Immutable Feature

An immutable feature is an input attribute whose value is fixed by nature, law, or logic and cannot be changed through user action. In counterfactual explanation systems, these features act as hard constraints—the algorithm is forbidden from suggesting changes to them. Classic examples include date of birth, place of birth, genetic markers, and historical events. The core principle is that a counterfactual that says 'you would have been approved if you were 10 years younger' is not actionable and therefore provides no meaningful recourse.

While overlapping, immutable features and protected attributes (under fairness law) are not identical sets:

• Immutable features: Cannot be changed physically or logically (e.g., birth year, native language)
• Protected attributes: Legally shielded from discrimination (e.g., race, gender, religion)
• Key difference: Some protected attributes may be mutable (e.g., marital status, religion), while some immutable features may not be legally protected (e.g., astrological sign). Counterfactual systems must respect both categories, but immutability is a physical/logical constraint, not a legal one.

Immutable features define the boundary of an action set—the space of permissible feature modifications available to a user. When generating counterfactuals:

• The algorithm must mask out immutable features from perturbation
• The search for a counterfactual occurs only in the subspace of mutable features
• If no valid counterfactual exists without altering an immutable feature, the system should report no feasible recourse rather than suggesting an impossible change. This constraint is critical for recourse feasibility and distinguishes actionable explanations from purely diagnostic ones.

Immutable features often serve as root nodes in causal graphs, exerting downstream influence on mutable features. For example, age (immutable) causally affects years of experience (mutable). A naive counterfactual system might suggest increasing experience without recognizing that age constrains the maximum plausible value. Advanced systems encode these dependencies through structural causal models (SCMs) and feasibility constraints that prevent counterfactuals from violating causal monotonicity—ensuring the recommended change respects the immutable feature's causal influence on other variables.

Immutable features are enforced through several technical mechanisms:

• Feature masking: Zeroing out gradients for immutable dimensions during gradient-based generation
• Constraint optimization: Adding hard equality constraints to the objective function (e.g., x_immutable == x_original)
• Action set specification: Defining a binary mask vector where 1 indicates mutable and 0 indicates immutable
• Post-hoc filtering: Generating candidates freely, then discarding any that modify immutable features. The masking approach is preferred as it is computationally efficient and guarantees constraint satisfaction during the search process.

The handling of immutable features directly impacts counterfactual fairness. A model is counterfactually fair if its prediction for an individual is identical to its prediction in a counterfactual world where only a sensitive, immutable attribute (e.g., race) is changed. Violations indicate the model relies on protected immutable features. Evaluation metrics include:

• Constraint violation rate: Percentage of generated counterfactuals that improperly alter immutable features
• Recourse rate by group: Whether protected groups have systematically lower access to actionable recourse due to immutable feature constraints
• Causal fairness gap: Difference in predictions between actual and counterfactual selves

In credit decisioning, immutable features form the backbone of regulatory compliance. Age and date of birth are classic immutable attributes that cannot be altered in a recourse recommendation—you cannot tell an applicant to be older to qualify for a loan. Similarly, country of origin and historical bankruptcy filings are temporally fixed. A valid counterfactual for a denied loan must hold these constant while suggesting changes to mutable features like credit utilization ratio or number of open accounts.

Medical counterfactuals must respect biological immutability. Genetic markers such as BRCA1/BRCA2 mutation status are fixed at birth and cannot be modified. Family medical history is a temporally immutable record—a patient cannot retroactively change their parents' health outcomes. When generating explanations for a disease risk prediction, the system must hold these features constant and instead explore changes to BMI, smoking status, or medication adherence to flip the prediction.

Algorithmic hiring tools must treat several features as immutable to avoid discriminatory recourse. Race, gender, and ethnicity are legally protected and biologically fixed. Educational pedigree—the specific institution attended—is temporally immutable once a degree is conferred. A counterfactual explaining why a candidate was rejected must not suggest changing their alma mater. Instead, it should focus on actionable features like years of experience, certification status, or skill endorsements.

Recidivism prediction models operate under strict immutability constraints. Prior conviction count and age at first offense are historical facts that cannot be altered. Place of birth and juvenile record status are similarly fixed. Counterfactual explanations for a high-risk classification must hold these constant while identifying mutable pathways such as employment status, substance abuse treatment completion, or housing stability to demonstrate what would change the assessment.

Actuarial models rely on several immutable features that counterfactuals must preserve. Date of first license issuance is a fixed historical timestamp. Congenital conditions present from birth cannot be reversed. Natural disaster zone classification for a property is geographically immutable. When explaining a premium denial, the system must not suggest relocating a house. Valid recourse focuses on installing safety systems, bundling policies, or increasing deductibles.

University admission models must respect temporal immutability. High school GPA is a sealed record that cannot be retroactively improved. Standardized test scores from past sittings are fixed data points. Socioeconomic background and first-generation student status are immutable demographic facts. Counterfactual explanations for a rejection must hold these constant and instead highlight changes to personal statement quality, extracurricular depth, or interview performance as actionable recourse paths.

A formal specification of the permissible modifications a user can make to each feature, defining the boundary between actionable and non-actionable changes. The action set explicitly marks immutable features as frozen, ensuring the counterfactual search algorithm never suggests altering them. This specification is critical for recourse feasibility and is often encoded as a set of inequality constraints or a binary mutability mask.

The degree to which a counterfactual recommendation respects real-world constraints, including immutable features, causal relationships, and user capabilities. A feasible counterfactual never suggests changing a protected attribute like race or birth_year. Instead, it operates entirely within the action set, ensuring the path to a favorable outcome is both logically sound and practically achievable by the end-user.

A counterfactual instance that lies within the high-density region of the training data distribution, ensuring the explanation is realistic and not an adversarial artifact. Plausibility constraints often implicitly respect immutable features by preventing the generation of instances that violate known data manifolds—for example, a 20-year-old with 30 years of professional experience would be flagged as implausible and rejected.