Counterfactual Prediction

Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate uncertainty quantification in existing methods. We introduce the Causal Diffusion Model (CDM), the first denoising diffusion probabilistic approach explicitly designed to generate full probabilistic distributions of counterfactual outcomes under sequential interventions. CDM employs a novel residual denoising architecture with relational self-attention, capturing intricate temporal dependencies and multimodal outcome trajectories without requiring explicit adjustments (e.g., inverse-probability weighting or adversarial balancing) for confounding. In rigorous evaluation on a pharmacokinetic-pharmacodynamic tumor-growth simulator widely adopted in prior work, CDM consistently outperforms state-of-the-art longitudinal causal inference methods, achieving a 15-30% relative improvement in distributional accuracy (1-Wasserstein distance) while maintaining competitive or superior point-estimate accuracy (RMSE) under high-confounding regimes. By unifying uncertainty quantification and robust counterfactual prediction in complex, sequentially confounded settings, without tailored deconfounding, CDM offers a flexible, high-impact tool for decision support in medicine, policy evaluation, and other longitudinal domains.

Data-driven decision making frequently relies on predicting counterfactual outcomes. In practice, researchers commonly train counterfactual prediction models on a source dataset to inform decisions on a possibly separate target population. Conformal prediction has arisen as a popular method for producing assumption-lean prediction intervals for counterfactual outcomes that would arise under different treatment decisions in the target population of interest. However, existing methods require that every confounding factor of the treatment-outcome relationship used for training on the source data is additionally measured in the target population, risking miscoverage if important confounders are unmeasured in the target population. In this paper, we introduce a computationally efficient debiased machine learning framework that allows for valid prediction intervals when only a subset of confounders is measured in the target population, a common challenge referred to as runtime confounding. Grounded in semiparametric efficiency theory, we show the resulting prediction intervals achieve desired coverage rates with faster convergence compared to standard methods. Through numerous synthetic and semi-synthetic experiments, we demonstrate the utility of our proposed method.

Evaluating football player transfers is challenging because player actions depend strongly on tactical systems, teammates, and match context. Despite this complexity, recruitment decisions often rely on static statistics and subjective expert judgment, which do not fully account for these contextual factors. This limitation stems largely from the absence of counterfactual simulation mechanisms capable of predicting outcomes in hypothetical scenarios. To address these challenges, we propose ScoutGPT, a generative model that treats football match events as sequential tokens within a language modeling framework. Utilizing a NanoGPT-based Transformer architecture trained on next-token prediction, ScoutGPT learns the dynamics of match event sequences to simulate event sequences under hypothetical lineups, demonstrating superior predictive performance compared to existing baseline models. Leveraging this capability, the model employs Monte Carlo sampling to enable counterfactual simulation, allowing for the assessment of unobserved scenarios. Experiments on K League data show that simulated player transfers lead to measurable changes in offensive progression and goal probabilities, indicating that ScoutGPT captures player-specific impact beyond traditional static metrics.

Counterfactual learning has become promising for understanding and modeling causality in complex and dynamic systems. This paper presents a novel method for counterfactual learning in the context of multivariate time series analysis and forecast. The primary objective is to uncover hidden causal relationships and identify potential interventions to achieve desired outcomes. The proposed methodology integrates genetic algorithms and rigorous causality tests to infer and validate counterfactual dependencies within temporal sequences. More specifically, we employ Granger causality to enhance the reliability of identified causal relationships, rigorously assessing their statistical significance. Then, genetic algorithms, in conjunction with quantile regression, are used to exploit these intricate causal relationships to project future scenarios. The synergy between genetic algorithms and causality tests ensures a thorough exploration of the temporal dynamics present in the data, revealing hidden dependencies and enabling the projection of outcomes under hypothetical interventions. We evaluate the performance of our algorithm on real-world data, showcasing its ability to handle complex causal relationships, revealing meaningful counterfactual insights, and allowing for the prediction of outcomes under hypothetical interventions.

This paper tackles the problem of time-to-event counterfactual survival prediction, aiming to optimize individualized survival outcomes in the presence of heterogeneity and censored data. We propose CURE, a framework that advances counterfactual survival modeling via comprehensive multimodal embedding and latent subgroup retrieval. CURE integrates clinical, paraclinical, demographic, and multi-omics information, which are aligned and fused through cross-attention mechanisms. Complex multi-omics signals can be adaptively refined using a mixture-of-experts architecture, emphasizing the most informative omics components. Building upon this representation, CURE implicitly retrieves patient-specific latent subgroups that capture both baseline survival dynamics and treatment-dependent variations. Experimental results on METABRIC and TCGA-LUAD datasets demonstrate that proposed CURE model consistently outperforms strong baselines in survival analysis, evaluated using the Time-dependent Concordance Index ($C^{td}$) and Integrated Brier Score (IBS). These findings highlight the potential of CURE to enhance multimodal understanding and serve as a foundation for future treatment recommendation models. All code and related resources are publicly available to facilitate the reproducibility https://github.com/L2R-UET/CURE.

The contemporary paradigm of trajectory learning operates fundamentally at the level of group dynamics, systematically reducing individual-level complexity to fit group-level models, thus rendering effective patient subtyping difficult and individual-level modeling largely out of reach. We propose a data-driven paradigm that introduces a dedicated individual-level temporal variable to capture Timing Attention (i.e., the degree of concentration of an event's timing distribution across the patient cohort), thereby rendering timing a computable dimension that enables individualized temporal features in trajectory learning. Instantiated as the Level-of-Individual Time Transformation (LITT) and applied to longitudinal EHR data from 3,276 breast cancer patients, the proposed paradigm demonstrates, for the first time to our knowledge: (1) automatic discovery of clinically significant patient trajectories, and (2) counterfactual timing deduction, that is, a What-If Machine. Both results are purely data-driven, requiring no prior domain knowledge. LITT further achieves strong performance on timing prediction and survival analysis tasks.

How would the probability of scoring change if a different player took the same shot? Although expected goals models describe the difficulty of scoring opportunities, comparing players on identical chances requires accounting for uncertainty in their estimated conversion probabilities. We address this question through a hierarchical Bayesian framework that evaluates alternative shooters under the same observed circumstances. Using 35,700 eligible shots from four leagues during the 2015/16 season, we compare a contextual benchmark with a primary player-intercept model and a provisional extension that allows player differences to vary with shooting conditions. Paired posterior draws preserve shared uncertainty when individual probability differences are aggregated across opportunities. Chronological validation demonstrates improved predictive performance relative to a constant-rate baseline, but introducing player effects provides negligible additional gains. Controlled single-seed experiments show that greater information per player improves estimation accuracy and narrows uncertainty intervals, although distinguishing small differences remains difficult and confident conclusions about near-null effects can become more frequent. Applications involving Giroud--Vardy and Berardi--Sansone similarly yield estimated differences that are small relative to their posterior uncertainty. These findings highlight an important distinction between predicting the outcome of a shot and establishing whether one player would be more likely to convert it. The proposed framework makes this distinction explicit by evaluating alternative shooters on fixed recorded opportunities while accounting for their contextual exposure. The resulting comparisons concern conditional conversion rather than the causal consequences of replacing a player in a match.

Average treatment effects summarize how interventions change outcomes, but individualized decisions require predictions and outcome distributions of what would have happened to the same individual under an alternative treatment. We develop PO-Flow, a continuous normalizing flow framework that represents treatment-specific outcome distributions through invertible transport maps. It supports potential-outcome generation, conditional average treatment-effect estimation, factual-conditioned counterfactual prediction, and density evaluation. To address treatment imbalance in observational data, we incorporate cross-fitted inverse-probability weighting into the flow-matching loss. We establish sufficient conditions under which encoding a factual outcome and decoding under an alternative treatment recovers the individual counterfactual. Under shared exogenous noise and a common encoded reference distribution, scalar recovery follows from increasing noise-to-latent maps. For multivariate outcomes, we assume triangularity or a convex-gradient structure. These conditions distinguish fitting outcome distributions from recovering their causal correspondence. Experiments on four scalar benchmarks and seven multivariate or image settings, with dimensions up to 784, compare against ten scalar and five multivariate baselines. Controlled ablations show IPW improves all reported scalar counterfactual RMSE, PEHE, and potential-outcome RMSE. PO-Flow achieves the lowest PEHE and potential-outcome RMSE on all four scalar benchmarks and attains or ties the lowest mean in 26 of 35 multivariate dataset--metric comparisons.