Age Predictors Through the Lens of Generalization, Bias Mitigation, and Interpretability: Reflections on Causal Implications

Debdas Paul; Elisa Ferrari; Irene Gravili; Alessandro Cellerino

cs.LGMar 17, 2026

Age Predictors Through the Lens of Generalization, Bias Mitigation, and Interpretability: Reflections on Causal Implications

Authors: Debdas Paul, Elisa Ferrari, Irene Gravili, Alessandro Cellerino

Organizations: Leibniz Institute on Aging — Fritz Lipmann Institute (FLI), Beutenbergstr. 11, Jena, 100190, Germany.

Abstract

Chronological age predictors often fail to achieve out-of-distribution (OOD) gen- eralization due to exogenous attributes such as race, gender, or tissue. Learning an invariant representation with respect to those attributes is therefore essential to improve OOD generalization and prevent overly optimistic results. In predic- tive settings, these attributes motivate bias mitigation; in causal analyses, they appear as confounders; and when protected, their suppression leads to fairness. We coherently explore these concepts with theoretical rigor and discuss the scope of an interpretable neural network model based on adversarial representation learning. Using publicly available mouse transcriptomic datasets, we illustrate the behavior of this model relative to conventional machine learning models. We observe that the outcome of this model is consistent with the predictive results of a published study demonstrating the effects of Elamipretide on mouse skeletal and cardiac muscle. We conclude by discussing the limitations of deriving causal interpretation from such purely predictive models.

Figures & tables

Notation	Description
$\mathbb{R}$	Set of real numbers
$\mathbb{R}_{\geq 0}$	Set of nonnegative real numbers
$\mathbb{Z}$	Set of integers
$\lceil x\rceil$	smallest integer greater than or equal to $x$
$(\Omega,\mathcal{F},\mathbb{P})$	Underlying probability space
$\mathcal{X}$	Input (feature) space

Table 1: List of notations used in this work

Figure 1: Different associations between

X

and

Y

as adopted from Figure 12 of [ 7 ] . A marginal correlation is the weakest form association that ignores dependencies among covariates. A stronger form is the regression relevant coefficients which captures partial correlation (non-zero correlation coefficients). Causal variables are a subset of regression variables under faithfulness assumption (A must non-zero coefficient of all parents (direct cause) of

Y

. Invariance set is identifiable even when parents of

Y

not forming a diluted notion of causality. This set is much more useful in practical applications as stated in [ 7 ] . Causal form of association is desirable but often hard to achieve.

Figure 2: For detailed caption, see Section 12

Figure 3: For detailed caption, see Section 12

Figure 4: For detailed caption, see Section 12

Figure 5: For detailed caption, see Section 12

Module	Layer	Dimension / Description
Feature Encoder: $\mathbb{FE}:X\rightarrow$ F
Input	Input layer	$(d)$ features
	Binary Stochastic Filter	Bernoulli mask per feature (learned prob.)
Block 1	Dense + BN + ReLU	$d\rightarrow 256$
Block 2	Dense + BN + ReLU + Dropout	$256\rightarrow 256$
Block 3	Dense + BN + ReLU + Dropout	$256\rightarrow 106$

Table 2: Summary of the encoder, predictor, and adversarial bias network architecture as depicted in Figure 2 A.

Figure SA1: Recovery of attributes in

\mathbb{S}

using Post-hoc Analysis Balanced accuracy of a linear probe ( LogisticRegression ) trained on the learned latent representation

Z

to predict attributes: sex, tissue, platform, and series ID, for each holdout dataset. Bars correspond to probe performance for different adversarial strengths

\alpha

. Red dashed lines indicate the permutation baseline, obtained by training the probe after randomly shuffling the attribute labels, thereby representing chance-level performance. A decreasing balanced accuracy with increasing

\alpha

suggests partial suppression of confounder-related information in

Z

. However, residual predictability remains, indicating that attribute signals are not fully eliminated from the representation. This observation is consistent with prior work showing that adversarial objectives do not guarantee complete removal of attribute information, and that post-hoc classifiers may still recover such signals from debiased representations [ 30 ] (see Discussions).

Figure SA2: Regression plots of fold-averaged predictions without the filtering layer (Figure 2 A) for each leave-one-dataset-out (LOSO) holdout setup. Each row corresponds to a different holdout dataset (GSE111164, GSE145480, GSE75192), and each column represents a different domain-adversarial strength (

\alpha

). For every subplot, predictions from all LOSO folds were aggregated and averaged per biological sample. Points represent the mean predicted age versus chronological age. Performance metrics (MAE and

R^{2}

) are computed using the averaged predictions. The diagonal line indicates the identity line (

y=x

Figure SA3: Regression plots of fold-averaged predictions without the filtering layer (Figure 3 A) for each leave-one-dataset-out (LOSO) holdout setup. Figure generation follows the same procedure as in Figure SA2

Figure SA4: Residual (absolute value) plot for by tissue fold-averaged predictions for GSE75192 as holdout. Predictions from all cross-validation folds were averaged for each sample before computing absolute value of residuals (

|\overline{y}_{\mathrm{pred}}-y_{\mathrm{true}}|

). Boxplots show the distribution of residuals across tissues for models trained with and without the feature filter under different values of

\alpha

OOD Generalization

Out-of-distribution generalization studies how machine-learning models perform when test data, domains, tasks, or environments differ from training.

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Interpretability research on large language models (LLMs) has yielded important insights into model behaviour, yet recurring pitfalls persist: findings that do not generalise, and causal interpretations that outrun the evidence. Our position is that causal inference specifies what constitutes a valid mapping from model activations to invariant high-level structures, the data or assumptions needed to achieve it, and the inferences it can support. Specifically, Pearl's causal hierarchy clarifies what an interpretability study can justify. Observations establish associations between model behaviour and internal components. Interventions (e.g., ablations or activation patching) support claims how these edits affect a behavioural metric (e.g., average change in token probabilities) over a set of prompts. However, counterfactual claims -- i.e., asking what the model output would have been for the same prompt under an unobserved intervention -- remain largely unverifiable without controlled supervision. We show how causal representation learning (CRL) operationalises this hierarchy, specifying which variables are recoverable from activations and under what assumptions. Together, these motivate a diagnostic framework that helps practitioners select methods and evaluations matching claims to evidence such that findings generalise.

Abstract

OOD Generalization

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