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An End-to-End Pipeline for Causal ML with Continuous Treatments: An Application to Financial Decision Making

Javier Moral Hernández, Clara Higuera-Cabañes, Álvaro Ibraín

arXiv:2609.30396v1stat.MEcs.LGstat.APstat.ML

TL;DR

Industrial causal inference faces high-dimensional data and continuous-treatment challenges, while available approaches have limited coverage of an end-to-end workflow. This paper presents a pipeline for dimensionality reduction, identification, estimation, and related tasks, and reports improved covariate-selection precision in its evaluation. Its methods are validated on a synthetic financial debt-collection dataset.

  • Problem

    High-dimensional data complicate causal discovery and estimation, and practical pipelines must address identifying covariates for causal-effect estimation.

    Source: §1 · p. 1

  • Method

    The pipeline assumes backdoor identifiability and uses two-stage dimensionality reduction to construct candidate covariates for causal identification.

    Source: §3 · p. 2, §3.1 · p. 3

  • Results

    Covariate-selection precision rose to 0.53 after dimensionality reduction and 0.80 after final identification, with recall maintained at 1.0 and all 8 true causal controls included.

    Source: §5.1 · p. 5

  • Takeaways & Limitations

    The approach is validated on a financial debt-collection use case and is designed for broader applicability across industries facing similar constraints.

    Source: §6 · p. 6

    Dimensionality reduction relies on linear partial correlation, which may miss nonlinear relationships and interactions; positivity detection may not account for unobserved confounding, and augmentation assumes monotonic treatment response.

    Source: §6 · p. 6

Abstract

from arXiv · show

This paper presents an end-to-end causal machine learning (ML) pipeline designed for real-world applications with continuous treatments. The proposed framework consists of six sequential steps: dimensionality reduction, causal identification, positivity assumption violation handling, estimation, refutation and evaluation, and policy optimization. We introduce practical contributions not currently available in existing causal ML toolkits, specifically: (1) a method for detecting and quantifying positivity violations in continuous treatment settings (2) a novel, scalable two-stage dimensionality reduction framework tailored for causal inference with high-dimensional data; (3) the adaptation of sensitivity analysis and estimation methods originally designed for binary treatments to the continuous treatment space and (4) an end-to-end integration of these components into a modular, reproducible workflow. These innovations address real-world challenges in causal inference that are often not covered in theoretical frameworks but frequently encountered in industrial applications. The methodology is validated with a synthetic dataset inspired in a real-world financial debt collection use case, however its design can be applied to analogous problems across different industries. Results demonstrate that the proposed methodology offers a more computationally efficient approach and produces less biased estimates compared to standard methods for problems with continuous treatment and high-dimensional data. A fully functional GitHub repository with documented code and numbered notebooks is made available ensuring reproducibility and practical implementation. The pipeline presented is intended to contribute to closing the gap between academic approaches and practical application in industry contexts where causal ML can be highly beneficial such as the financial sector.

1 Introduction

The introduction argues that causal ML addresses industrial questions requiring cause-and-effect insight, but practical use is constrained by high-dimensional data, continuous treatments, positivity violations, and fragmented tooling. The paper introduces an end-to-end framework validated on a financial debt-collection use case.

1 Introduction

  • Industrial causal inference faces computational and statistical challenges as high dimensionality complicates causal discovery, validation, expert review, and adjustment-set selection.Constraint-based discovery can have exponential worst-case complexity, while conditional-independence testing grows combinatorially.Source: §1 · p. 1
  • Continuous treatments remain difficult for standard tools: common T- and X-learners target binary treatments, and E-values are typically not formulated for continuous interventions.This limits the applicability of these estimation and sensitivity-analysis tools in practice.Source: §1 · p. 2
  • Positivity violations arise when some individuals lack support for treatment levels; existing diagnosis and remedies are described as mainly binary-focused or as addressing limited-overlap regions.The passage cites Petersen et al. and continuous-treatment approaches by Guo et al..Source: §1 · p. 2
  • Existing causal frameworks leave a gap in practical pipelines that jointly handle high-dimensional data, continuous treatments, positivity violations, and few samples.The introduction contrasts DoWhy [33] and EconML [25], noting limits in continuous outcomes or high-dimensional data and an emphasis on estimation rather than a complete pipeline.Source: §1 · p. 2
  • The financial sector has applications for causal inference, but heterogeneous client profiles, sparse intervention histories, and many available methods complicate implementation; the paper proposes a framework validated on debt collection.The framework is intended to address these challenges in finance and analogous applications.Source: §1 · p. 2

2 Problem statement / Case study

Debt-collection decisions must balance repayment and loss, while the effect of different write-down levels is uncertain. Randomized trials are impractical, so observational estimates must contend with confounding.

2 Problem statement / Case study

  • Debt-collection teams use refinancing, debt sales, or write-downs for clients in loan default, but repayment after a write-down varies across clients.The practical objective is choosing write-down amounts that support repayment while limiting losses.Source: §2 · p. 2
  • Expert judgment traditionally balances repayment likelihood and loss minimization, but prediction alone cannot establish how different write-down levels affect repayment.The case therefore calls for causal understanding of treatment effects.Source: §2 · p. 2
  • Randomized trials are impractical because of ethical and regulatory barriers, leaving observational data vulnerable to confounding by clients’ financial health.Clients in worse financial health typically receive larger reductions, complicating isolation of causal effects.Source: §2 · p. 2
  • The stated objective is to use causal inference for personalized counterfactual insights to optimize debt-collection strategies effectively and fairly.The motivation combines trial infeasibility, confounding, and the need for individualized decisions.Source: §2 · p. 2

3 Methods

The methods form a sequential pipeline for causal problems involving high-dimensional data, continuous treatments, or positivity violations. Its stages reduce and identify covariates, assess overlap, estimate effects, validate estimates, and support policy optimization.

3 Methods

  • The pipeline assumes the estimand is identifiable by the backdoor criterion and focuses covariate selection on variables that close backdoor paths.The authors state that correctly detecting these controls is important to avoid residual bias.Source: §3 · pp. 2–3

3.1 Dimensionality Reduction

  • Two-stage dimensionality reduction selects treatment predictors and outcome-relevant covariates, then leaves causal identification and domain expertise to refine the candidate adjustment set.Treatment-related features are selected predictively, while partial-correlation analysis addresses confounders and outcome-only predictors; the approach is intended to preserve confounding structure while scaling.Source: §3.1 · p. 3

3.2 Identification

  • Causal identification combines PC, FCI, and GES as hypothesis-generating methods with expert graph refinement and validation to determine the adjustment set.Validation uses testable implications, and the refined graph supports backdoor-based selection.Source: §3.2 · p. 3

3.3 Positivity Assumption Violation Quantification

  • A model-agnostic three-step procedure detects continuous-treatment positivity violations by predicting treatment, estimating residual density, and quantifying interval overlap.Low generalized-propensity probability flags a practical violation; its scalar value measures severity and can guide trimming or reweighting.Source: §3.3 · pp. 3–4

3.4 Estimation

  • The estimation stage targets conditional average dose-response curves and benchmarks regression adjustment, an S-learner, and continuous-treatment augmented IPTW.The augmented IPTW combines generalized-propensity weights with an outcome model and is described as consistent if either component is correct.Source: §3.4 · p. 4

3.5 Refutation and Evaluation

  • Refutation and evaluation combine placebo-treatment and random-common-cause tests, a continuous-treatment E-value sensitivity curve, and Qini-AUC for uplift ranking.Together, the tests, sensitivity metrics, and uplift curve form the proposed validation suite.Source: §3.5 · p. 4

4 Experimental setup

The evaluation uses a synthetic dataset inspired by financial debt collection because a public real-data version cannot be provided. It assesses causal-variable recovery, dose-response accuracy, computational efficiency, and component ablations.

4 Experimental setup

  • The synthetic debt-collection dataset preserves essential characteristics of sensitive financial data without exactly replicating the unavailable real dataset.The decision objective is selecting debt write-downs to minimize total expected loss.Source: §4 · p. 4
  • The generated data include continuous debt-loss treatment from 0 to 100, nonlinear heterogeneous effects, structured confounding, 410 features, and deliberate positivity violations.The features include relevant causal variables and noise; limited treatment overlap is created through a logistic assignment mechanism.Source: §4 · pp. 4–5
  • Evaluation measures causal-variable retrieval, conditional average dose-response accuracy, and computational efficiency; dose-response bias is computed across 100 treatment levels.The final average-bias metric is paired with refutation-test filtering, E-value sensitivity analysis, and Qini-AUC comparisons.Source: §4 · p. 5
  • An ablation disables dimensionality reduction and causal discovery to isolate their contributions to identification, estimation accuracy, and computational efficiency.Configuration details are documented in Appendix B to support transparency and reproducibility.Source: §4 · p. 5

5 Results

The framework improved variable identification and reduced estimation bias, while treatment-level results and the debt-collection case study show its performance and decision-making outputs.

5.1 Causal identification improvement

  • Dimensionality reduction raised precision to 0.53 at recall 1.0 with 15 covariates, and identification reached 0.80 precision with 10, including all eight true controls.Source: §5.1 · p. 5, Table 1 · p. 5
  • The proposed approach reduced causal-discovery runtime from over 600 minutes to 4 minutes: 3 for dimensionality reduction and 1 for identification.Source: §5.1 · p. 5

5.2 Estimates Performance

  • B = 0.117 (95% CI [0.105, 0.131]) represented a 60% mean-bias reduction versus baseline under the complete pipeline.Source: §5.2 · p. 5, Table 2 · p. 6
  • The complete proposed methodology achieved superior performance, with mean bias B = 0.117 (95% CI [0.105, 0.131]), a 60% reduction versus baseline; residual bias persisted due to unaddressed positivity violations.Source: §5.2 · p. 5
  • The S-learner was selected for estimation after AIPTW failed the placebo replacement test at extreme debt-loss percentages and S-learner outperformed Linear Regression on AUC curves.Source: §5.2 · pp. 5–6
  • Across treatment levels, the proposed method had maximum RMSE 0.20 versus 0.5 for baseline and RMSE below 0.20 across the 20–80% midrange.Source: §5.2 · p. 6
  • The ablation attributed 32% of total bias reduction to adjustment-set identification and 68% to positivity-violation handling through domain-informed synthetic data.Source: §5.2 · p. 6

5.3 Case Study Solution

  • In the case study, the estimated DAG identifies customer-characteristic confounders, while heterogeneous dose-response curves indicate uniform write-down policies would be suboptimal.Source: §5.3 · p. 6

6 Discussion and Future Work

The paper presents an adaptable end-to-end pipeline for industrial causal ML, validated in debt collection and intended for analogous settings. It identifies methodological and modeling limitations that bound its current scope.

6 Discussion and Future Work

  • The pipeline addresses high-dimensional data, positivity violations, and continuous treatments, with a debt-collection validation and intended applicability to analogous industrial settings.Source: §6 · p. 6
  • Linear partial correlation may miss nonlinearities and interactions; GPS/KDE positivity detection may omit unobserved confounding, and monotonic augmentation may not fit nonmonotonic responses.Source: §6 · p. 6

A Synthetic Data-Generation

The synthetic financial dataset combines continuous debt-loss treatment, confounding, positivity violations, and heterogeneous treatment effects with a high-dimensional feature space. Its design creates known causal structure and treatment-response patterns for evaluating the pipeline.

A Synthetic Data-Generation

  • Five confounders affect both treatment assignment and repayment, alongside three outcome-only and two treatment-only variables.This structure makes treatment assignment systematically biased by variables that also affect repayment.Source: A Synthetic Data-Generation · p. 8
  • The non-linear assignment mechanism maps debt-loss treatment to 0–100% while making some treatment regions practically inaccessible for certain covariate profiles.The construction is intended to mirror rigid financial writedown policies and violate positivity.Source: A Synthetic Data-Generation · p. 8
  • Treatment effects vary across covariate profiles, producing distinct customer dose-response curves and a gap between true and observed average treatment-outcome relationships.Figures 1–3 depict the heterogeneous effects, observed individual outcomes, and Simpson’s paradox, respectively.Source: A Synthetic Data-Generation · p. 8, Figure 1 · p. 8, Figure 2 · p. 8
  • The feature space adds 100 correlated redundant features and 300 noise features to test selection of relevant variables amid high dimensionality.The noise features have no systematic relationship with treatment or outcome.Source: A Synthetic Data-Generation · p. 9

B.1 Dimensionality Reduction

Dimensionality reduction uses two stages to select treatment predictors, then refine confounder and outcome-predictor sets through partial correlations.

B.1 Dimensionality Reduction

  • FCBF followed by CatBoost-based Sequential Forward Selection identifies treatment-predictive variables, using three-fold RMSE minimization to guide feature inclusion.FCBF uses a 0.0001 threshold, and selection stops when adding a feature no longer reduces cross-validated RMSE.Source: §B.1 · p. 9
  • Partial-correlation analyses retain confounders at a 0.01 threshold and outcome predictors at a 0.1 threshold.The confounder criterion measures change in the treatment–outcome partial correlation; the outcome criterion measures association conditional on treatment.Source: §B.1 · p. 9
  • Both partial-correlation analyses apply a 0.5 correlation threshold to remove multicollinear features.The authors describe the dual thresholds as balancing sensitivity to weak confounders with computational efficiency.Source: §B.1 · p. 9

B.2 Identification

For the synthetic experiment, domain expertise is restricted to temporal priors and correcting directional inconsistencies, avoiding use of the known data-generating structure.

B.2 Identification

  • Domain expertise enforces the temporal order in which covariates and treatment precede the outcome, and corrects directional inconsistencies in algorithms lacking temporal constraints.The restriction is intended to avoid artificially inflating performance metrics by using knowledge of the known data-generating process.Source: §B.2 · p. 9
  • The experiment excludes expert identification of missing relationships, spurious-correlation detection, and general edge-direction refinement.These components are part of the broader real-world approach but are omitted in this controlled setting.Source: §B.2 · p. 9
  • When discovery algorithms produce cyclic graphs, a simplified programmatic procedure breaks cycles instead of using domain knowledge to refine them.This avoids relying on the known underlying causal structure.Source: §B.2 · p. 9

B.3 Positivity assumption violation

The positivity workflow detects low-support regions in the continuous treatment domain and addresses them through monotonicity-based synthetic data augmentation grounded in banking-domain assumptions.

B.3 Positivity assumption violation

  • Regions where conditional treatment probability falls below 0.001 are flagged, with the treatment domain divided into consecutive 2% intervals for analysis.The interval partition supports granular analysis of violation patterns across the continuous treatment range.Source: §B.3 · p. 9
  • Domain-knowledge data-propagation adds synthetic outcomes at more favorable or less favorable writedown levels based on the observed repayment or default outcome.The procedure assumes repayment probability is monotonic with debt loss: repayment at a 60% writedown implies repayment at higher writedowns, while default at 40% implies default at lower ones.Source: §B.3 · p. 9
  • Augmentation targets about 20% of the training sample in violation regions and is applied only to training data to preserve validation-split integrity.Samples are generated randomly across problematic regions for balanced coverage.Source: §B.3 · p. 9
  • The authors frame augmentation as a practical compromise because restricting to positivity-compliant regions can leave prohibitively small samples, while limiting adjustment variables risks confounding bias.The approach balances practical constraints against methodological rigor.Source: §B.3 · pp. 9–10

B.4 Estimation

The estimation appendix specifies CatBoost-based S-learner and AIPTW implementations and gives synthetic treatment and outcome generation details. Its figures document the pipeline, estimated curves, refutation and sensitivity analyses, and bias comparisons.

B.4 Estimation

  • The S-learner uses a CatBoost classifier, while AIPTW combines propensity and outcome models with a final model trained on cross-validated pseudo-outcomes.The AIPTW propensity model uses a CatBoost regressor with kernel density estimation; its outcome model is a CatBoost classifier, and its final CatBoost regressor is followed by logistic-regression calibration.Source: §B.4 · p. 10

C Variables Definitions

  • The appendix identifies X1i as years since default and states that all features are standardized before the treatment-assignment formula is applied.Variable descriptions are located in the appendix's variable definitions.Source: C Variables Definitions · p. 10, §C.1 · p. 10

C.1 Treatment assignment formula

  • Treatment assignment uses a linear predictor with weighted feature terms and log-transformed features, plus noise described as following a truncated normal distribution.The supplied predictor fragment includes terms for X1i, log(1 + X2i), X3i, and log(1 + X4i).Source: §C.1 · p. 10

C.2 Outcome generation formula

  • Outcome generation first models each individual's positive-outcome probability, then bounds probabilities and samples outcomes binomially under domain-specific monotonicity constraints.The stated rule assigns 0 to a non-event when the intervention is at or below observed treatment, and 1 to an event when it is at or above observed treatment.Source: §C.2 · p. 10

D Figures

  • The appendix figures include the pipeline diagram, dose-response estimates, placebo and random-common-cause tests, sensitivity and cumulative-gain results, a causal DAG, and bias by debt-loss percentage.Figure captions identify the plotted topics but do not provide plotted values.Source: Figure 4 · p. 10, Figure 5 · p. 11, Figure 6 · p. 11
  • Individual dose-response curves and treatment-level bias comparisons are also listed among the appendix figures.The bias figure is described as covering debt-loss percentages; the individual-curves figure caption does not specify axes or methods.Source: Figure 10 · p. 11, Figure 12 · p. 12
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