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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>R. I. Shithy);</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Selective Post-hoc Bias Mitigation via Counterfactual Sensitivity</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Roti Islam Shithy</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Maria Stratigi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kostas Stefanidis</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Data Science Research Centre, Tampere University</institution>
          ,
          <country country="FI">Finland</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2026</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0003</lpage>
      <abstract>
        <p>Fairness concerns in recommender systems arise when predictions are sensitive to protected attributes, leading to unequal treatment of users and groups. While existing approaches often address either individual or group fairness through model retraining or constrained optimization, such methods can be difficult to deploy and audit in practice. In this work, a post-hoc counterfactual fairness framework has been proposed that jointly analyzes and mitigates individual- and group-level bias using a single, interpretable mechanism, without modifying or retraining the underlying model. This approach identifies unfair decisions through counterfactual sensitivity and applies a selective neutralization rule that removes the influence of sensitive attributes while preserving non-sensitive preference signals. Experiments on the MovieLens dataset using a logistic regression recommender demonstrate that the proposed method substantially reduces counterfactual sensitivity and demographic parity differences, while maintaining predictive accuracy. These results demonstrate that effective fairness auditing and mitigation can be achieved through simple, deployment-friendly post-hoc interventions.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Counterfactual explanations</kwd>
        <kwd>bias detection and mitigation</kwd>
        <kwd>post-hoc fairness</kwd>
        <kwd>explainable AI</kwd>
        <kwd>1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Recommender systems increasingly shape user exposure and decision-making in online platforms. As a result,
concerns about fairness have gained significant attention, particularly when recommendation outcomes depend on
protected attributes such as gender, age, or occupation. Such dependencies may lead to unequal treatment of users
or systematic disadvantages for certain demographic groups, raising ethical and societal concerns.</p>
      <p>Fairness in recommender systems is challenging because unfair behavior can manifest at multiple levels. At the
individual level, unfairness may arise when a user’s recommendation outcome changes solely due to a modification
of a protected attribute. At the group level, unfairness may appear as disparities in outcome distributions across
demographic groups. While existing work has proposed numerous fairness-aware learning approaches, many focus
on either individual or group fairness in isolation and often require model retraining, additional constraints, or
complex optimization procedures.</p>
      <p>Throughout this work, we operationalize unfairness as counterfactual sensitivity, defined as the extent to which
a model’s predictions change when protected attributes are altered while all other features remain fixed. Throughout
the remainder of the paper, we use the term bias to refer to empirically measured unfairness, operationalized via
counterfactual sensitivity at the individual level and its aggregation at the group level. This clarification allows us to
consistently distinguish between the conceptual notion of unfairness and its measurable manifestations in
experimental analysis.</p>
      <p>Counterfactual sensitivity operationalizes a causal notion of individual fairness: a prediction is considered
sensitive if it changes solely due to variation in a protected attribute while all other features remain fixed. Under this
interpretation, fairness auditing becomes a test of whether protected attributes exert direct influence on model
decisions, aligning with counterfactual definitions of individual fairness in prior work (Sandra Wachter, 2017); (Matt
Kusner, 2017). This theoretical grounding clarifies why counterfactual sensitivity can serve as a principled signal for
both bias detection and mitigation.</p>
      <p>
        A large body of prior work addresses fairness during model training through regularization, adversarial learning, or
constrained optimization
        <xref ref-type="bibr" rid="ref1">(Alex Beutel, 2019)</xref>
        ; (Ninareh Mehrabi, 2021); (Joachims, 2018). Although effective, such
inprocessing approaches may be difficult to deploy in practice, especially in systems where models are already trained,
proprietary, or costly to retrain. In contrast, post-hoc approaches aim to analyze and mitigate unfairness after
deployment, offering greater flexibility and auditability (Sandra Wachter, 2017). However, existing post-hoc methods
typically focus on either bias detection or bias mitigation and often emphasize a single notion of fairness (Ninareh
Mehrabi, 2021); (Sandra Wachter, 2017).
      </p>
      <p>In this paper, we propose a post-hoc counterfactual fairness framework that jointly analyzes and mitigates
individual- and group-level bias using a single, interpretable mechanism. Our approach first identifies biased
predictions through counterfactual sensitivity analysis and then applies a selective neutralization rule that removes
the influence of protected attributes only when they affect the predicted outcome. Importantly, this process operates
entirely at the prediction level and does not require retraining, constraint optimization, or modification of ranking
objectives.</p>
      <p>Unlike many fairness-aware recommender approaches that rely on model retraining or constraint-based
optimization, this work adopts a post-hoc perspective that prioritizes interpretability and practical deployability. The
focus is on lightweight analysis and intervention mechanisms that can be applied to existing systems without
modifying their internal structure.</p>
      <p>The contributions of this work are summarized as follows:
• We introduce a unified post-hoc framework that uses counterfactual sensitivity to analyze both
individualand group-level bias within the same mechanism.
• We propose a simple and selective neutralization strategy that mitigates biased predictions without
retraining or modifying the underlying recommender model.
• We empirically demonstrate that the proposed approach reduces counterfactual sensitivity and group-level
disparity on a real-world dataset, while preserving predictive accuracy.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        Fairness in recommender systems has been widely studied due to concerns that personalized recommendations may
amplify data and societal biases. Early work showed that collaborative filtering and ranking-based methods can
introduce popularity, exposure, and demographic biases, resulting in unequal treatment of users and items (T.
Kamishima, 2011);
        <xref ref-type="bibr" rid="ref4">(Burke, 2017)</xref>
        ; (Ekstrand, 2018). Such biases may disadvantage minority users and reinforce
stereotypes, motivating fairness-aware recommendation research.
      </p>
      <p>
        Fairness is commonly examined from two perspectives: group fairness and individual fairness. Group fairness focuses
on reducing disparities across demographic groups and is often measured using demographic parity or related
metrics
        <xref ref-type="bibr" rid="ref3">(Asia J. Biega, 2018)</xref>
        ; (Ninareh Mehrabi, 2021). Individual fairness requires that similar users receive similar
recommendations regardless of sensitive attributes
(Sandra Wachter, 2017); (Matt Kusner, 2017). Prior studies note that optimizing one notion may negatively impact
the other, highlighting the need for balanced approaches (Lucic, 2022).
      </p>
      <p>
        Several methods address fairness during model training using regularization, adversarial learning, or constrained
optimization (Joachims, 2018);
        <xref ref-type="bibr" rid="ref1">(Alex Beutel, 2019)</xref>
        . Although effective, these in-processing approaches often increase
model complexity and reduce interpretability. Pre-processing techniques, such as data reweighting, attempt to
correct biased distributions but may distort preference signals
        <xref ref-type="bibr" rid="ref5">(Cowgill, 2020)</xref>
        .
      </p>
      <p>Post-hoc mitigation strategies provide a practical alternative by modifying predictions without retraining. These
methods are particularly attractive in deployment settings and have been shown to improve fairness while preserving
utility (Ninareh Mehrabi, 2021). Counterfactual explanations play a central role in post-hoc fairness auditing by
assessing whether predictions change when sensitive attributes are altered while other features remain fixed (Sandra
Wachter, 2017); (Dandl, 2020); (Poyiadzi, 2020); (Yash Goyal, 2019).</p>
      <p>Recent work further improves counterfactual quality by optimizing feasibility and interpretability (Lucic, 2022).
Fairness has also been explored beyond single-user recommendations. (Stefanidis, 2021) studied fairness in
multiround group recommendation, demonstrating how repeated interactions affect equity over time. (Stratigi, 2025)
extended counterfactual reasoning to group recommendations using a model-agnostic framework, showing its
effectiveness in heterogeneous settings.</p>
      <p>Fairness in recommender systems has also been examined from broader and longer-term perspectives. (Eirini
Ntoutsi, 2016) discussed early challenges related to bias and fairness in data mining and decision-making systems,
highlighting how unfair outcomes may emerge and persist over time. Subsequent research has explored fairness
beyond single-shot recommendations, including temporal and long-term considerations. (Rodrigo Borges, 2020)
investigated long-term fairness in recommender systems using variational autoencoders, illustrating how fairness
objectives can be incorporated into representation learning over extended recommendation horizons. Similarly, the
study (Rodrigo Borges, 2021) introduced variational autoencoder-based debiasing to mitigate popularity bias,
showing that generative latent modelling can substantially reduce item over-exposure while maintaining ranking</p>
      <sec id="sec-2-1">
        <title>3.4. Data Splitting</title>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>4. Methodology</title>
      <sec id="sec-3-1">
        <title>4.1. Model Training</title>
        <p>
          quality. More recent studies further examine fairness-related challenges in contemporary recommender and
datadriven systems, including analyses of bias and fairness considerations in modern recommendation settings
          <xref ref-type="bibr" rid="ref2">(Ali,
2025)</xref>
          ; (Hasan, 2024);
          <xref ref-type="bibr" rid="ref6">(Dalla Vecchia, 2025)</xref>
          .
        </p>
        <p>
          Despite these advances, many existing approaches either (i) integrate fairness constraints during training, (ii)
apply adversarial or optimization-based mitigation strategies, or (iii) focus exclusively on fairness auditing without
a corresponding mitigation mechanism (Ekstrand, 2018);
          <xref ref-type="bibr" rid="ref1">(Alex Beutel, 2019)</xref>
          . In contrast, the proposed framework
operates entirely at prediction time and uses counterfactual sensitivity as a single unifying mechanism for both bias
detection and mitigation. Group-level effects are not enforced through explicit constraints but emerge from
consistent removal of individual counterfactual sensitivity. This distinction positions the approach as a lightweight,
deployment-friendly alternative to retraining-based or constraint-driven fairness methods.
        </p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>3. Dataset and Preprocessing</title>
      <sec id="sec-4-1">
        <title>3.1. Dataset</title>
        <p>We conduct our experiments using the MovieLens 1M dataset, a widely used benchmark for recommender system
research. The dataset contains 1,000,209 explicit ratings provided by 6,040 users on 3,900+ movies. In addition to
user–item interactions, the dataset includes demographic attributes such as gender, age, and occupation, which are
essential for fairness analysis across sensitive user groups.</p>
        <p>The scale and demographic richness of MovieLens 1M make it suitable for evaluating bias detection and
mitigation methods under realistic conditions, while providing sufficient data for stable group-level analysis.</p>
      </sec>
      <sec id="sec-4-2">
        <title>3.2. Label Construction</title>
        <p>The recommendation task is formulated as a binary classification problem. Explicit ratings are converted into binary
labels following common practice in fairness-aware recommendation studies. Ratings greater than or equal to 4 are
labeled as positive (liked), while ratings below 4 are labeled as negative (not liked). This binarization simplifies
evaluation and enables direct comparison of positive outcome allocation across demographic groups.</p>
      </sec>
      <sec id="sec-4-3">
        <title>3.3. Feature Representation</title>
        <p>Each user–item interaction is represented by a feature vector combining user and item attributes. User features
include gender, age, and occupation. Gender is encoded as a binary variable, while occupation is transformed using
one-hot encoding to avoid ordinal assumptions. Age is retained as a numerical attribute to preserve demographic
variation for fairness analysis. Item features consist of movie genres, represented using a multi-hot encoding scheme
to capture multiple genre memberships. The final input vector is obtained by concatenating user and item features
into a fixed-length representation suitable for linear classification models.</p>
        <p>The dataset is divided into training and test sets using an 80/20 stratified split. Stratification preserves the distribution
of positive and negative labels as well as demographic attributes across splits. This setup ensures that fairness and
accuracy evaluations before and after mitigation are not affected by sampling imbalance.</p>
        <p>This section describes the proposed post-hoc fairness framework for detecting and mitigating bias in recommender
systems using counterfactual explanations. The framework is model-agnostic and operates entirely at the prediction
level, preserving the original learning process.</p>
        <p>We employ logistic regression as the base recommender model due to its interpretability and efficiency. The task is
formulated as binary classification, where the model predicts whether a user likes an item.</p>
        <p>Let  ∈ ℝ × denote the feature matrix and  ∈ {0,1} the binary labels. The logistic regression model estimates:
 ̂ =  ( ), (1)
Where  (⋅) is the sigmoid function and  represents model parameters.</p>
        <p>The dataset is split into training and test sets using an 80/20 stratified split. The trained model produces baseline
predictions on the test set, which are later used for fairness analysis and mitigation.</p>
      </sec>
      <sec id="sec-4-4">
        <title>4.2. Counterfactual Bias Detection</title>
        <p>Bias is detected using counterfactual reasoning by evaluating prediction sensitivity to changes in sensitive attributes.
For each test instance   , a counterfactual instance  ′ is generated by modifying only one sensitive attribute (e.g.,
gender) while keeping all other features unchanged. Counterfactual instances are generated by modifying exactly
one protected attribute at a time while keeping all remaining features fixed. For binary attributes such as gender, the
value is flipped (e.g., 0 ↔ 1). For categorical attributes such as occupation, a single alternative valid category is
assigned to construct the counterfactual instance. No optimization-based search or multiple counterfactual
candidates are generated. The objective is to test local prediction sensitivity under minimal attribute intervention
rather than to explore the full counterfactual space. This design ensures determinism and reproducibility of the
sensitivity test.</p>
        <sec id="sec-4-4-1">
          <title>4.2.1. Individual-level Bias</title>
          <p>Individual-level bias is identified by comparing the model’s predictions for   and its counterfactual  ′ :
1, if  ̂(  ) ≠  ̂( ′) (2)
  = {0, otherwise</p>
          <p>A prediction flip (  = 1) indicates that the model’s decision for instance  depends on the sensitive attribute,
suggesting individual-level unfairness.</p>
        </sec>
        <sec id="sec-4-4-2">
          <title>4.2.2. Group-level Bias</title>
          <p>Group-level bias is measured by aggregating individual flips within demographic groups. Let  denote a demographic
group (e.g., female users). The group-level bias rate is defined as:</p>
          <p>1 (3)
  = ∣  ∣ ∑  [  ̂(  ) ≠  ̂( ′)],</p>
          <p>∈</p>
          <p>Where  [⋅] is the indicator function. Higher values of   indicate stronger sensitivity of model predictions to the
sensitive attribute within group  . In reporting results, this bias rate is expressed as a percentage (  × 100) to
facilitate comparison across demographic groups. This metric captures systematic disparities that may not be visible
through individual analysis alone.</p>
        </sec>
      </sec>
      <sec id="sec-4-5">
        <title>4.3. Post-hoc Counterfactual Neutralization</title>
        <p>To mitigate detected bias, we apply a post-hoc counterfactual neutralization strategy. For each test instance, the
original prediction is compared with its counterfactual prediction.</p>
        <p>The fairness-adjusted prediction  ̂ , is defined as:</p>
        <p>̂ , = { ̂̂(( ′)),, if  ̂o(th e)r≠wiŝe( ′) (4)</p>
        <p>The selective neutralization rule in Eq. (4) is intentionally designed as a minimal and deterministic post-hoc
intervention. Rather than enforcing global fairness constraints or uniformly adjusting predictions, the rule intervenes
only when a prediction is counterfactually sensitive to a protected attribute. Predictions that remain invariant under
counterfactual changes are left unchanged. This design ensures that mitigation is targeted, interpretable, and avoids
unnecessary distortion of non-sensitive preference signals, while preserving model utility and decision fidelity.
Importantly, the approach can be applied without retraining or modifying the underlying recommender system.</p>
        <p>No group-specific optimization is performed. Group-level bias reductions emerge solely from the application of
the same selective neutralization rule to individual predictions, followed by aggregation across demographic groups.
As a result, bias detection and mitigation are unified through a single counterfactual sensitivity signal, rather than
treated as separate stages.</p>
        <p>A natural alternative to post-hoc mitigation is the removal of sensitive features or the unconditional use of
counterfactual predictions. However, feature removal does not guarantee fairness, as protected attributes may
remain implicitly encoded through correlated features, and it prevents auditing whether individual decisions are
sensitive to protected attributes. Similarly, always switching to counterfactual predictions or applying demographic
post-processing would uniformly alter outcomes, including those that are already unbiased. In contrast, selective
neutralization intervenes only when counterfactual inconsistency is detected, enabling targeted and auditable
mitigation.</p>
        <p>In addition to counterfactual sensitivity, we report standard group-level fairness indicators, namely positive
outcome rates (POR) and demographic parity difference (DPD), computed before and after post-hoc mitigation.</p>
      </sec>
      <sec id="sec-4-6">
        <title>4.4. Evaluation Metrics</title>
        <p>The proposed framework is evaluated using both fairness and utility metrics. Fairness is primarily assessed through
counterfactual bias, measured as the rate of prediction changes when protected attributes are counterfactually
modified while all other features remain fixed. This analysis is conducted at both the individual level and the group
level across demographic attributes including gender, age, and occupation. To complement counterfactual bias, we
also report standard group-level fairness indicators, positive outcome rates (POR) and demographic parity difference
(DPD), before and after post-hoc mitigation. Model utility is evaluated using classification accuracy on the test set.
All metrics are computed before and after selective neutralization to examine the resulting fairness–utility trade-off.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Experimental Results</title>
      <p>This section presents the evaluation of the proposed post-hoc counterfactual fairness framework on the MovieLens
1M dataset. We analyze bias at both the individual and group levels before and after selective neutralization, followed
by an analytical summary of absolute and relative bias reductions. We further examine the impact of mitigation on
model utility using prediction accuracy, and report standard group-level fairness indicators, including positive
outcome rates (POR) and demographic parity difference (DPD), to provide a comprehensive assessment of fairness–
utility trade-offs.</p>
      <sec id="sec-5-1">
        <title>5.1. Individual-level Bias</title>
        <p>Individual-level bias is measured as the proportion of test instances whose predicted outcome changes when gender
is counterfactually flipped.
5.2. Group-level Bias
Group-level bias was analyzed across age, gender, and occupation by aggregating counterfactual prediction flips
within each demographic group.
Younger age group (&lt;18) show higher baseline bias (6.5%) with consistent reductions (3.7%) after mitigation, and all
other groups also show lower bias after mitigation.</p>
        <p>These results show consistent bias reduction across individual predictions and group levels. Relative reductions
range from 35% to 46%, with larger absolute reductions observed for attributes exhibiting higher baseline bias. This
pattern indicates that the selective neutralization mechanism primarily affects predictions with strong counterfactual
sensitivity, resulting in targeted mitigation rather than uniform adjustment across all users.
5.3. Accuracy
To assess the impact of post-hoc mitigation on model utility, prediction accuracy before and after selective
neutralization has been reported.</p>
        <p>The results indicate DPD decreases across all attributes after selective neutralization, with the largest reduction
observed for gender and more moderate decreases for age and occupation. This indicates reduced group-level
disparity without explicit group-level constraints.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Discussion</title>
      <p>This work demonstrates that counterfactual sensitivity can serve as a unified mechanism for both fairness auditing
and mitigation at prediction time. By applying a deterministic selective neutralization rule, biased predictions are
adjusted without retraining or optimization, while invariant predictions remain unchanged. The framework is
modelagnostic and requires only prediction-level access. While logistic regression enhances transparency of prediction
behavior, the counterfactual sensitivity test and selective neutralization rule remain applicable to more complex
architectures, where interpretability refers primarily to the transparency of the mitigation mechanism rather than
full model introspection.</p>
      <p>We intentionally focus on an interpretable model (logistic regression) evaluated on a widely used benchmark
dataset (MovieLens 1M) to isolate the effect of post-hoc counterfactual mitigation from confounding factors
introduced by model complexity. This design allows observed fairness improvements to be attributed directly to the
proposed intervention and aligns with practical deployment scenarios where retraining or architectural modification
is undesirable.</p>
      <p>Results show consistent reductions in individual and group bias with minimal accuracy impact, indicating a
favorable fairness–utility trade-off. The proportion of modified predictions corresponds to the counterfactual
sensitivity rate; thus, only instances exhibiting prediction flips under protected attribute variation are adjusted, while
most predictions remain unchanged. Complementary group-level indicators further show POR shift across
demographic groups, while DPD is reduced after mitigation. These patterns suggest that selective neutralization
performs targeted corrections for groups with higher baseline bias rather than uniformly altering outcomes.</p>
      <p>The study has limitations. The evaluation is limited to a binary relevance setting, a single dataset, and one
interpretable model, and counterfactual analysis considers only one sensitive attribute at a time. Modifying a
protected attribute while keeping other features fixed may produce less plausible user profiles. Here, such
counterfactuals are used strictly as diagnostic probes for sensitivity analysis rather than realistic simulations.
Additionally, group-level metrics do not capture longer-term exposure or feedback dynamics. The approach is not
compared with state-of-the-art mitigation methods, as the goal is to demonstrate the feasibility and behavior of a
unified counterfactual sensitivity mechanism. Future work will extend the framework to ranking-based
recommendations, more complex models, intersectional fairness settings, and longitudinal evaluations.</p>
    </sec>
    <sec id="sec-7">
      <title>7. Declaration on Generative AI</title>
      <p>During the preparation of this work, the authors used GPT-4 and Grammarly in order to: Grammar and spelling
check. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for
the publication’s content.
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