, draws a subtle distinction between the
two. Contrastive explanations primarily identify the features responsible for a classification (e.g., “The
household is energy-poor because of its low income”) [48], whereas counterfactuals identify the minimal
changes that would alter the outcome (e.g., “The household would not be energy-poor if its income
were increased by X”) [
To obtain a small set of representative borderline cases, we first define borderline profiles as those for which the model predicts class 1 with low confidence. Specifically, when the predicted probability (x) lies in the range [0.5, 0.5 + ], with = 0.05. That is, the borderline sample set is defined as
= {x | (x) ∈ [0.5, 0.55] and , ^ = 1} , where ^ = arg max (x) denotes the predicted class label.
We then compute the empirical mean of the set = {x}=1 as x = 1 ∑︁ x.
=1 1 = arg mx∈in ‖x − x‖2 .
The first prototype 1 is chosen as the observation in closest to this mean, i.e., Subsequent prototypes { }=2 are selected using the farthest-first traversal rule: ︂[
︂] = arg max x∈ 1≤m<in ‖x − ‖2 , = 2, . . . , , 27–43 (7) (8) (9) (10) (11) (12) (13) ensuring that each new prototype maximizes its minimum Euclidean distance to the already-selected set. This procedure yields diverse, actual observations from the borderline region, with 1 capturing the central tendency and the remaining { }≥2 spanning the range of variability in feature space.
In our application, we selected = 3 prototypes.
Predictive Model (Contribution 1): A grid search was conducted to optimize the balanced bagging classifier’s configuration for = 8. The best setup included 100 estimators with bootstrapping of features but not samples. Each estimator sampled 50% of the data, and the sampling strategy ensured an equal representation of energy-poor and non-energy-poor instances. Replacement was used in the resampling process.
Our approach predicts energy poverty status in the eighth year for each household, using information from the previous seven years as input features. The model achieved a ROC AUC of 70.01%, which indicates that the model can discriminate between energy-poor and non-energy-poor households across varying decision thresholds. For class-specific metrics, sensitivity was 73.25%, meaning that the model correctly identified most energy-poor cases. The specificity of 66.77% indicates an acceptable rate of correctly classifying non-energy-poor households.
These results show that the model favors sensitivity. This is useful for policy design, where identifying the most energy-poor households is more important than avoiding the misclassification of some nonenergy-poor households. High sensitivity supports early interventions from a prevention perspective, while reasonable specificity keeps misclassifications within an acceptable range.
Overall, our results support the use of balanced ensemble methods with appropriate sampling and parameter selection to model energy poverty using historical data.
Counterfactuals (Contribution 2): To interpret the predictive model and develop actionable insights, we conducted a counterfactual analysis on three representative prototype profiles, as described in Section 3. Each prototype represents a borderline energy-poor household, where the model predicts energy poverty with relatively low confidence. It is important to note that, for interpretability, all features were transformed back to their original scale by applying the inverse of the preprocessing transformation. Moreover, the immutable features include demographic attributes such as age and age group classifications, marital status (including being married, divorced, or widowed), the presence of a disability, the presence of children in the household, and the household size.
For each prototype, we generated 50 diverse counterfactual examples that change the predicted class from energy-poor to non-energy-poor (i.e., from class 1 to class 0), while requiring only minimal and realistic changes to the input features. All generated counterfactual profiles satisfy the classification constraint (x′) = 0.
We examined the full set of generated counterfactuals and analyzed the types of changes required to shift a household’s classification. Among these, we identified a subset of counterfactuals that involved only a single actionable modification. In all such one-action counterfactuals, the feature that was changed was household income. That is, all one-action classification changes across the three prototypes were achieved solely through an increase in income. No other individual feature was suficient to produce a change in predicted energy poverty status when modified in isolation.
The timing of these interventions varied across diferent counterfactuals. Successful income changes tended to occur in more recent years, most frequently in = 6 and = 7, but also appeared in earlier years, including = 1 and = 2. This indicates that while recent changes in income have strong predictive power, improvements in earlier years can also contribute meaningfully to reducing energy poverty risk. The scale of required income changes was generally modest, but varied slightly depending on the year. In year = 1, the required increase ranged from 3.18% to 3.81%; in = 2, from 2.76% to 4.03%; in = 6, from 1.83% to 4.93%; and in = 7, from 1.30% to 4.82%. These ranges show that efective interventions can occur across multiple time points and typically demand income increases of less than 5%. This suggests that relatively small financial improvements, whether recent or distributed over a longer time horizon, can be suficient to prevent energy poverty for households at the margin.
Figure 1 shows several connected counterfactual (with more than one action) pathways that lead from an energy-poor to a non-energy-poor household profile at time = 8. Each path represents a sequence of minimal changes to selected features in earlier years. The figure illustrates the range of time steps and features through which this transition can be achieved.
Across all paths, an increase in household income appears as a consistent component. Income changes are present at multiple time points, including = 1, = 2, = 6, and = 7. The required increases range from 2.26% to 4.36%, confirming earlier results that show small changes in income are efective in changing the classification of households that are near the energy poverty threshold.
In addition to income, other features involved in the transitions include energy price, unemployment rate, and part-time employment rate. Decreases in energy prices at = 1 and = 3, and reductions in unemployment at = 4 and = 7, contribute to multiple successful pathways. Several paths combine income changes with labor market improvements, such as a decrease in the part-time employment rate at = 6 or = 7.
The timing of the changes is also significant. While most changes occur in the final time step ( = 7), efective changes in earlier years, especially ≤ 4 , also appear. This suggests, similar to the one-action counterfactuals, that both recent and earlier interventions can influence future energy poverty status.
Time Periods 1 2 3 4 5 6 7 8
Energy-poor Household Energy price (↓ 1.88%) Household income (↑ 2.26%) Household income (↑ 4.28%) Unem(p↓lo4y.5m6%en)t rate Change on energy price (↓ 2.10%) Part-time employment
rate (↓ 1.03%) Household income (↑ 4.28%) Unem(p↓lo4y.9m7%en)t rate Household income
(↑ 4.10%) Household income
(↑ 2.82%) Household income
(↑ 4.36%) Part-time rate (↓ 1.47%)
Non-energy-poor
Household
Shocks (Contribution 2): To further explore how households may avoid energy poverty under diferent conditions, we present in Table 1 a set of scenarios based on selected multi-feature counterfactuals. These scenarios describe situations in which a change in a macroeconomic or household-level factor (in other words, a shock) increases the risk of energy poverty. For each situation, we identify the minimal change that the model associates with successfully avoiding this outcome.
In one scenario, energy prices rise by 3.03% in year = 4. The model finds that a compensating income increase of 2.92% in year = 7 is required to prevent the household from entering energy poverty. Similarly, when energy prices increase by 3.16% in year = 6, a larger income adjustment of 4.82% in = 7 is needed to ofset the rising cost burden.
Changes in labor force participation also play a role. When the total labor force participation rate → → →
drops by 2.15% in year = 5, the model identifies a 3.23% income increase in = 7 as suficient to prevent energy poverty. Shifts in energy cost volatility show a similar pattern. When the energy price change rate increases by 3.46% in year = 2, future income must increase by 3.73% in = 7 to avoid a negative classification.
A final scenario involves a complete loss of employment, with the individual becoming fully unemployed in year = 2. In this case, a modest income increase of 1.83% in year = 6 is suficient to counterbalance the risk introduced by the unemployment shock.
These scenarios show that while the causes may difer, income remains the most frequent feature requiring adjustment. Small income increases, aligned with observed external conditions, are often enough to reduce the likelihood of energy poverty according to the learned model.
Our study suggests a novel approach to energy poverty prevention by combining a machine learning algorithm with counterfactual analysis. We used a machine learning algorithm to predict energy poverty one year in advance and identify minimal-efort interventions. With this, our work shifts the focus from reactive mitigation to proactive prevention.
The primary contribution of this work is a framework that not only identifies households at risk of future energy poverty but also provides actionable, human-interpretable pathways to avoid it. Our model achieved a ROC AUC of 70.01%, and can therefore distinguish between future energy-poor and non-energy-poor households using only historical data. The model’s sensitivity (73.25%) is significant from a policy perspective as it focuses on accurately identifying households at risk, which is essential for successful early intervention. This provides the Contribution 1 of this work.
Our counterfactual analysis highlights the central role of household income. In all the prototype profiles, a modest rise in household income was always the most efective way to change a household’s predicted condition from being energy-poor to not being energy-poor. This was true for both singleaction and multi-feature counterfactuals. The required income increases were often less than 5%, suggesting that for households on the borderline, relatively small financial improvements can make a significant diference.
Our results also highlight the long-term nature of energy poverty. The use of data from the preceding
seven years confirms that energy poverty is not merely a consequence of immediate circumstances but
is related to a household’s long-term socioeconomic trajectory. This challenges the conventional focus
on contemporaneous factors and suggests that policies must consider the cumulative impact of past
conditions. Interestingly, our analysis revealed that interventions could be efective at various time
points. For example, both recent income gains (in years = 6 and = 7) and earlier improvements
(in years = 1 and = 2) were shown to reduce future risk. This implies that both sustained financial
health and timely support can be critical for prevention. We highlight here that the contemporaneous
relation between income and energy poverty has been highlighted in previous work [
Other indicators of energy poverty include the unemployment rate, the rate of part-time employment,
and the cost of energy. Concerning energy prices, their connection to energy poverty aligns with recent
research [
In addition to the counterfactual analysis, we examined whether small year-to-year income increases are associated with improvements in MEPI values in the observed data. The results indicated that households experiencing a modest income increase of less than 5% exhibit a lower average MEPI (0.051) compared to households without such an increase (0.062). Regression results in Table 2 of Section B confirm that these diferences are statistically significant. A small income increase is associated with an average reduction in MEPI of 0.011 ( < 0.001), even after controlling for year fixed efects and clustering standard errors at the household level. These findings support the plausibility of our counterfactual scenarios, showing that the small changes in income identified through the framework align with realistic transitions found in the HILDA dataset.
All things considered, the findings of this study ofer concrete guidance for policymakers and social support organizations. The predictive model can serve as a tool to identify households that are likely to face energy poverty. This allows for early, targeted support to prevent the problem before it fully develops. The counterfactual analysis complements the model’s predictions by generating interpretable scenarios for intervention. It also provides evidence-based strategies with minimal interventions to prevent energy poverty.
For policymakers, this framework supports the design of more eficient and cost-efective programs. Instead of implementing broad, untargeted subsidies, governments could deploy precise interventions, such as small, targeted income supplements, financial counseling, or employment support for households lfagged by the model. The scenarios presented in Table 1 illustrate how such support could be tailored to ofset specific external shocks, like rising energy prices or a drop in labor force participation. This counterfactual analysis constitutes the Contribution 2 of our work.
For non-governmental and community organizations, our findings reinforce the importance of programs aimed at improving income stability. The evidence that even small income increases can be highly efective provides a strong rationale for prioritizing such initiatives.
However, we acknowledge several limitations in this explanatory study. First, the predictive power of our model (ROC AUC of 70.01%) is good but not perfect. Misclassifications are inevitable, and it is important to consider their real-world consequences. A false positive (wrongly flagging a household as at-risk) may lead to ineficient allocation of resources, while a false negative (failing to identify a household that will become energy-poor) means a missed opportunity for prevention. Second, our counterfactual analysis is based on the patterns learned by the model, but these should not be interpreted as definitive causal links. For instance, while an income increase is associated with avoiding energy poverty, our study does not model the underlying cause of that increase (e.g., a new job, a promotion, or a government benefit), which could have its own complex efects. The prototype approach does not distinguish cases where profiles are close in feature space but difer in which features contribute to that similarity. Another limitation is the uniform treatment of households, which overlooks heterogeneity in responses to energy poverty predictors. In other words, this approach implicitly assumes that all households above the threshold experience energy poverty in a similar way. However, in practice, households may face very diferent forms of deprivation. Factors such as income, age, education, and personal traits likely influence how individuals experience and respond to energy challenges [ 49]. Finally, our findings are based on data from the HILDA survey. The specific drivers of energy poverty and the efectiveness of certain interventions may difer in other countries with diferent climates, energy markets, economic conditions, and social safety nets. Therefore, the generalizability of our results to other contexts should be approached with caution.
This work was partially supported by FCT-Fundação para a Ciência e a Tecnologia, Portugal through project PRODY: PTDC/CCI-COM/4464/2020; by NOVA LINCS ref. UIDB/04516/2020 (https://doi.org/10.54499/UIDB/04516/2020) and ref. UIDP/04516/2020 (https://doi.org/10.54499/UIDP/04516/2020) with the financial support of FCT.IP; by LARSyS ref. LA/P/0083/2020 (https://doi.org/10.54499/LA/P/0083/2020) and ref. UIDP/50009/2020 (https://doi.org/10.54499/UIDP/50009/2020) the financial support of FCT.IP; and with the financial support provided by the 2022 R&D&I National Projects and 2021 Strategic Projects Oriented to the Ecological and Digital Transition by the Spanish Ministry of Sciences and Innovation (Refs: PID2022-143254OB-I00 and TED2021-132824B-I00).
Diogo Nuno Freitas was supported by the Portuguese Foundation for Science and Technology with the grant number 2021.07966.BD (https://doi.org/10.54499/2021.07966.BD).
We thank Fábio Mendonça (https://orcid.org/0000-0002-5107-3248) for reviewing the introduction and methodology sections of this work and providing valuable feedback.
During the preparation of this work, the authors used GPT-4o and Grammarly in order to: Grammar and spelling check. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content. [47] I. Stepin, J. M. Alonso, A. Catala, M. Pereira-Fariña, A survey of contrastive and counterfactual explanation generation methods for explainable artificial intelligence, IEEE Access 9 (2021) 11974–12001. doi:10.1109/ACCESS.2021.3051315. [48] A. Dhurandhar, P.-Y. Chen, R. Luss, C.-C. Tu, P. Ting, et al., Explanations based on the missing: Towards contrastive explanations with pertinent negatives, in: Proceedings of the 32nd International Conference on Neural Information Processing Systems (NeurIPS), volume 31 of Advances in Neural Information Processing Systems, Curran Associates Inc., Montréal, Canada, 2018. doi:10.48550/arXiv.1802.07623. [49] S. Cong, D. Nock, Y. L. Qiu, B. Xing, Unveiling hidden energy poverty using the energy equity gap, Nature communications 13 (2022) 2456. doi:10.1038/s41467-022-30146-5. A. Model selection and grid search parameters To identify the optimal hyperparameter configurations for predicting energy poverty, a grid search approach was implemented. This process systematically tested combinations of model parameters and evaluated their performance using cross-validation.
We used 5-fold cross-validation on the training dataset to ensure that the models were validated on various data splits and that the hyperparameters chosen were robust across diferent subsets of data. The best set of hyperparameters was then chosen based on the highest average ROC AUC score from the validation folds. The ROC AUC score measures the model’s ability to discriminate between energy-poor and non-energy-poor households.
Additionally, the grid search utilized the one-vs-rest framework, which creates a binary classifier for each class.
All models were optimized and trained using Python, and the scikit-learn library for model implementation and evaluation. The model description and the parameters used in the grid search optimization are detailed below.
Balanced bagging
A balanced bagging classifier [
The parameter grid included the following parameters: • Number of estimators: 10, 50, 100 • Maximum samples (proportion): 0.5, 1.0 • Maximum features (proportion): 0.5, 1.0 • Bootstrap sampling: True, False • Bootstrap feature selection: True, False • Sampling strategy (proportion): Auto, 0.5, 1.0 • Replacement: True, False B. Robustness Check: Income Increases and MEPI
Results are based on OLS regression with robust standard errors clustered by household. Households experiencing a modest year-to-year income increase of less than 5% exhibit a lower average MEPI (0.051) compared to households without such an increase (0.062). Regression results confirm that these diferences are statistically significant.
A small income increase is associated with an average reduction in MEPI of 0.011 ( < 0.001), even after controlling for year fixed efects and clustering standard errors at the household level.
These findings support the plausibility of our counterfactual scenarios by showing that the small income changes highlighted by the framework correspond to realistic and observed transitions in the HILDA dataset.
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