Childhood obesity is a persistent challenge for society since it is highly related to insulin resistance and a wide range of other chronic diseases, which impair not only the health of the people, but also the health system itself due to extra costs of treating them. In this context, it is imperative to consider innovative approaches, like eXplainable Artificial Intelligence, to understand the factors underlying childhood obesity. Data imbalance has been thoroughly studied in classification, but scarcely studied in regression since classes do not exist. However, extreme values in continuous domains, which are usually minority are often the most clinically relevant. Facing the imbalance in regression while obtaining explainable models has never been studied. In this application work, we adopt a Machine Learning approach to obtain explainable regression models for imbalanced continuous targets in childhood obesity, as HOMA-IR and Waist Circumference. We consider 79 variables, including targeted metabolomics, targeted proteomics, exposomic data (e.g., the physical activity subdomain), hematological parameters and anthropometry of Spanish children from 3 to 18 years with significant imbalance ratios around 12% in HOMA-IR and Waist Circumference. Even though we mainly focus on extensions of linguistic fuzzy rule-based systems, particularly designed for explainability, we also consider highly accurate complementary approaches as Random Forest that could additionally provide contrast interesting information by post-hoc SHAP. The models so obtained are better considering the relevant minority information (17% improvements in F1). Moreover, they seem to properly explain biologically meaningful relations, as in the case of physical activity data or the one with the follicle stimulating hormone, among others.
Childhood obesity entails a persistent challenge for society with consequences in the short
and long term. It represents a risk factor for adult obesity, Insulin Resistance (IR) and the
metabolic syndrome (metS), which pose an increased risk of cardiovascular diseases, type 2
diabetes, stroke, etc. Furthermore, it is also related to other chronic diseases, such as respiratory
disorders, musculoskeletal disorders and liver disease. [
Thus, the need for innovative and personalized approaches for the prevention and treatment
of childhood obesity arises. This research involves the analysis of omics data (genomics,
epigenetics, exposomics, metabolomics, etc.), and advanced tools, such as Machine Learning
(ML), which enable the integration of these data and provide a more holistic vision of the issue.
It is evident but crucial that the models generated in health-related issues must not only predict
the variables of interest, but also provide detailed insights on the underlying factors. Following
this idea, eXplainable Artificial Intelligence (XAI) [
In addition, real-world problems frequently involve imbalanced data due to limitations in data collection, the scarcity of cases, etc. For instance, in a study on childhood obesity, while most children may present a slightly elevated Body Mass Index (BMI), there may be a lack of children who are severely obese, the most clinically relevant. A considerable imbalance seriously impacts and biases the models, so it must be treated. This problem has been extensively studied in classification, but scarcely studied in regression since classes do not exist.
Some of the current proposals are pre-processing techniques, such as the over-sampling
method SMOTE for regression [
In this application work, we explore a pioneering approach that, for the first time, concurrently
addresses both explainability and imbalanced regression. Our aim is to develop interpretable
regression models for two imbalanced continuous targets in childhood obesity: The
HOMAIR and Waist Circumference z-scores (zHOMA-IR and zWC, respectively). We mainly focus
on the extension of a linguistic fuzzy rule-based system, originally called LING [
We consider 79 variables, including targeted metabolomics (e.g., cardiometabolic and
hormonal biomarkers), targeted proteomics (e.g., inflammatory and hepatic biomarkers), some
subdomains of the exposome (e.g., the physical activity subdomain, obtained by accelerometry,
family history, and socioeconomic and demographic factors), as well as hematological
parameters and anthropometry, of Spanish children from 3 to 18 years. Although all children are obese
or overweight, zHOMA-IR and zWC present significant imbalance ratios around 12% due to a
lack of representation of exceptionally high values, which are in fact the most clinically relevant
cases. The said modification of the linguistic algorithm FSMOGFS +TUN proposed in [
The models generated through the proposed approaches exhibit notable improvements in considering the relevant minority information, resulting in F1 1 increases over 17%. These models efectively enlighten biologically significant relationships among the variables and the predicted targets, as in the case of physical activity data or the one with the follicle stimulating hormone (FSH), among others.
This work is organized as follows. In Section 2, we explore the concept of imbalanced regression and its implications in real-world problems. In Section 3, we focus on childhood obesity prediction, as we describe the case study (Section 3.1), the challenges of omics and data pre-processing (Section 3.2) and the importance of considering imbalance in this particular regression problem (Section 3.3). In Section 4, we present our linguistic rule-based system for explainable imbalanced regression. Section 5 describes the experimental design, while Section 6 presents the performance results obtained in both problems (Section 6.1) and explores the relevant variables and explains a model example (Section 6.2). Finally, Section 7 discusses the ifndings, limitations and future perspectives.
In classification, imbalance refers to an uneven representation of classes. As minority groups are easily identifiable, this issue has been thoroughly studied. However, in regression, imbalance refers to a skewed distribution of the data in the target variable, this is, an underrepresentation of certain specific subdomains, often those clinically relevant. Since classes do not exist, there is scarce emphasis on the need for a complete representation of the continuous variable domain. Identifying subdomains seems challenging, as they are usually not uniformly relevant and there is typically poor representation of the relevant subdomains, so it has been hardly studied.
Real-world problems frequently involve imbalanced data due to various factors, such as limitations in data collection or the scarcity of cases. For instance, in a study on childhood obesity, most children fmay present a slightly elevated Body Mass Index (BMI); in a study on type 2 diabetes, the majority of the patients may present moderately elevated levels of glucose; in a study in Chronic Obstructive Pulmonary Disease (COPD), most patients present a moderate reduction in pulmonary capacity. In all these examples, there is a lack of representation of the most clinically relevant cases (extreme values): children who are severely obese, patients with significantly elevated glucose levels, and patients with severe reductions in pulmonary capacity, 1Adaptation of the well-known F1 for classification. respectively. A considerable imbalance seriously impacts the models, biasing towards the most frequent values and limiting generalization to underrepresented cases, so it must be treated.
In order to formally introduce the concept of imbalanced regression [
1 1 + − * ( − ) where is the center of the sigmoid, that is, the value where Φ( ) = 0.5, and is the shape of the sigmoid (see [13] for more details). Since both, low extreme values and high extreme values could exist, Φ( ) is defined with two diferent sigmoid functions. Moreover, they also adapted some of the metrics used in imbalanced domains, as the well-known F-Measure, F1 when = 1 (harmonic mean of Recall and Precision): = ( 2 + 1) * * 2 * + This adaptation draws upon well-established classification concepts: Recall ( + where TP represents True Positives and FN represents False Negatives) and Precision ( + where FP represents False Positives). To achieve this, they establish a non-trivial connection between instances exhibiting an acceptable margin of error (efectively classified in classification problems) and their relevance, so that they can further quantify those relevant bad predictions (see [13] for further insights into this adaptation).
As stated previously, imbalanced regression has been hardly studied. The few existing
techniques can be categorized as [
Within “passive” techniques, SMOTE for regression is outlined [
As said, even in the case of the linguistic algorithm, it was not particularly designed to
provide fully transparent and therefore explainable regression models. In this work, we extend
LING [
In this section, we will delve into the challenge of predicting continuous variables related to pediatric obesity in overweight and obese children. We will begin with a description of the case study and predictive targets, followed by a discussion on the challenges in omic data analysis and pre-processing. Finally, we will explore the relevance of considering imbalanced regression.
Childhood obesity presents an enduring challenge for nowadays society given its strong relation with insulin resistance, metabolic syndrome, and numerous other chronic diseases. These not only afect the health of the population, but also the health system itself due to the additional costs of treating them. In this case study, we consider a database from national project of the Carlos III Health Institute [15]. It corresponds to the IBEROMICS project [16], which focuses on overweight or obese children between 3 and 18 years old in Santiago de Compostela and Zaragoza. Since we aimed to provide a comprehensive analysis that captures potential interactions and influences on the target variables, we consider 79 variables of interest, including targeted metabolomics (e.g., cardiometabolic and hormonal biomarkers), targeted proteomics (e.g., inflammatory and hepatic biomarkers), some subdomains of the exposome (e.g., the physical activity subdomain, obtained by accelerometry, family history, and socioeconomic and demographic factors), as well as hematological parameters and anthropometry. This approach let us explore the relationships between a wide range of variables. Fuzzy rule-based algorithms ensure that only the most relevant variables contribute to each rule, maintaining model interpretability and relevance, while Random Forest are known for their ability to handle high-dimensional data and their robustness to irrelevant features.
We established two variables as continuous prediction targets in childhood obesity: zHOMAIR (n = 190) and zWC (n = 204). HOMA-IR (Homeostasis Model Assessment for Insulin Resistance) is an indicator of insulin resistance, which is strongly related to obesity since fat cells release biochemical substances that can interfere with the normal insulin response. Waist Circumference is an indicator to evaluate central obesity and visceral fat distribution. It is related to insulin resistance since visceral abdominal fat is metabolically active and produces several biochemicals, including adipokines and cytokines, that may contribute to it. A z-score is a statistical measure that represents the number of standard deviations a data point is from the mean of a reference population dataset: negative z-scores indicate below-average values and positive z-scores indicate above-average values, with the absolute value representing the deviation from the mean. This standardization ensures that comparisons are fair and meaningful, especially when analyzing variables where values can vary significantly based on age and height, as in this case. The HOMA-IR z-score was calculated using Stavnsbo as reference (see [17] for more details), whereas the Waist Circumference z-score was calculated using Ferrández as reference (see [18] for further insights).
This case study mirrors a real-world health-related scenario, necessitating interpretability (models must ofer not just variables but also meaningful explanations) and a consideration of imbalanced data. This dual focus represents a novel approach.
The application of ML to Omics data implies unique challenges in pre-processing and analysis. Additionally, to ensure robust and reliable models, it was crucial to efectively handle missing values, noise, outliers and batch efects, among others.
In this case study, we conducted data cleaning to ensure the reliability of the dataset. Raw accelerometry data were transformed using the Actilife v.6.13.3 software into variables of interest, such as the number of steps or measures of sedentary lifestyle and exercise of diferent levels corresponding to weekdays, weekends, or in total. Also, several variables (e.g., HOMA-IR, BMI, triglycerides, blood pressure, etc.) were transformed to z-scores. Specifically, these variables are WC ([18]), HOMA-IR, HDL and TG ([17]), BMI ([19]), DBP and SBP ([20]). Additionally, to ensure robust and reliable models, it was crucial to efectively handle missing values, noise, outliers and batch efects, among others. Categorical variables were transformed by label encoding. Variables with more than 15% missing values were removed, followed by a non-parametric missing value imputation using the MissForest algorithm, based on Random Forest [21]. An exploratory analysis ensured that this imputation did not significantly afect data distribution.
Real-world problems frequently involve imbalanced data due to various factors, such as limitations in data collection or the scarcity of cases. A considerable imbalance seriously impacts the models, biasing towards the most frequent values and limiting generalization to underrepresented cases, so it must be treated. For example, if the majority of the children of a hypothetical dataset had an average body mass index (BMI), the model would be biased towards normal-weight children.
According to Section 2, the imbalance ratio is calculated as the percentage of instances with a phi(Y) value over 0.8, that is, number of instances with Φ( ) > 0.8
total number of instances · 100
In this case study, although all the children are overweight obese, there is still a lack of representation for those with exceptionally high values in zHOMA-IR and zWC, which present significant imbalance ratios ( 12.105% and 12.745%, respectively). This means that children with severe insulin resistance and children with a severe accumulation of abdominal fat, which are in fact the most clinically relevant cases, are underrepresented. Since it may appreciably afect and bias the models, the imbalance existent in these datasets must be considered for obtaining not only transparent/interpretable regression models, but also more reliable ones.
In [
GM3M measures (ranging from 0.0 to 1.0) the semantic interpretability at the level of linguistic partitions, where values close to 1.0 represent a really high proximity to the membership functions associated with the initial linguistic terms (in our case, equally distributed strong linguistic partitions). See an example of linguistic partition with GM3M equal to 0.8 in Figure 1. RMI measures (also raging from 0.0 to 1.0) the semantic interpretability at the rule base level, with values close to 1.0 representing the absence of inconsistent rules (i.e., the output of the rule is consistent with the whole model output in the corresponding rule core domain). GM3M or RMI associated to a whole model are computed as the worst case from all the linguistic terms or rules, respectively. Thus, having GM3M=0.7 and RMI=0.8 for one regression model means that all membership functions have GM3M equal or higher than 0.7 and that all the rules have RMI values equal or higher than 0.8.
The algorithm combines two key elements: A new linguistic fuzzy grammar and an interpretable linear extension. This approach helps to efectively reduce the number of rules, maximize the semantic interpretability (both GM3M and RMI), minimize errors, and maintain the rule length (number of conditions) within reasonable bounds. It operates on a two-stage tree-based hybrid evolutionary multiobjective algorithm: • First stage: This involves learning the initial linguistic partitions and associated rules.
Here, an embedded multiobjective evolutionary learning of the linguistic partitions (number of linguistic terms and their definitions) is employed, aiming to minimize both number of rules and errors measured as the /2 (MSE divided by 2). It utilizes a multiobjective evolutionary approach to learn the linguistic partitions and applies a rapid method to derive rule sets for each definition of the linguistic partitions. It builds upon a hybridization with an innovative linguistic tree-based rule learning technique, extending the renowned M5-prime method to derive rule sets for each evolved linguistic partitioning. • Second stage: This stage entails post-processing to further refine the learned solutions. It employs an advanced multiobjective evolutionary algorithm to fine-tune membership functions and for rule selection. This refinement process aids in minimizing number of rules, maximizing linguistic interpretability (GM3M and RMI), and reducing errors ( /2) in the initial global structure obtained in the first stage, which was initially based on strong fuzzy partitions.
Unlike other methods, the adaptability of evolutionary algorithms allows them to adjust to specific problems in a versatile manner. Leveraging this characteristic, in this contribution, we introduce a solution called LING-ImbR, that guides the algorithm towards the said outcomes (number of rules, GM3M, RMI and /2) but by also considering the imbalance through a refined evaluation function enriched with additional information. The idea is to replace /2 in the second stage by an objective function maximizing the performance obtained in the set of relevant data (guided by the relevance function), without unbalancing the performance that we obtain in the rest of the data (guided by /2). In order to do this, we define a Weighted MSE ( /2 ) attending to the following equations: || =1 = ∑︁( () − )2 * ( + Φ( )), || =1 = ︁( (︀ ∑︁ + Φ( ))︀ + || .
︁)
represents a weight factor that combines the contributions from the relevant and
nonrelevant data, since ∑︀|=1| + Φ( ))︀ is the sum of a constant value () and the relevance
function (Φ( )), and is the number of instances in the non-relevant set. Based on another
work [
=1 /2 = +
* 2 and is the sum of the squared errors for the non-relevant data, without additional weighting.
where /2 is the weighted MSE, normalized by .
In this work, we mainly focus on the proposed extension of the linguistic fuzzy rule-based system
LING [
Since error estimation depends on the training and test data, we used a repeated 10-fold stratified cross-validation to reduce the loss of diversity when partitioning the data and preserve the minority set representation. For each dataset (the dataset with zHOMA-IR as target and the one with zWC), we use a 10-fold cross-validation strategy, that is, the original data is divided into 10 subsets or folds. This is done two times. Thus, we created 20 partitions per dataset.
The stratification used in these regression problems consisted in the discretization of the
continuous target variables into in cuts, that is, a specified number of bins which result from
dividing the number of examples of our dataset by the number of desired partitions. However,
it must be applied separately to relevant and non-relevant data. In order to achieve this, based
on another work [
Also, we need to consider metrics to properly evaluate the algorithms performance. In this study, we mainly consider two metrics: the said adaptation of F1 for regression (see Section 2) and the Mean Square Error (MSE). F1 is a metric that allows us to evaluate how well are the models addressing the imbalance problem. MSE is a classical metric to evaluate accuracy. It measures the average squared diference between the predicted and the actual values. Considering both will help us assess the models performance not only on the relevant data but also on the overall set.
In this section, we will delve into the performance results obtained in both problems (zHOMA-IR and zWC). Also, we will explore the relevant variables and explain a model example.
Firstly, we will compare the results for all the algorithms, which are shown in Table 2. Each row corresponds to an algorithm, with those actively addressing imbalanced marked in grey. The table is divided in two sections, one per problem (zHOMA-IR and zWC). Within each section, for each algorithm, the first column shows the number of variables (when applicable) and the second column, the number of rules (when applicable). The third and forth columns show the average MSE and F1 values in the test sets, respectively.
The results show that when SMOGN is applied, the F1 for all the algorithms values are better compared to those obtained with the original data. This means that addressing imbalance through the previously mentioned passive imbalance pre-processing technique improves the performance in the relevant set. However, the results show that applying SMOGN implies a cost in MSE, that is, an increased error in predicting our continuous outcomes. The results obtained in F1 by the algorithms that actively address imbalance within the learning process (those marked in gray) are slightly worse or better (depending on the problem) than those obtained when using SMOGN, whereas MSE values are notoriously better, similar to the results obtained without considering the imbalance, specially for zWC. LING-ImbR presents the best values for F1 in both problems. While Random Forest outperforms the fuzzy rule-based models in MSE in both problems, it provides less detailed information, relying solely on post-hoc SHapley Additive exPlanations (SHAP) analysis. For both linguistic algorithms, the number of variables and rules are similar in the original algorithm, the SMOGN approach and the extended version. Nevertheless, the number of variables and rules is lower in LING compared to LING, which contributes to the interpretability of the model, since LING is particularly designed for explainability. Furthermore, the errors are in 10 to 15% of the output domains, so the models explain from 85 to 90% of the domain.
Secondly, we will compare the linguistic algorithms. Table 3 shows the interpretability metrics obtained by the linguistic fuzzy algorithms. Each row corresponds to an algorithm. The columns are also divided in two sections: the results for the zHOMA-IR and the zWC dataset. In each section, the first columns represents the GM3M value and the second column, the RMI value. As we stated previously, GM3M measures the semantic interpretability at the level of linguistic partitions, whereas RMI measures the semantic interpretability at the rule base level. Thus, having GM3M=0.7 and RMI=1.0 for one algorithm in the table means that, in average the 20 runs, all membership functions have GM3M equal or higher than 0.7 and that all the rules have RMI values equal to 1.0 (all the rules in the 20 runs are fully consistent rules). For both zHOMA-IR and zWC, LING, LING using SMOGN and the modified version of LING have consistently low GM3M and RMI values, indicating the existence of significant interpretability problems. In contrast, LING, LING using SMOGN and LING-ImbR show quite high GM3M and RMI values, indicating a very high level of transparency. GM3M values for this algorthim, which are close to 1.0, represent a high proximity to the membership functions associated with the initial linguistic terms. RMI values, which are even 1.0 in the case of LING and LING-ImbR, represent the absence of inconsistent rules.
Table 4 shows the variables that appeared in the models shown by importance. For LING, variables are shown from more to less times used (#T), whereas for Random Forest, variables are shown from more to less importance for the model output based on SHAP rankings.
In the zHOMA-IR dataset, it is noteworthy that all but one of the rule bases include a variable associated with accelerometry (see those in blue in Table 4). However, in the zWC dataset, accelerometry variables are present in only half of the generated rule bases, suggesting that these variables may not always be significant. This suggests complex factors beyond physical activity influence in waist circumference during childhood obesity. Further analysis and context exploration are necessary for deeper insights into this fact.
Moreover, the rules for zWC consistently incorporate the variable zBMI in each line. However, in the zHOMA-IR dataset, the variable zBMI appears 15 times, while the variable Adiponectinleptin ratio appears 13 times, indicating the presence of specific rule bases containing both zBMI and Adiponectin-leptin ratio. The Adiponectin-leptin ratio has been associated with insulin resistance in overweight and obese children [22]. The thyroid-stimulating hormone (TSH) appears 11 times, as abnormal levels of TSH seem positively correlated to insulin resistance [23] independently of the body status [24].
SHAP rankings let us contrast to the most variables used in Random Forest models. For the zHOMA-IR problem, the z-score of triglycerides is the most important variable in the Random Forest models, followed by the mean cell hemoglobin (MCH), an accelerometry measure, zBMI, which is the most repeated variable for the linguistic models, etc. For the zWC problem, the most important variables for the output are zBMI, some accelerometry measures, the follicle stimulating hormone (FSH), which is the third most repeated variable for the linguistic models, etc.
Figure 2 represents a summary graph for a model generated via Random Forest in the zHOMA-IR dataset. It shows the contribution of the 20 most important variables, ordered from more important (top) to less important (bottom). Each point represents an instance, where its horizontal position indicates the impact that the feature has in the model output (positive or negative), and its color indicates the feature value (blue for low values, red for high values). Triglycerides, MCH, and SedentaryWd are the most influential features for predicting zHOMA-IR. Thus, both clinical measures (e.g., lipids, blood counts) and lifestyle factors (e.g., sedentary physical activity) are important, demonstrating the multifactorial nature of insulin resistance. Nevertheless, other characteristics with lower SHAP values contribute cumulatively, emphasizing the need for a broader view in the prediction and management of insulin resistance.
Figure 3 represents a summary graph for a model generated via Random Forest in the zWC dataset. This graph provides an overview of how features afect the model predictions, with zBMI being notoriously the variable with the highest impact on the model output. However, this does not imply that the other variables are irrelevant, but that their individual impacts are smaller compared to zBMI. This means that these features contribute to the model through their cumulative efects, even if their individual SHAP values are smaller. Furthermore, features can interact with each other in complex ways, so a small individual SHAP value might still be crucial when considered in combination with other features.
Figure 4 represents an example of a linguistic model obtained for zWC. The arrangement of variables in the figure corresponds to the sequence of splits generated in the decision tree during the rule-learning process. Each split is a division of the data, from more general to more specific in each split. Colors are used to aid in distinguishing the various cases depicted by the rules, with each split and variable sharing the same color. Gray text elements are not part of the rules, but provide extra information, as well as percentages of covered instances and the GM3M and RMI values. These values provide insights into the semantic quality of each partition and rule, respectively. Notably, all rules exhibit an RMI value of 1.0, indicating that any single rule assert actually matches the real output of the model. Moreover, all variables display GM3M values exceeding 0.7, and even reaching 0.9, suggesting equidistant strong linguistic partitions. The MSE in test (0.572) is almost a half of the one obtained by RF in average without imbalance consideration (0.944) while F1 in test is over 0.75. Consequently, it seems that the method efectively characterizes the overall behavior of the dataset and actually improves the consideration of the relevant data, which could help to appropriately discern the principal relationships among predictor variables.
The model was able to accurately retrieve the zWC of children with obesity using just 4 variables (which included the Follicle stimulating hormone (FSH) blood concentrations, the child age (decimal age), the amount of light physical activity, and the zBMI). Interestingly, despite the presence of clear zWC indicators among predictors (such is the case of zBMI), the model chose a non-typical metabolic risk marker to be placed in the first level of division (at the rule tree-based generation splitting) for each rule; the FSH hormone. FSH showed an intriguing and non-obvious relationship with the zWC in this population. As can be seen in rule R3, high and very high ("from High") values of FSH were directly linked to low zWC values, with a zBMImediated efect modification of +/- 0.27 per unit +/-. Individuals with higher concentrations of this hormone will therefore tend to present less central obesity, with a small contribution of increases in their zBMI.
In rules R1 and R2, on the other hand, the opposite zWC-FSH relationship was evidenced. While in R1, "up to Low" values of FSH were linked to medium ("between Low and High") zWC (as expected from R1), in R2, these same values (up to low values of FSH) were linked to "Low" zWC, with child’s age jumping on the scene as an efect modifier in this case (i.e., younger children with up to low FSH tend to present "between Low and High" zWC, while medium aged and older children with up to low FSH present low zWC). Interestingly, the cutofs in the age variable proposed by the method for generating the fuzzy intervals that diferentiate these two rules expand exactly in the estimated ages for normal puberty onset, suggesting a plausible involvement of the sexual maturation procedure in the FSH-zWC relationship.
Scientific literature has extensively pointed FSH as a significant player in human metabolic disorders. Epidemiological studies have established a strong correlation between FSH levels and metabolic diseases, while experimental research has delved into the underlying mechanisms both in vivo and in vitro [25]. From in vitro and in vivo studies, now we know that FSH is a risk marker for metabolic dysfunction given its direct role in promoting adipogenesis and insulin resistance. Nevertheless, epidemiological studies have shown an inverse relationship; individuals with obesity tend to present lower FSH values (which goes in line with our findings from R3 and R1). To account for this apparent contradiction, a hypothesis has been proposed: FSH stimulates obesity, leading to elevated estrogen levels, which subsequently diminish FSH levels through negative feedback mechanisms. Moreover, since FSH is a sexual hormone, its production gets increased after puberty initiation, and its efects could be influenced by even more complex feedback mechanisms, highlighting the relevance of this period for the study of its efects in obesity and cardiometabolic health (as evidenced by our model in R2) [26].
Our model therefore adds some evidence to the existing findings relating high FSH with lower obesity (R1 and R3), reporting in this case an important and novel contribution of sexual development in this relationship (R2). Further epidemiological studies and in vitro studies would be needed to deepen into presented hypotheses.
In this application work, we have adopted a Machine Learning approach to obtain explainable regression models for two imbalanced continuous targets in childhood obesity, the z-score of HOMA-IR and the Waist Circumference, with significant imbalance ratios around 12%. The models obtained by the proposed approaches are better considering the relevant minority information, with F1 improvements over 17%. Furthermore, the linguistic fuzzy models generated by LING and the proposal, LING-ImbR exhibit superior interpretability (elevated GM3M and RMI and low number of variables and rules), since they have been specifically designed for explainability. LING-ImbR presents the best values for F1, that is, the metric that allows us to evaluate the models in the imbalanced set, while relatively preserving the MSE value. Moreover, they seem to properly explain biologically meaningful relations among the involved factors and the predicted targets. The identification of accelerometry variables, specially in zHOMA-IR, and novel relationships, such as FSH levels in predicting zWC, could inform clinical practice by highlighting new biomarkers and pathways for intervention in childhood obesity.
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