Handling missing values in machine learning presents significant challenges, impacting both model predictive performance and fairness. While unstructured missingness, where values are randomly absent, has been extensively studied, structured missingness remains relatively underexplored. Structured missingness occurs when the absence of one or more features influences the absence of others. In this paper, we investigate the impact of both structured and unstructured missingness on fairness. We introduce a novel approach for simulating structured missingness and propose a training methodology designed to enhance model robustness under these conditions. We evaluate how diferent state-of-theart imputation methods for handling missing data afect fairness across multiple benchmark tabular datasets. Our empirical results demonstrate that structured missingness leads to a degradation in model fairness, particularly when the missingness mechanism is conditioned on protected attributes such as race or gender. In these cases, minority groups experience higher error rates, contributing to disparities in metrics like equalized odds. We propose a preprocessing step, Missingness Robustness Augmentation, that is shown to increase model robustness towards the presence of missing values.
As machine learning systems increasingly influence high-stakes decisions in healthcare [
This missingness mechanism is particularly prevalent in the medical domain [
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Current state-of-the-art methods for handling missing data are largely impute-then-classify
approaches [
Besides model performance, fairness concerns towards a machine learning model play an
increasingly important role. It has already been extensively studied how imputation impacts
fairness [
Types of missingness. The fundamental theoretical background of missingness mechanisms has
been defined in [
Albeit imputation ofers a versatile technique of dealing with missing values, there is some
concern about bias that might be introduced when used in conjunction with a machine learning
pipeline [
Fairness. There exist various (often mutually exclusive) formalizations of fairness in machine learning which account for diferent normative intuitions and practicability [ 49]. A common distinction refers to group fairness metrics (e.g., demographic parity, equalized odds) [50], which refers to distinct groups of persons as characterized by a specific sensitive attribute such as gender or ethnicity, and individual fairness metrics (e.g., counterfactual fairness, consistency) [51]), which focus on a fair treatment of individual persons in comparisons to the whole group. Due to their eficient evaluation, group fairness methods such as equalized odds which essentially refer to the distribution of errors among the vulnerable group as compared to the reference group, enjoy a wide popularity. In contrast, individual fairness measures which rely on semantically meaningful modeling of the scenario such as a latent causal model as used within counterfactual fairness, are sometimes praised as particularly meaningful, but might sufer from lack of causal information, or even reduce to statistical group methods in practice [52].
Fairness and missing values. As pointed out in [53], missing values are inherently related to
the topic of algorithmic fairness. Currently, it is common practice within the fairness literature
to simply remove missing values [
Yet, there is a lack of work evaluating common imputation methods on downstream task
performance, with recent work providing explorations of diferent missingness mechanism [
Let X ∈ ℝ× denote a dataset with samples and features. The missingness in the data is represented by a binary indicator matrix M ∈ {0, 1}× , where = 1 if is missing and 0 otherwise. The primary missing data mechanisms are the following: Missing Completely at Random (MCAR): The probability of missingness is independent of both observed and unobserved data. Formally,
( M ∣ X) = ( M)
Under MCAR, the missingness does not introduce bias in parameter estimates, allowing
for unbiased analysis using complete cases [
Missing at Random (MAR): The probability of missingness may depend on observed data but not on the missing data itself:
( M ∣ X) = ( M ∣ Xobs)
This assumption permits the use of methods like multiple imputation to obtain unbiased
estimates, provided that the model for the missingness mechanism is correctly specified
[
Missing Not at Random (MNAR): The probability of missingness depends on unobserved data:
( M ∣ X) ≠ ( M ∣ Xobs)
MNAR mechanisms require modeling the missingness process for unbiased estimates, as
the missingness is informative and cannot be ignored [
Structured missingness (SM) refers to scenarios where the pattern of missing data exhibits dependencies among variables or across observations. Each version of structure can be applied to each missingness mechanism, as example we state the definition of MAR. The two notable structure types are: MAR with Weak Structure (MAR-WS): Missingness in one variable depends on observed data and the missingness indicators of other variables:
( M ∣ Xobs, M− )
where M is the missingness indicator for variable , and M− represents missingness
indicators for other variables [
MAR with Strong Structure (MAR-SS): Missingness in one variable depends on observed data, missingness indicators, and the missing values of other variables:
( M ∣ Xobs, Xmis, M− )
This scenario is more complex and requires advanced modeling techniques to handle the
dependencies efectively [
Having SM in the data can have a significant impact on the fairness of a predictive model, especially if the protected attribute is related to the missingness structure. In order to systematically analyze SM in a controlled environment, we introduce Structured Feature Dropout, detailed in algorithm 1, a novel method to induce SM within datasets. This approach centers on a sensitive attribute to simulate realistic missingness patterns pertinent to algorithmic fairness studies. While tailored for fairness evaluations, the methodology is adaptable for broader applications involving structured missingness.
First of all, to induce a structure in the missingness mechanism, a domain knowledge of the problem is needed. We propose to construct a Bayesian Network (BN), a probabilistic graphical model that represents attributes as random variables and their conditional dependencies. This approach aims to maximize the likelihood of generating the observed dataset. Specifically, we utilize the Bayesian networks previously developed by [53]. Although BNs are used here for their flexibility in capturing feature dependencies, other graph-based approaches may also be suitable. We would like to stress that it is not necessary to construct a complete causal model to implement this procedure, but any knowledge of protected features would sufice.
To induce missingness, first, we generate an unstructured missingness mask by randomly masking an fraction of features correlated with the sensitive attribute. Next, we induce structured missingness by masking an additional fraction of features directly related to the target label, reflecting the worst-case scenario in which the missingness mechanism directly impacts predictive features.
Figure 1 provides a visual illustration of the procedure described in algorithm 1. By incorporating domain knowledge and data-driven insights, we construct a graphical model that captures feature dependencies. Missingness is then introduced according to a specified mechanism; for instance, in the depicted example, a Missing At Random (MAR) strategy is employed,
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K Protected 1
Feature 1 Feature 2
Feature 4
Protected 2 Feature 3
Unstructured Missingness
Feature 7
Feature 5 Feature 8
Feature 6
Protected 2
Feature 3
Feature 1 Feature 2
Feature 4 Label Protected 1
Feature 1 Feature 2
Feature 4
Protected 2 Feature 3 Feature 7
Feature 5
Feature 7
Feature 5 Feature 8
Feature 6
Feature 8
Feature 6 where the probability of missingness depends on an observed variable, specifically the attribute labeled "Protected 1". Red dashed edges indicate the dependency paths used to determine which features are selected for missingness in a given step, while red crosses denote features in which missing values were introduced at that stage. Red crosses indicate features in which missing values were artificially introduced according to the missingness mechanism. This process results in a missingness mask M, with selected feature values removed. In this simulation, SM was introduced solely based on Protected 1, ensuring that Feature 3 remained fully observed throughout. For clarity and consistency across datasets we selected only a single protected attribute; the approach naturally extends to settings involving multiple protected variables. In a second iteration, missingness is induced in features that are directly associated with the target label, thereby simulating a more structurally dependent form of missingness. Features previously marked with black crosses remain unchanged and do not receive additional missing values.
Input: Dataset ∈ × ; probability distributions , Output: Modified dataset with structured missingness (SM) clean(X) ; // Optional preprocessing or normalization ← computeFeatureRelation( ) ; // Determine feature relationships M ← missingMask( , , ) ; // Apply base-level missingness M′ ← structuredMask(M, , ) ; // Inject structured missingness setMissing( , M + M′) ; // Apply total missingness mask return D
Whenever missing values occur during deployment of a machine learning model, it might be susceptible to reduced performance and fairness. To counteract this efect, we propose Missingness Robustness Augmentation, a novel method which aims to increase the robustness of an ML model when dealing with structured missingness. The core idea of our proposed method is to enrich the training data with artificially induced missing values. By exposing the model to these conditions during training, we improve its ability to generalize when faced with similar missingness during inference. Importantly, our approach enhances fairness robustness without compromising predictive performance.
The proposed method is listed in algorithm 2. Missingness Robustness Augmentation augments the training data by randomly sampling a proportion of the dataset and artificially removing a predefined set of features from these samples. This induces additional structured missingness (SM) in the training set, informed by domain knowledge. By doing so, the model is exposed to missingness patterns that resemble those expected at deployment, thereby improving its robustness to fairness and performance degradation under test-time SM.
This algorithm is particularly efective if there is a distributional shift of the missingness pattern from the training data to the testing data. This shift is reduced by adding randomly drawn samples from the dataset and reinserting those into the training set, but with certain features masked/missing.
Training a model on data that includes imputed values can enhance its robustness, provided that the same imputation strategy is consistently applied during both training and testing phases. algorithm 2 is to be applied before the initial imputation step takes place. Exposing the model to a suficient volume of imputed data during training, allows it to better approximate the potentially skewed distribution it may encounter in real-world scenarios.
The core insight underlying our method is that, in many practical applications, the patterns
of structured missingness are at least partially understood or can be inferred from domain
expertise [
In cases where this distribution is unknown, feature selection methods and uniform sampling across the entire dataset may provide reasonable performance. However, care must be taken when determining the number of augmented samples, as excessive additions may introduce noise and increase the computational burden, while insuficient augmentation may fail to capture the underlying data distribution.
Input: Dataset with rows; missingness ratio ∈ [
To analyze how SM impacts the fairness of binary classification tasks, we set up a data processing pipeline that was applied to a variety of imputation methods, classifiers, and datasets. The selection of data sets is based on the survey [53], where the authors also provide the bayesian network for each dataset. Both the imputation methods and the classifiers were selected from state-of-the-art methods in the literature. An overview of the datasets used in our experiments is provided in Table 1. The column with the number of entries refers to the cleaned version Data preparation
Training data Dataset 5 fold crossvalidation Validation data
Data manipulation reVmalouveal impVuatluaetion WWSSMMSSMNCMMAMAANRAARRARRR MiSsMKsimIFNCpoNElreest reVmalouveal impVuatluaetion Target Encoder categorical features
Standard Scaler Training data
MXLGmBooodsetl: Trained Model EqEuvaMalilzFuoe1addteioOlnd:ds Validation data of each dataset, with all samples containing missing values removed prior to experimentation. Although several datasets include multiple protected attributes, we report only the specific attribute used to induce missingness in our experiments, as this was the sole attribute considered when evaluating fairness metrics. The code and additional results of this work are available at https://github.com/fairness_SM.
We use imputation methods from statistics and classical machine learning. Due to the small
size of the data, we do not use DL imputation [
To employ KNN imputation, we slightly modified the approach to work with categorical features. Every categorical feature is one-hot encoded, and during imputation, all encoded values are set to missing and imputed individually. Then we compute their maximum, and the final imputed value is the corresponding categorical feature.
Pipeline. To set up a controlled environment we applied similar data cleaning steps as in [53], removing all missing values which are included in the dataset. To ensure consistency and reduce statistical noise we employed a 5-fold cross-validation-scheme. The original dataset was first partitioned into training and testing subsets, after which missingness was artificially introduced into both. A detailed overview of the entire pipeline can be seen in Figure 2, it consists of 5 steps: (1) Data preparation, to split the dataset in train/validation with the 5-fold cross validation strategy. (2) Data manipulation, to first induce the missing values in train and validation data, with multiple percentage (0%, 10%,30%, 50%, 70%), and then impute the missing values. (3) Data pre-processing, using target encoder [57], to encode categorical features, and then standardize the data to zero mean and unitary varriance. (4) Training of the ML model XGBoost, as it is the state-of-the-art in ML for tabular datasets [58]. (5) Post-processing, to evaluate the trained model with fairness and performance metrics.
Preprocessing. Following the 5-fold cross-validation split, missingness induction, and imputation, we applied a standardized preprocessing pipeline. Given the presence of categorical features in most datasets, we employed target encoding to transform these variables, as it is considered a state-of-the-art approach for supervised learning tasks [59]. Finally, the resulting data were standardized to have zero mean and unit variance to ensure consistent model performance. The full pipeline, outlined in Figure 2, consisted of 5 steps: To ensure controlled experimentation, we eliminate all initial missing values from the dataset before invoking algorithm 1. This step isolates the efects of induced structured missingness (SM), allowing for clearer attribution of observed outcomes to the experimental conditions. Specifically, we avoid mixing diferent missingness mechanisms to focus exclusively on the impact of SM on fairness. Missing Mechanisms. Our primary objective is to evaluate the practical implications of SM in real-world applications. Although it is theoretically possible to construct a structured version of MCAR, such a formulation holds limited practical significance. Consequently, we exclude structured MCAR from our analysis. Instead, we focus on MAR and MNAR mechanisms, where missingness is conditioned on or influenced by the protected attribute. For MNAR scenarios, we simulate a latent confounder by removing the protected attribute from the dataset after inducing missingness. This reflects settings in which sensitive variables afect the missingness process but are not explicitly available at training or inference time. We evaluate both weakly and strongly structured variants of MAR and MNAR. Missingness is introduced using a unified procedure (algorithm 1) that generates both structured and unstructured missingness masks in a consistent and reproducible manner.
Evaluation Metrics As our primary interest lies in evaluating downstream task performance and fairness, we do not consider reconstruction error, commonly used to assess imputation quality, as it does not necessarily correlate with performance or fairness in predictive modeling tasks. Instead, we focus on well-established metrics from the machine learning literature that directly reflect model behavior: the F1 score for predictive performance and Equalized Odds (EO) for fairness, as we are in a supervised learning setting [60]. EO evaluates fairness based on error rate parity across groups, ofering a measure of fairness in classification tasks, particularly in domains where label information is meaningful, and error disparities are critical. For fairness evaluation, we focus on group-level metrics rather than individual fairness. Although individual fairness ofers a more fine-grained notion of equitable treatment, it often relies on access to a well-defined causal model, an assumption that is frequently impractical or unverified in real-world applications.
In this section, we present and analyze our findings on the impact of SM. We begin by evaluating the efect of diferent imputation strategies employed during preprocessing. Subsequently, we investigate the model’s behavior under varying degrees of missingness in both the training and test sets, with a particular focus on the asymmetry between the two.
For simplicity, we discuss the results on the Adult dataset [61], as it is a common benchmark in the fairness literature [53], and the trend of the results is qualitatively similar to the other datasets investigated in this work, listed in Table 1.
Shortcoming of Imputation Methods. Figure 3 presents both predictive performance (F1score) and group-level fairness metrics (EO) for the Adult and Bank marketing dataset, under conditions when training and test sets have matching levels of missingness. Across all imputation strategies evaluated, a consistent trend emerges: SM leads to the most pronounced degradation in both performance and fairness metrics. This pattern is clearly reflected in Figure 3, where Simple imputation
Mice
MissForest Simple imputation
Simple imputation
KNN
KNN
KNN
increasing overall missingness correlates with declines in F1 score and EO. The consistency of
this trend is evident across multiple datasets, including representative results from the Adult
and Bank Marketing datasets. These results align with prior findings [
Our results indicate that missingness confined to training had negligible efects on performance and fairness, while test-time missingness introduced considerably more degradation across metrics. Missing training data
Missing test data (b) EO on Adult dataset.
Equal missing training and test data 20Missing percentage 60 40
Furthermore, the magnitude of this efect scales with the degree of mismatch between training and test missingness levels. This is particularly problematic in real-world deployments, where ground-truth labels are unavailable at test time, limiting the ability to detect post-hoc fairness degradation. These findings underscore the importance of anticipating structured missingness and implementing mitigation strategies during the model development phase, rather than relying solely on downstream audits.
Setup. Motivated by the observed limitations of existing techniques under structured missingness, we developed Missingness Robustness Augmentation, a preprocessing approach aimed at improving robustness and fairness. For clarity, recall that our proposed method is applied in step two of the pipeline proposed in Figure 2. To evaluate its efectiveness, we conducted a comparative analysis against three baseline strategies widely used in fair machine learning: (i) a standard model without any fairness intervention, (ii) a reweighting scheme that adjusts the 60 40
20 0 20 Missing percentage difference (test - train) 40
60 influence of training samples to mitigate biasparticularly by assigning higher weights to instances from the minority group with missing values [62], and (iii) a post-processing method that enforces the EO criterion by modifying classifier outputs [ 63]. For our evaluation of Missingness Robustness Augmentation we set to about 10% of total dataset size.
Evaluation. Figure 5 summarizes the overall performance of all data processing strategies evaluated. The -axis denotes the diference in missingness rates between the training and test sets; higher values indicate a greater proportion of missing data in the test set relative to the training set.
The reweighting strategy utilized in our study is based on the presence of missing values in the training data, applying more weight to data points with missing values. Similarly, when applying Equalized Odds (EO) postprocessing, discrepancies between the distribution of missingness in the training and test sets diminish the fairness improvements while also negatively impacting model performance. In contrast, Missingness Robustness Augmentation remains efective under such distribution shifts, provided the augmented features accurately reflect the missingness patterns expected at test time. However, in scenarios where this alignment cannot be guaranteed, our results (see Figure 4) indicate only marginal efects on both fairness and performance. Consequently, incorporating Missingness Robustness Augmentation presents minimal risk but ofers potential benefits, especially in deployment settings where structured missingness may emerge.
Significance. In order to assess the statistical significance of the results across multiple datasets, we use the Friedman non-parameteric test with 0.05 confidence level, followed by Nemenyi posthoc test [64], and the we plot the results with the Critical Distance (CD) plot in Figure 6. We focus on where the test set exhibits a higher proportion of missing values than the training set, we observe significant diferences among data processing methods in both predictive performance and fairness.
Although EO post-processing achieves the best fairness outcomes, it does so at the cost of (a) Critical distance for F1 score. 2 1
MRA No Intervention MRA EO Postprocessing
(b) Critical distance for EO. reduced accuracy. In contrast, the proposed Missingness Robustness Augmentationofers the second-best performance in terms of fairness, while also outperforming all other methods in predictive accuracy. This suggests that our method provides a favorable balance between fairness and performance under conditions of mismatched missingness.
Structured missingness arises from complex real-world processes and interactions, posing unique
challenges for machine learning systems, as highlighted by [
To address the efects of SM we introduce a simple and generalizable preprocessing method designed to improve model robustness in the presence of structured missingness. Our approach requires no architectural changes, is easy to implement, and maintains predictive accuracy across tasks. While improvements in fairness are modest, the method yields consistent and stable gains across a range of missingness scenarios, and outperforms standard reweighting and post-processing baselines in terms of reliability and sensitivity to test-time conditions. As our approach does not rely on a complete causal model, we deliberately refrained from evaluating counterfactual fairness, though exploring this perspective remains a promising direction for future work.
Our findings suggest that this method is most beneficial in settings where test-time missingness is prevalent and unevenly distributed across groups, which is common in real-world deployment contexts. Additionally, performance is determined by the alignment between the induced and the test-time missingness. When the induced distribution deviated significantly from the true test-time distribution, the impact on the metrics evaluated was minimal. In contrast, when the distributions aligned closely, we observed a clear improvement in these metrics.
Structured missingness remains an underexplored but pressing challenge in fair machine learning, and our results highlight the need for proactive, pipeline-level strategies that account for missingness during both development and deployment phases.
Our proposed method relies on domain knowledge to implement realistic and efective preventive strategies. Designing approaches that are agnostic to such prior knowledge or that leverage learned feature representations to approximate it remains an important direction for future work. Additionally, addressing the challenges posed by structured missingness when both the training and test sets exhibit comparable levels of missingness remains a complex and unresolved issue.
Future work should explore dynamic or adaptive methods that respond to missingness patterns at inference time, as well as deeper theoretical frameworks to understand the interaction between data missingness and fairness constraints. Another practical suggestion is to explore the impact of structured missingness on deep learning systems, as such systems gain more traction when dealing with tabular data.
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