Causal Inference

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Causal inference asks what would change if a treatment, policy, or other factor were different, rather than merely measuring which variables move together. Researchers use randomized and quasi-experiments, causal graphs with adjustment, instrumental variables and proxies, and semiparametric or machine-learning estimators. Causal discovery from observational, time-series, and network data seeks structures that support these analyses, while counterfactual models help evaluate individual outcomes and policies. Results depend on assumptions—especially about hidden confounding, interference, and transport across populations—so sensitivity analysis, partial-identification bounds, and credible evaluation remain central challenges as generative and foundation models are explored.

Latest papers

318 papers34 papers in the last four weeks, up 13% on the four weeks before. 0.2% of all new papers.

Feb 17, 2026

Causal Effect Estimation with Latent Textual Treatments

Understanding the causal effects of text on downstream outcomes is a central task in many applications. Estimating such effects requires researchers to run controlled experiments that systematically vary textual features. While large language models (LLMs) hold promise for generating text, producing and evaluating controlled variation requires more careful attention. In this paper, we present an end-to-end pipeline for the generation and causal estimation of latent textual interventions. Our work first performs hypothesis generation and steering via sparse autoencoders (SAEs), followed by robust causal estimation. Our pipeline addresses both computational and statistical challenges in text-as-treatment experiments. We demonstrate that naive estimation of causal effects suffers from significant bias as text inherently conflates treatment and covariate information. We describe the estimation bias induced in this setting and propose a solution based on covariate residualization. Our empirical results show that our pipeline effectively induces variation in target features and mitigates estimation error, providing a robust foundation for causal effect estimation in text-as-treatment settings.

Omri Feldman, Amar Venugopal, Jann Spiess +1

School of Computer Science and Engineering, The Hebrew University of Jerusalem · Department of Economics, Stanford University · Graduate School of Business, Stanford University

Causal Effect Estimation Causal Inference Causal Interventions in Language Models

Feb 17, 2026

CEPAE: Conditional Entropy-Penalized Autoencoders for Time Series Counterfactuals

The ability to accurately perform counterfactual inference on time series is crucial for decision-making in fields like finance, healthcare, and marketing, as it allows us to understand the impact of events or treatments on outcomes over time. In this paper, we introduce a new counterfactual inference approach tailored to time series data impacted by market events, which is motivated by an industrial application. Utilizing the abduction-action-prediction procedure and the Structural Causal Model framework, we first adapt methods based on variational autoencoders and adversarial autoencoders, both previously used in counterfactual literature although not in time series settings. Then, we present the Conditional Entropy-Penalized Autoencoder (CEPAE), a novel autoencoder-based approach for counterfactual inference, which employs an entropy penalization loss over the latent space to encourage disentangled data representations. We validate our approach both theoretically and experimentally on synthetic, semi-synthetic, and real-world datasets, showing that CEPAE generally outperforms the other approaches in the evaluated metrics.

Tomàs Garriga, Gerard Sanz, Eduard Serrahima de Cambra +1

Novartis · Barcelona Supercomputing Center

Causal Counterfactual Generation Causal Inference

Feb 16, 2026

Use What You Know: Causal Foundation Models with Partial Graphs

Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a single step. However, in their current state, they do not allow for the incorporation of any domain knowledge, which can lead to suboptimal predictions. We bridge this gap by introducing methods to condition CFMs on causal information, such as the causal graph or more readily available ancestral information. When access to complete causal graph information is too strict a requirement, our approach also effectively leverages partial causal information. We systematically evaluate conditioning strategies and find that injecting learnable biases into the attention mechanism, together with a graph-convolutional encoder, is a highly effective method to utilise full and partial causal information. Our experiments show that this conditioning allows a general-purpose CFM to match the performance of specialised models trained on specific causal structures. Overall, our approach addresses a central hurdle on the path towards all-in-one causal foundation models: the capability to answer causal queries in a data-driven manner while effectively leveraging any amount of domain expertise.

Arik Reuter, Anish Dhir, Cristiana Diaconu +6

University of Cambridge, Cambridge, United Kingdom · Max Planck Institute for Intelligent Systems, Tübingen, Germany · Gatsby Computational Neuroscience Unit, University College London +5

Causal Foundation Models Causal Discovery Causal Inference

Feb 16, 2026

Bounding Probabilities of Causation with Partial Causal Diagrams

Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates, require complete causal graphs, or rely on restrictive binary settings, limiting their practical use. In real-world applications, causal information is often partial but nontrivial. This paper proposes a general framework for bounding probabilities of causation using partial causal information. We show how the available structural or statistical information can be systematically incorporated as constraints in a optimization programming formulation, yielding tighter and formally valid bounds without full identifiability. This approach extends the applicability of probabilities of causation to realistic settings where causal knowledge is incomplete but informative.

Yuxuan Xie, Ang Li

University of Ottawa, Ontario, Canada · Department of Computer Science, Florida State University, FL, U.S.A.

Causal Inference Causal Identifiability

Dec 28, 2025

From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only transacted quantities and prices can be observed, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of

\Tilde{\mathcal{O}}(\sqrt{T}\wedgeσ_S^{-2})

. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we use simulations and offline counterfactuals from Talabat and Lyft data to illustrate the potential revenue implications of our approach.

Rui Ai, David Simchi-Levi, Feng Zhu

MIT

Causal Effect Estimation Instrumental Variable Estimation Causal Inference Dynamic Pricing

Oct 9, 2025

Spatial Deconfounder: Interference-Aware Deconfounding for Spatial Causal Inference

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions--without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.

Ayush Khot, Miruna Oprescu, Maresa Schröder +2

University of Illinois at Urbana-Champaign · Cornell University, Cornell Tech · LMU Munich, Munich Center for Machine Learning (MCML) +1

Causal Effect Estimation Causal Inference Causal Inference with Unobserved Confounding

May 30, 2025

Aligning Language Models with Observational Data: Opportunities and Risks from a Causal Perspective

Large language models are being widely used across industries to generate text that contributes directly to key performance metrics, such as medication adherence in patient messaging and conversion rates in content generation. Pretrained models, however, often fall short when it comes to aligning with human preferences or optimizing for business objectives. As a result, fine-tuning with good-quality labeled data is essential to guide models to generate content that achieves better results. Controlled experiments, like A/B tests, can provide such data, but they are often expensive and come with significant engineering, logistical, and ethical challenges. Meanwhile, companies have access to a vast amount of historical (observational) data that remains underutilized. In this work, we study the challenges and opportunities of fine-tuning LLMs using observational data. We show that while observational outcomes can provide valuable supervision, directly fine-tuning models on such data can lead them to learn spurious correlations. We present empirical evidence of this issue using various real-world datasets and propose DeconfoundLM, a method that explicitly removes the effect of known confounders from reward signals. In simulation experiments, DeconfoundLM more accurately recovers causal relationships and mitigates failure modes of methods that assume counterfactual invariance, achieving over 16% higher objective score than ODIN and other baselines, when entangled confounding is present. Please refer to the project page for code and related resources.

Erfan Loghmani

Foster School of Business University of Washington Seattle, WA 98195

LLM Alignment LLM Fine-Tuning Causal Inference

Apr 3, 2025

Semiparametric Inference for Counterfactual Regression under Intervention-Driven Shift

We study counterfactual regression, which maps features to outcomes under hypothetical scenarios that differ from those observed in the data. This problem is central to decision-making under distribution shift, where treatment patterns may change at deployment. We develop a semiparametric framework for counterfactual regression along a prespecified incremental-intervention path. The target is a finite-dimensional constrained projection of counterfactual risk, estimated using cross-fitted influence-function representations of the program components. For smooth programs with fixed constraints and finite-dimensional programs with estimated linear constraints, we establish consistency and local stability of the optimizer under class-specific conditions, and derive pointwise and uniform first-order expansions. These results yield asymptotically valid inference, including simultaneous confidence bands for the counterfactual regression path. Simulations and an application to SMS reminders illustrate the finite-sample performance and practical applicability of the proposed approach.

Kwangho Kim

Department of Statistics, Korea University

Distribution Shift Robustness Semiparametric Inference Causal Inference Counterfactual Learning Causal Intervention

Mar 25, 2025

Quantifying Symptom Causality in Clinical Decision Making: An Exploration Using CausaLM

Current machine learning approaches to medical diagnosis often rely on correlational patterns between symptoms and diseases, risking misdiagnoses when symptoms are ambiguous or common across multiple conditions. In this work, we move beyond correlation to investigate the causal influence of key symptoms-specifically "chest pain" on diagnostic predictions. Leveraging the CausaLM framework, we generate counterfactual text representations in which target concepts are effectively "forgotten" enabling a principled estimation of the causal effect of that concept on a model's predicted disease distribution. By employing Textual Representation-based Average Treatment Effect (TReATE), we quantify how the presence or absence of a symptom shapes the model's diagnostic outcomes, and contrast these findings against correlation-based baselines such as CONEXP. Our results offer deeper insight into the decision-making behavior of clinical NLP models and have the potential to inform more trustworthy, interpretable, and causally-grounded decision support tools in medical practice.

Alexander Romanus, Mehul Shetty, Connor Jordan

Clinical Decision-Making Causal Interpretability Causal Inference Causal Interventions in Language Models

Feb 27, 2025

Causal Effect Estimation under Networked Interference without Networked Unconfoundedness Assumption

Estimating causal effects under networked interference from observational data is a crucial yet challenging problem. Most existing methods mainly rely on the networked unconfoundedness assumption, which guarantees the identification of networked effects. However, this assumption is often violated due to the latent confounders inherent in observational data, thereby hindering the identification of networked effects. To address this issue, we leverage the rich interaction patterns between units in networks, which provide valuable information for recovering these latent confounders. Building on this insight, we develop a confounder recovery framework that explicitly characterizes three categories of latent confounders in networked settings: those affecting only the unit, those affecting only the unit's neighbors, and those influencing both. Based on this framework, we design a networked effect estimator using identifiable representation learning techniques. From a theoretical standpoint, we prove the identifiability of all three types of latent confounders and, by leveraging the recovered confounders, establish a formal identification result for networked effects. Extensive experiments validate our theoretical findings and demonstrate the effectiveness of the proposed method.

Weilin Chen, Ruichu Cai, Jie Qiao +2

School of Computer Science, Guangdong University of Technology, Guangzhou, 510006, China · School of Computer Science, Guangdong University of Technology, Guangzhou, 510006, China and Peng Cheng Laboratory, Shenzhen, China · Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom

Causal Effect Estimation Causal Identifiability Causal Inference

Dec 6, 2024

SPARC: Scalable Path-Specific Counterfactual Fairness via Causal Conditional Independence

Deep learning models exhibit fairness concerns when predictions are inadvertently influenced by sensitive attributes. However, existing attempts to make Path-Specific Counterfactual Fairness optimizable rely on estimating marginal potential outcome probabilities-an approach that fundamentally requires high-dimensional conditional density estimation and breaks down in modalities such as medical images, where the curse of dimensionality renders reliable estimation infeasible. To address this limitation, we reduce the problem of enforcing Path-Specific Counterfactual Fairness to a causal conditional independence constraint and prove that satisfying this constraint is sufficient to eliminate the unfair causal effect. This reduction replaces intractable counterfactual estimation with a discriminative optimization objective that remains scalable in high-dimensional settings.

Bowei Tian, Yexiao He, Ziyao Wang +3

University of Maryland, College Park, MD 20742, USA · Clemson University, Clemson, SC 29634, USA

Debiased ML Algorithmic Fairness Counterfactual Fairness Causal Inference Counterfactual Learning

Oct 29, 2024

Identifiability Analysis of Linear ODE Systems with Hidden Confounders

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time

t

. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

Yuanyuan Wang, Biwei Huang, Wei Huang +2

The University of Melbourne · University of California, San Diego

Parameter Identifiability Causal Identifiability Causal Inference

Jul 12, 2024

Granger Causality in Extremes

We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among time-varying variables. While this notion gains heightened importance during extreme and highly volatile periods, state-of-the-art methods primarily focus on causality within the body of the distribution, often overlooking causal mechanisms that manifest only during extreme events. Our framework is designed to infer causality mainly from extreme events by leveraging the causal tail coefficient. We establish equivalences between causality in extremes and other causal concepts, including (classical) Granger causality, Sims causality, and structural causality. We prove other key properties of Granger causality in extremes and show that the framework is especially helpful under the presence of hidden confounders. We also propose a novel inference method for detecting the presence of Granger causality in extremes from data. Our method is model-free, can handle non-linear and high-dimensional time series, outperforms current state-of-the-art methods in all considered setups, both in performance and speed, and was found to uncover coherent effects when applied to financial and extreme weather observations.

Juraj Bodik, Olivier C. Pasche

Faculty of Business and Economics, University of Lausanne, Switzerland · Department of Statistics, UC Berkeley, California, USA · Research Institute for Statistics and Information Science, University of Geneva, Switzerland +1

Time-Series Causal Discovery Causal Inference

Jun 12, 2024

Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework

Existing evaluations of tabular synthesis models rely primarily on low-order statistics and downstream task performance, leaving multivariate causal relationships that go beyond pairwise correlations largely unmeasured. We argue that a systematic evaluation on high-order structural information is a crucial first step in addressing this issue in tabular data synthesis. In this paper, we present high-order structural causal information as a natural form of prior knowledge and introduce a benchmark framework to evaluate tabular synthesis models. This framework allows us to generate benchmark datasets through a flexible range of data generation processes, allowing for the training of tabular synthesis models using these datasets for further evaluation. We propose multiple benchmark tasks, high-order metrics, and causal inference tasks as downstream tasks for evaluating the quality of synthetic data generated by the trained models. Our experiments demonstrate the effectiveness of the benchmark framework in evaluating the model's ability to capture high-order structural causal information. Furthermore, our benchmarking results provide an initial assessment of state-of-the-art tabular synthesis models. These results reveal significant gaps between ideal and actual performance and highlight how baseline methods differ. We position the framework as a controlled diagnostic benchmark for causal fidelity, complementing existing low-order and downstream evaluations. We open source the benchmark framework, including both code and data along with documentation, to support further research in this area.

Zineb Senane, Axel Karlsson, Lele Cao +6

KTH Royal Institute of Technology · Stockholm, Sweden · King AI Labs, Microsoft +2

Synthetic Benchmark Generation Causal Inference Tabular Data Synthesis Synthetic Data Evaluation

Dec 25, 2023

Clustered Switchback Designs for Experimentation Under Spatio-temporal Interference

We consider experimentation in the presence of non-stationarity, inter-unit (spatial) interference, and carry-over effects (temporal interference), where we wish to estimate the global average treatment effect (GATE), the difference between average outcomes having exposed all units at all times to treatment or to control. We suppose spatial interference is described by a graph, where a unit's outcome depends on its neighborhood's treatments, and that temporal interference is described by an MDP, where the transition kernel under either treatment (action) satisfies a rapid mixing condition. We propose a clustered switchback design, where units are grouped into clusters and time steps are grouped into blocks, and each whole cluster-block combination is assigned a single random treatment. Under this design, we show that for graphs that admit good clustering, a truncated Horvitz-Thompson estimator achieves a

\tilde O(1/NT)

mean squared error (MSE), matching the lower bound up to logarithmic terms for sparse graphs. Our results simultaneously generalize the results from \citet{hu2022switchback,ugander2013graph} and \citet{leung2022rate}. Simulation studies validate the favorable performance of our approach.

Su Jia, Nathan Kallus, Christina Lee Yu

Cornell University

Causal Effect Estimation Causal Inference

Jan 27, 2023

Epsilon-Identifiability of Causal Quantities

Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the available data sources. This paper shows how approximate identifiability is still possible for several probabilities of causation. We term this epsilon-identifiability and demonstrate its usefulness in cases where the behavior of certain subpopulations can be restricted within sufficiently narrow bounds. In particular, we show how unidentifiable causal effects and counterfactual probabilities can be epsilon-identified when such allowances are made. Often, these allowances are easily measured and reasonably assumed. Finally, epsilon-identifiability is applied to the unit selection problem.

Ang Li, Scott Mueller, Xin Shu +1

Cognitive Systems Laboratory, Department of Computer Science, University of California, Los Angeles, Los Angeles, California, USA.

Causal Identifiability Causal Inference Causal Effect Estimation Parameter Identifiability

May 19, 2021

Multiply Robust Causal Mediation Analysis with Continuous Treatments

In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimation strategy. Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.

Yizhen Xu, AmirEmad Ghassami, Numair Sani +1

Division of Biostatistics, Department of Population Health Sciences, University of Utah, USA · Department of Mathematics and Statistics, Boston University, USA · Department of Computer Science, Johns Hopkins University, USA

Causal Effect Estimation Causal Mediation Analysis Causal Inference

Nov 16, 2020

Policy design in experiments with unknown interference

This paper studies experimental designs for estimation and inference on policies with spillover effects. Units are organized into a finite number of large clusters and interact in unknown ways within each cluster. First, we introduce a single-wave experiment that estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, we propose a policy optimality test and improve the population's average outcome through marginal changes. Second, we design a multi-wave experiment to estimate optimal treatment rules, with strong regret guarantees. We provide an implementation in a large-scale field experiment studying climate adaptation.

Davide Viviano, Jess Rudder

Department of Economics, Harvard University, 1805 Cambridge St, Cambridge, MA 02138. · Department of Economics, Oregon State University, 1500 SW Jefferson Way, Corvallis, OR 97331.

Causal Effect Estimation Policy Optimization Causal Inference Policy Learning