Causal Inferences

Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.

AI-generated covariates from notes, conversations, images, and wearable streams can change the causal question when their roles are left unspecified. A generated feature may represent a treatment version, pre-action state, history, design variable, mediator, outcome proxy, observation process, or intercurrent event; these roles are not interchangeable. We formulate a causal type discipline for sequential experiments: a versioned representation map, a causal role classifier, a claim-status filter, and an estimand lock. The lock fixes a standardized proximal effect before generated covariates enter the analysis. Under audit correctness and standard identification assumptions, admissible role assignments preserve this estimand. We apply the established conditional-covariance characterization of compression bias to substitution of generated representations for design-relevant states. A standardized decomposition separates compression, conditional-law, and standardization drift. Further results cover mediator adjustment, post-action leakage, marker-intervention conflation, outcome-guided discovery, and state-measurement error. Cluster-level orthogonal estimators distinguish empirical and superpopulation targets under repeated sessions and missing outcomes. Simulations show that refinement helps when it retains design-relevant information, whereas design erasure, leakage, and same-data marker selection can produce bias or undercoverage. The framework places causal semantics and claim status before confirmatory inference with generated representations.

Generative artificial intelligence changes how firms reach customers, but standard marketing data do not record how often users see and notice a firm's name in generated answers. We develop Generative Marketing Mix Modeling (GMMM) to estimate the causal effects of Generative Engine Optimization (GEO) and Generative Engine Marketing (GEM). For GEO, GMMM combines repeated generated answers with question counts, shares of use across generative systems, and notice probabilities. For GEM, it combines records of sponsored placements with notice probabilities. GMMM compares expected business responses under alternative treatment sequences and establishes sufficient conditions for identifying the resulting effects. We investigate the empirical performance of the proposed method using simulated answers to product recommendation in English and Japanese.

Existing causal-inference benchmarks for LLMs mostly score method descriptions or whether generated code runs, not whether the executed workflow recovers the target causal estimate. CausalVerify studies this verification problem for structured econometric causal-estimation workflows by separating realistic interpretation from verifiable computation. It pairs 259 published economics papers (reconstructed research question, data description, institutional context) with 100 fixed-seed synthetic scenarios that realise CSV datasets for difference-in-differences, event study, instrumental variables, and regression discontinuity designs. Experiment A (real-paper text agreement) scores method-family and direction agreement against four-LLM consensus labels. Experiment B (synthetic execution) runs model-written R code and checks whether the extracted treatment-effect estimate matches a canonical estimator on the same realised dataset; this execution-grounded correctness layer is L2b+, distinct from L2b, which records only whether the code executes. A calibration arm asks whether self-reported confidence separates correct from incorrect workflows. On Experiment B, seven LLMs reach L2b+ pass rates of 10% to 88% at the default 50% tolerance, and 66 of the 426 workflows that execute (15.5%) return a wrong estimate. Execution ranking (L2b) agrees with L2b+ far better than text-direction scoring (L4): Kendall $τ=0.81$ and Spearman $ρ=0.93$, versus Kendall $τ$ between $-0.20$ and $0.10$ for L4. Llama-3.3-70B-Instruct shows the same qualitative gap, and reported confidence does not reliably separate correct from incorrect workflows. The claims are confined to standardized single-shot workflows in these four design families under the evaluated R backend and model panel; the benchmark does not measure general causal-inference ability. Code, data, cached outputs, and a datasheet are released.

Blackwell's 4-bit floating-point (FP4) tensor cores do not automatically make attention faster because softmax conversion and on-chip dependencies dominate once its matrix products shrink. We address this with \emph{Direct-P} for noncausal inference and a causal path that passes the forward quantization directly into backward. Direct-P maps scores directly to FP4 probabilities and reaches up to 2.13$\times$ the bfloat16 (BF16) forward throughput on an NVIDIA GB200. The causal path reconstructs probabilities from saved quantized queries and keys and uses 8-bit floating-point (FP8) gradient operands, accelerating a complete single-GPU 8-billion-parameter update by up to 1.14$\times$. Matched distributed training retains FP8 probabilities and values; every tested MXFP4 probability/value training trajectory diverges.

Causal inference is the practice of estimating the effect of a treatment or intervention from data. It traditionally requires a bespoke pipeline for every new problem: first proposing a causal mechanism, selecting a compatible estimator, and finally training it. Meanwhile, across diverse settings and modalities, much of machine learning has shifted to the paradigm of foundation models: networks pretrained once at scale and applied to new tasks without fine-tuning. Causal foundation models (CFMs) bring this paradigm to causal inference. CFMs are pretrained neural networks that estimate causal quantities, such as the average treatment effect, on entirely new datasets using in-context learning without requiring model updates. This work provides a practical introduction to this emerging area. We summarize the necessary background in causal inference and machine learning before discussing CFMs. Throughout, we include example code and Jupyter notebooks.

In many settings, studying causal questions based on text data requires adjusting for confounding information within texts. Yet there is a tradeoff in constructing text representations for adjustment: they must be sufficiently large and/or dense to preserve the confounding variables necessary for unbiased effect estimation, but sufficiently small and/or sparse to satisfy finite-sample overlap and yield low-variance estimates. To address this tradeoff, we turn to sparse autoencoders (SAEs), and propose a novel causal adjustment pipeline that iteratively selects a minimal set of SAE features via conditional independence tests. We find that SAE representations achieve better adjustments (lower bias and and higher coverage) than alternative representations in standard semi-synthetic evaluations with binary confounders, and their interpretability offers opportunities for falsification. We also introduce a more realistic semi-synthetic evaluation that uses multi-label data as the unobserved confounders and find off-the-shelf adjustment methods require increased investigation for these more complex settings. Code: https://github.com/mianzg/sae-text-confounder

Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with causal estimator performance may differ across performance measures. We studied this question in a partially linear model using Monte Carlo simulations. We compared ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost), evaluating nuisance-function prediction error, bias, RMSE, and 95% confidence interval coverage. We also examined a simple joint-error measure based on the absolute cross-product of estimation errors from the exposure and outcome nuisance functions. Across the simulated settings, XGBoost had the lowest RMSE among the non-oracle methods, while DML-XGBoost generally provided better confidence interval coverage. Prediction error did not consistently track causal bias across methods and settings, and the method with the best point-estimation performance did not necessarily have the best confidence interval coverage. The joint-error measure was only weakly associated with causal bias and did not provide a useful standalone measure of causal performance. These results suggest that prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.

The performance of large language model (LLM)-based multi-agent systems (MAS) largely depends on effective communication topologies. Existing topology generation methods, however, typically learn communication topologies through black-box optimization driven solely by task-level rewards. While effective, such optimization provides little insight into why particular communication edges are selected, making it difficult to identify the critical communication subgraphs responsible for successful collaboration. To address this limitation, we propose E2-Explainer, a model-agnostic framework for providing interpretable explanations of communication topologies produced by arbitrary topology generators. Specifically, we formulate topology explanation as a causal attribution problem that identifies compact communication subgraphs supported by edge-level evidence of task preservation. We obtain this evidence with a Granger-style objective that measures how masking each communication channel changes the task outcome and the stability of the final response. The resulting budgeted subgraphs are then distilled into an amortized explainer, enabling efficient post-hoc explanation without repeated edge-level evaluations at deployment. Extensive experiments on multiple reasoning and coding benchmarks demonstrate that E2-Explainer identifies critical communication subgraphs that preserve successful collaboration. These subgraphs can also be executed directly to prune redundant communication edges, substantially reducing communication costs while maintaining competitive task performance.

Structured potential outcomes such as microscopy images may be recorded after an unknown, unit-specific transformation. If that transformation can depend on treatment, covariates or the intrinsic outcome, raw-coordinate analyses may mix biological effects with acquisition geometry. We study the unrestricted observation model X = Γ . Y(A) and characterize its observable information: a target is uniformly recoverable exactly when it is constant on group orbits, while a Borel maximal invariant retains every measurable invariant target. We then distinguish observability from statistical losslessness. A quotient-faithful reconstruction theorem shows that quotient reduction is sufficient for the full transformed experiment exactly when the conditional law of the raw observation given treatment, covariates and the quotient has a parameter-free version. Conditional Haar contamination on a compact group yields Blackwell equivalence as a special case; it is not imposed in the main model. We also separate independent site-specific product actions from shared diagonal actions and show why componentwise canonicalization can discard relative cross-site information. Under explicit metric and kernel regularity, an approximate-contamination theorem bounds quotient-law Wasserstein error and the induced perturbation of population maximum mean discrepancy. For finite-support multichannel lattice images, we construct a maximal invariant under integer translations and quarter turns, combine its characteristic Gaussian kernel with a complete paired-swap test, and retain the original simulations and RxRx1 HUVEC study. Under the sharp null, the quotient test rejected in 0.052 of simulation replicates; at unit effect strength its power was 0.992. The primary RxRx1 contrast had an enumerated paired-swap p-value of 0.0078.

Conditional Independence (CI) tests are the statistical engine of constraint-based causal discovery: in algorithms such as PC (Peter-Clark) and FCI (Fast Causal Inference), skeleton pruning and key orientations follow directly from CI decisions. This survey reviews CI testing with emphasis on assumptions, robustness, and scalability in high-dimensional and mixed-type settings common in biomedical domains. The survey organizes widely used CI methods into six families: partial-correlation, contingency-table, regression, nearest-neighbor, kernel, and machine-learning-based. Special emphasis is provided on the robustness layers that address the limitations of these families. For each family, the survey examines when CI decisions reflect the data-generating distribution and when they fail. By this, we link test-level properties, including power decay with conditioning set size and asymmetric type I/II error consequences, to graph-level errors in skeleton recovery and v-structure orientation. The survey also compares adoption across major R and Python libraries and summarizes open challenges, including mixed-type CI testing without discretization, small-sample error control, and strategies for improving scalability of CI-testing.

Estimating counterfactual outcomes over time from longitudinal observational data is central to clinical decision support. Existing methods rely on domain confusion -- adversarial training that renders representations invariant to treatment assignment -- yet this invariance creates a mutual information conflict: it suppresses treatment-correlated covariate signals necessary for accurate outcome prediction. We formalise this tension via a Jensen-Shannon divergence bound on counterfactual prediction error and develop two complementary models. CSSD (Causal State-Space model with Direct decoder) adapts selective State Space Models with a parallel multi-step decoder that eliminates accumulated rollout error by producing all prediction horizons simultaneously in a single forward pass. CSSPD (Causal State-Space model with Predictive regularisation and Direct decoder) augments CSSD with Contrastive Predictive Coding and Local Information Maximisation to reinforce temporal predictability in the balancing representation and recover local covariate information destroyed by domain confusion. On MIMIC-III, CSSPD achieves lower counterfactual RMSE than the Causal Transformer at every horizon tau >= 2 at O(T) encoder cost, with gains from 0.02 (2-step) to 0.07 (6-step). On Cancer Simulation across confounding strengths gamma in {0,1,2,3,4}, CSSPD outperforms CT at gamma <= 3 (margins 25.9%--37.0%), and CSSD achieves the lowest overall average RMSE (12.7% reduction over CT), confirming the MI conflict analysis. To our knowledge, this is the first work to formalise the balancing-prediction MI conflict and propose a structured resolution through complementary predictive and information-theoretic training objectives.

We developed a unified covariate-adjusted causal inference framework for estimating the desirability of outcome ranking (DOOR) probability for benefit-risk evaluation in randomized trials and observational studies. The framework expresses the DOOR probability as a bilinear functional of the marginal ordinal outcome distributions under the two treatment strategies, estimates conditional ordinal distributions through sequential risk-set hazards, and derives the efficient influence function (EIF) of the DOOR probability. The point-estimation simulations compared G-computation, normalized inverse probability weighting (IPW), augmented IPW (AIPW), and targeted maximum likelihood estimation (TMLE), with nuisance functions estimated using generalized linear models or Super Learner (SL). TMLE-SL showed the strongest and most consistent point-estimation performance, with AIPW-SL ranking second. EIF-based inference was then evaluated for AIPW-SL and TMLE-SL, with and without cross-fitting, across settings varying in overlap, treatment-effect heterogeneity, and treatment allocation. CVTMLE-SL showed the strongest overall performance across DOOR-scale bias, recovery of the underlying ordinal distributions, standard-error accuracy, and confidence-interval coverage. We illustrate the methodology using data from the multidrug-resistant organism network of the Antibacterial Resistance Leadership Group.

Causal inference has traditionally centered on scalar outcomes: whether a patient recovers, how much a worker earns, or how many visits a website receives. Modern studies increasingly ask causal questions about outcomes with richer form, such as clinical notes, open-ended survey responses, and images. A hospital may want to know how an AI documentation tool changes the notes physicians write, or how a nurse training program alters what patients say in survey responses. For such outcomes, the usual average treatment effect is ill-defined: one cannot meaningfully subtract one text or image from another. To this end, we propose a causal query for unstructured outcomes. The key idea is to learn what features of the outcome are most causally affected by the treatment, which we call the maximally contrasting feature (MCF). To estimate the MCF, we learn a feature-scoring function that maps each outcome to a scalar and exposes the sharpest contrast between treated and control potential outcomes. We develop identification conditions and estimation algorithms for this query, and extend it to heterogeneous effects by allowing the feature-scoring function to depend on observed covariates. We also handle settings where both the treatment and the outcome are unstructured. Empirical studies on text and images show that the algorithm recovers salient aspects of an outcome changed by a treatment.

Estimating causal effects from real-world spatiotemporal data is challenging due to hidden confounders and interference. Standard causal identification methods assume conditional exchangeability given observed covariates, which fails whenever hidden confounders affect both treatment and outcomes - a common setting in domains such as climate, environmental policy, epidemiology, and regional economics. In this paper, we propose a novel spatiotemporal proximal causal inference framework that extends proximal identification theory to spatiotemporal settings. The proposed method jointly captures local and neighborhood-level confounding information by introducing treatment- and outcome-inducing proxies, and we derive a spatiotemporal outcome confounding bridge function that identifies the potential outcome without requiring direct recovery of the hidden confounder. We establish the identifiability of this bridge function under proxy exclusion restrictions and a spatiotemporal completeness condition, and show that the resulting estimator recovers the outcome through a proximal generalization of the g-computation formula. To operationalize this identification result, we propose a neural architecture that learns proxies via transformer-based spatiotemporal encoders - coupled with a conditional mutual information critic to enforce exclusion restrictions and a moment-matching network to guarantee that the learned bridge function satisfies the underlying identifying equation. We further introduce a stabilized weighting scheme to address treatment support imbalance. Experiments on synthetic datasets demonstrate that our approach achieves comparable performance to baseline causal inference methods, while providing, to our knowledge, the first theoretically grounded outcomes for the hidden confounding in the presence of spatiotemporal interference through a proximal causal inference framework.

Causal inference usually concerns a scalar treatment, yet in many problems the treatment is unstructured: a text, an image, or a sequence of clinical decisions. Consider an instructor writing a course description to attract more students: the treatment is the course description, and the outcome is enrollment. The standard target, the average treatment effect of fixing the treatment to one exact value versus another, runs into two problems. It cannot be estimated, because almost no exact description recurs across courses, leaving no comparable group from which to measure its effect; and it would be of little use even if it could, since no one wants every course to carry the same description. What the instructor actually wants to know is which features of a description raise enrollment, and which of those features can be acted on across many courses. To this end, we propose a causal query for unstructured treatments: the maximally influential feature (MIF), the feature of the treatment that most strongly influences the outcome. We formalize the MIF as a binary feature of the treatment, defined by a feature-scoring function, constrained so that both of its values stay well populated, and chosen to maximize the causal effect it induces. Turning the feature on shifts the distribution of treatments toward those that display it, turning it off shifts away, and the MIF effect contrasts the two average potential outcomes. We study identification conditions for the MIF, develop algorithms to estimate it, and make it actionable through a nudging algorithm that revises a treatment along the MIF into an outcome-improving version. We illustrate the MIF algorithm across applications in text, image, and dynamic treatment sequences.

Longitudinal causal studies often record histories as irregular functional fragments: laboratory values, physiologic signals, sensor streams, and image-derived summaries measured at unequal and informative times. Standard doubly robust estimators usually require scalar summaries, whereas sequence learners optimize prediction losses that need not stabilize the efficient influence function. We propose Doubly Robust Functional Representation Learning (DR-FRL), a cross-fitted workflow that turns irregular histories into estimand-targeted states for observed-history regimes. Functional and temporal encoders map point clouds and prior histories into states; nuisance heads estimate outcome, treatment, and censoring functions; and EIF-targeted validation, calibration, overlap, tail, and ablation diagnostics assess whether the state supports the estimating equation. If the selected state preserves the nuisance information needed by the EIF, representation error enters the same second-order product remainder as ordinary nuisance error, and the mean estimator is asymptotically linear under explicit rate, overlap, calibration, and stability conditions. Catoni aggregation is treated separately as a bounded-influence point estimator, not a replacement for Wald inference. Simulations show gains when functional confounding is high-dimensional, measurement is informative, support is weak, or pseudo-outcomes are heavy-tailed. A VitalDB audit shows that DR-FRL can use irregular laboratory point clouds and deliver a useful negative finding: for this ICU-disposition endpoint, scalar laboratory summaries already carry much endpoint-relevant information.

The rapid development of large language models (LLMs) has renewed interest in agent-based modeling (ABM). However, current LLM-based ABM research faces several key challenges: modeling evolving agent-environment interactions, enabling flexible counterfactual reasoning, and automating simulation workflows for scientific research. In this paper, we propose Eco3S, a socio-economic system simulation framework for economic research and policy analysis that addresses these challenges through three key mechanisms: (1) Co-evolving Environment Design, a bidirectional feedback loop where agents and the environment co-evolve, producing realistic emergent behaviors; (2) Structural Causal Simulation, a structural causal model (SCM)-inspired counterfactual mechanism that allows flexible interventions for diverse causal inference tasks; (3) Simulation-Analysis-Refinement Paradigm, a self-corrective mechanism that iteratively refines experimental designs based on prior simulation results. Experiments on diverse economic scenarios confirm \textit{Eco3S}'s effectiveness in replicating multiple established economic studies (canal decay, origins of governance, and information propagation) and phenomena across domains. Additional results further demonstrate its scalability and generalizability, highlighting the framework's potential for rigorous economic research and policy-making.

Most benchmarks for causal inference over time series are observational, small, or domain-specific, leaving interventional and counterfactual estimation under-served exactly where it matters most, such as in healthcare, policy evaluation, and climate science. We introduce \textbf{DoTime}, an open, scalable, and theoretically grounded generator of multivariate temporal structural causal models (TSCMs) with interventions, released as the \code{dotime} PyPI package together with four frozen evaluation suites. Beyond existing work, it adds capabilities absent from prior generators: continuous-time intervention \emph{windows}, counterfactual sampling modes with a positivity guard, regime-switching SCMs as a strict generalization of interrupted time series, non-stationary dynamics by construction with switching SCM parameters, and deterministic ramp and sinusoidal intervention profiles that place trends and structural breaks \emph{inside} the evaluation window. Moreover, it demonstrates the suitability of the generator as a prior for a causal foundation model reference implementation. The released suites span a training-scale snapshot of $100{,}000$ trajectories and eight named identification structures, each with exact ground truth: paired interventional trajectories from the same SCM throughout, and shared-noise counterfactuals in the continuous-time suite. We ship reference baseline implementations with an evaluation harness, and pose a falsifiable claim: interventional training buys a measurable direction-accuracy advantage over an observational model of identical capacity. It is tested across three training seeds per arm. Under structure-matched evaluation on held-out episodes, the interventional prior-fitted network's (PFN) gap is positive in every structure, trajectory length, and seed tested.

Estimating causal effects of linguistic properties from observational text is difficult because the same document can contain both the treatment of interest and the non-treatment textual attributes needed for adjustment. Existing approaches often learn representations from the full text to capture latent confounding, but when treatment status is itself encoded by words in the text, these representations can directly encode treatment. This creates a confounder trap: richer representations can make treated and control documents separable, inducing overlap violations even when the underlying causal problem satisfies overlap. We study latent text treatments that are encoded through lexicons or other treatment-defining lexical information, and propose masking-based adjustment representations that remove this lexical treatment signal before representation learning. We formalize representation-induced overlap failure, prove that deletion masking preserves overlap for bag-of-words/topic-model representations, and characterize replacement masking as a natural relaxation for large language models that hides treatment-defining tokens while preserving word order and context. Across simulations, masking improves overlap diagnostics, stabilizes treatment effect estimates, and reduces bias relative to adjustment methods that learn from the unmasked text.

Automating theoretical research requires generating candidate results and evaluating them reliably. Models keep getting better at the first, while the second remains hard. A common approach asks one large language model (LLM) to review what another produced, yet such reviewers are empirically unreliable: they may accept fabricated papers and catch the fabrication at close to chance rates~\citep{badscientist2025}. We present \textsc{CausalSmith}, a framework for automated theoretical research in causal inference built on the Lean proof assistant, where a proof is checked by a program rather than read by a referee. \textsc{CausalSmith} rests on \textsc{Causalean}, a foundational Lean library for causal inference holding 8,179 machine-checked definitions and theorems, developed with language-model assistance under human design and review. Around it, we build a self-improving agentic pipeline that selects research topics, proposes results, formalizes statements, constructs proofs, and presents the resulting artifacts for human inspection. Moreover, the pipeline pairs Lean verification with a statement audit that compares each formal theorem against the informal claim behind it. We evaluate the system using artifacts produced by completed autonomous research runs. The source code, formal library, and run records are available at https://github.com/Jiyuan-Tan/CausalSmith.

Let $p(x)$ be the joint density of variables $X$, and let $ψ(x)=\nabla_x\log p(x)$ be its score field. Geometry constructed from $p$ and $ψ$ alone cannot identify causal direction: structural models with the same observational distribution have the same score geometry. I develop an interventional analogue. A hard intervention $\operatorname{do}(X_k=ξ)$ does not merely reweight the joint law; it restricts the distribution to the submanifold ${x_k=ξ}$. Its score should therefore be defined on the remaining $d-1$ free coordinates. I define causal influence $X_k\rightsquigarrow X_j$ as variation of the interventional marginal distribution of $X_j$ with $ξ$, and show that the corresponding derivative of the marginal interventional score gives a local sufficient condition for influence. Projecting the observational score onto admissible intervention directions does not generally recover causal response: two models may share the same observational score and admissible set yet respond differently. I therefore introduce an interventional response field supplied by structural information. A causal metric is defined as the Fisher information metric on a family of interventions with a common target, avoiding ill-posed comparisons across targets. The framework yields a geometric dictionary for randomized trials, instrumental variables, and conditional-independence designs, clarifying what each does and does not identify. A bivariate Gaussian example gives two models with the same observational score but different interventional score derivatives. The framework organizes relations among designs, interventions, and score fields, but adds no identification beyond the underlying assumptions. In Pearl's Ladder of Causation, observational score geometry belongs to association, intervention-indexed score fields to intervention, and unit-level counterfactual geometry is left for future work.

Observational causal analyses increasingly pool records across sites, vendors, and collection systems, creating vulnerability to append-only attacks in which plausible records are strategically selected to alter a reported treatment effect. We develop a data-poisoning audit for augmented inverse-probability-weighted estimation. The analyst specifies a finite catalog of feasible records, an append budget, and nested source capacities, and the adversary selects a feasible subset to maximize movement in a prespecified direction. With preprocessing and nuisance fits held fixed, we propose a greedy scan that computes the exact finite-sample worst-case movement at every append budget. To account for nuisance refitting, we go on to derive a total-influence score combining each record's direct contribution with its effect through the propensity and outcome models. We further obtain a conservative finite-budget bound for the fully refitted estimate. Extensive simulations validate the exact result and show that total influence improves local refit prediction, while multisite and public-data analyses demonstrate material sensitivity at small append budgets. By translating adversarial data-composition risk into movement curves and critical budgets, the framework supports more reliable causal reporting and the design of source-level safeguards.

We propose one-step and two-step methods for policy learning with retrieval-augmented generation (RAG). We formulate RAG-based action selection under the potential outcome framework. In the two-step method, vector search retrieves action-specific neighboring evidence in an embedding space, the generator estimates conditional expected outcomes or their contrasts, and a plug-in rule selects an action. This formulation connects action-specific vector search with nearest-neighbor matching in causal inference. We decompose the regret of the two-step method into candidate-generation regret and within-candidate choice regret, and we bound the latter using prediction-error guarantees for nearest-neighbor estimators and transformers. We evaluate the one-step method directly as a policy because its intermediate computation is unobserved.

We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.

Positive-Unlabeled (PU) learning aims to achieve high-accuracy binary classification with limited labeled positive examples and numerous unlabeled ones. Existing cost-sensitive-based methods often rely on strong assumptions that examples with an observed positive label were selected entirely at random. In fact, the uneven distribution of labels is prevalent in real-world PU problems, indicating that most actual positive and unlabeled data are subject to selection bias. Building on the SAR-PU propensity-weighted framework of Bekker et al., we study a PU learning enhancement (PUe) framework using normalized propensity scores and normalized inverse probability weighting (NIPW). PUe's main contributions are a normalized inverse-probability-weighted PU risk formulation; additional theoretical analyses of normalized sample-weight error and common PU estimators under biased labeling; regularized deep propensity-score estimation; integration with modern cost-sensitive PU methods; and support for selectively labeled negative classes. Experiments on MNIST, CIFAR-10, and ADNI demonstrate improvements over several PU baselines under non-uniform label distributions.

Causal inference using front door intervention and multi-instance learning (MIL) has advanced the analysis of Whole Slide Images (WSI) in digital pathology. These methods adjust feature distributions of subtle evidence sub-images to correctly associate them with WSI-level diagnoses. We propose and prove 2 hypotheses for evaluating such methods: 1) Causal inference MIL introduces an independent classification channel that effectively completes WSI classification; 2) Greater difference between features extracted by the new and baseline channels increases effectiveness in eliminating false correlations. This hypothesis describes the core of causal inference MILs: overlaying parallel, independent channels to eliminate false associations between WSI-level diagnostic and non-diagnostic evidence sub-images by increasing deep feature diversity. Based on these hypotheses, we evaluated several causal inference MILs on breast cancer and non-small cell lung cancer datasets. This hypothesis provides a new theoretical perspective for applying causal inference to WSI analysis.

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

Workload-based differentially private (DP) synthetic data methods privately measure aggregate queries and post-process the noisy answers into synthetic records. Generic workloads can achieve strong distributional fidelity, but causal estimands such as the average treatment effect (ATE) depend on treatment-arm balance and outcome moments that generic marginals need not preserve. We propose causal workloads: DP query sets designed around the orthogonal moments used by doubly robust causal estimators. The released workload can be used directly by stable moment-map estimators or reconstructed by maximum-entropy calibration into reusable synthetic data; our theory decomposes ATE error into sampling, privacy, workload-approximation, Monte Carlo, and calibration terms. We also introduce Causal-AIM, an adaptive workload selector, and a noise-aware multiple-imputation (NA+MI) procedure for confidence intervals from DP synthetic data. Because the workload is released once, the same DP synthetic table can support ATE, ATT, and subgroup analyses without additional privacy spending. Empirically, causal workloads are most useful at strict privacy budgets and for calibrated uncertainty, while generic workloads often retain an advantage for point RMSE as privacy relaxes. The broader lesson is a tradeoff: distributional fidelity can help point accuracy, but valid causal inference requires preserving causal moments and propagating DP noise rather than treating synthetic rows as real.

Scientists often seek to draw causal inferences from structured data that is not independently and identically distributed, such as spatial data, network data, or molecular data. We develop geometric causal models (GCMs), a framework for causal inference from dependent data that exploits underlying symmetries of the data generating process. For example, in spatial data, we consider processes that are symmetric under translations, or in graph data, symmetric under permutations of the nodes. We show how symmetries, formalized with group theory, can enable causal identification and estimation. We deploy ergodic theory for amenable groups to establish identification, and combine geometric deep learning with scalable Bayesian inference for estimation. We recover i.i.d. causal models and do-calculus when the data is a sequence and the symmetry is permutation equivariance, and find novel types of causal models when we use alternate structures and symmetries. As an example, we construct a causal model that satisfies the symmetries of DNA. This GCM enables new estimators for the effects of genetic variation, combining deep functional genomics models to describe outcomes and DNA language models to describe propensities. We illustrate on semisynthetic data.

In Large Language Model (LLM) training, data mixing plays a pivotal role in determining model performance. Recent methods optimize mixture weights via proxy models, but they rely on the assumption of static data distributions. As a result, when the underlying data pool shifts, these methods require costly retraining from scratch. This limitation restricts their ability to scale seamlessly from small settings to larger data pools and model sizes. In this paper, we propose CausalMix to address this limitation by casting data mixture optimization as a causal inference problem. We formulate the statistical features of the data pool as covariates and the domain mixture as the treatment. After fitting a causal model on 512 runs of Qwen2.5-0.5B to estimate the Conditional Average Treatment Effect (CATE), we extrapolate the optimal mixture for an 800K data pool and apply it to train a 7B model. Furthermore, we successfully generalize the framework to long chain-of-thought data on Qwen3-4B-Base. By leveraging causal modeling to isolate confounding biases, CausalMix dynamically infers state-dependent optimal data mixtures. Extensive experiments show that the mixture guided by CausalMix consistently improves performance across multiple downstream tasks, outperforming RegMix and other baselines. In addition, we use the CATE Interpreter to provide visual analysis of the learned mixing strategy. Overall, CausalMix offers a causal and interpretable framework for optimizing LLM data mixtures.

Airbnb is a community based on connection and belonging -- many hosts on Airbnb are everyday people who share their worlds to provide guests with the feeling of connection and being at home; Airbnb strives to connect people and places. Among our efforts to connect guests and hosts, we provide tools to enable hosts to set competitive prices, which helps improve affordability for guests while helping hosts get more bookings. We also personalize the guest experience to show them the listings that match their needs. To help inform these efforts, we combine economic modeling and causal inference techniques to understand how guests book stays based on the prices hosts set, among other factors, and how that preference varies across different guests and listings. Such understanding helps us identify opportunities for Airbnb to support the marketplace and better connect guests and hosts. For example, understanding how much guests respond to different prices helps optimize the tools that we provide to hosts, in order to enable hosts to choose and set competitive prices that further balance demand and supply. As another example, understanding heterogeneity in guest preferences helps us personalize the guest experience and better match them with the listings that meet their needs, based on how much they respond to different prices and other factors.

In two-sided marketplaces with heterogeneous products, it is important to understand the causal relationship between additional supply and marketplace outcomes, such as the total quantity transacted or transaction value in the marketplace. This paper studies a causal machine learning approach to estimating this relationship across product segments. We use the Airbnb marketplace as an example, focusing on the impact of additional listing supply on total bookings, but the methodology applies to other two-sided marketplaces. Our approach combines double/debiased machine learning with a hierarchical Bayesian framework that leverages pre-existing knowledge as priors. We construct tractable and informative features for the model by leveraging measures of product segment similarity from the geospatial literature. We find that such a model provides plausible estimates of the marketplace returns to additional supply and strong out of sample performance.

Multicollinearity is a long lasting challenge in observational causal inference, especially in regressions -- highly correlated independent variables make it hard to isolate their individual impacts on outcomes of interest. While common solutions such as shrinkage estimators and principal component regressions are helpful in prediction problems, a crucial limitation hinders their applicability to causal inference problems -- they cannot provide the original causal relationships. To fill the gap, we present an innovative and intuitive solution, by employing hierarchical clustering to aggregate data in a way that effectively alleviates collinearity. This method is generally applicable to causal problems featuring multicollinearity. We use a marketing application to demonstrate how and why it works. Expenditures on different advertising channels often exhibit correlations, making it exceedingly difficult to separately measure their impact. Many previous studies proposed to leverage granular cross-sectional data for better identification but, to our knowledge, none explicitly addressed multicollinearity, which undermines causal identification even with granular data. We propose to hierarchically cluster geographic units based on marketing spend correlation to reduce collinearity, and to implement a Bayesian Marketing Mix Model with cluster-level data. Such clustering happens in two steps -- we first normalize and demean geo-level data to establish a common scale and to eliminate the common trends; we then calculate pairwise distance to summarize marketing spend correlation between geos and cluster the ones with moderate to strong correlation. Both descriptive evidence and regression analysis affirm that such hierarchical clustering effectively mitigates collinearity and facilitates the separate identification of the impact of different marketing channels.

We propose doubly robust adaptive conformal inference (DR-ACI), which constructs prediction intervals for doubly robust pseudo-outcomes under temporal dependence.

Decision theory provides a formal framework for how agents should make choices under uncertainty, drawing on ideas from philosophy, probability, and causality. Despite significant progress, the field still lacks a unified modeling language, and key concepts - such as the distinction between subjective and objective elements, or what it means for a decision theory to perform well - are often left implicit. This can make it difficult to evaluate and compare competing theories, particularly in controversial cases. In this paper, we address these issues by introducing a formal framework for decision theory based on nonparametric structural equation models (NPSEMs), a well-established tool in causal inference. NPSEMs provide a unified foundation for representing agents, counterfactuals, and causal relationships, allowing for unambiguous definitions of EDT and CDT. Building on this foundation, we propose a novel decision theory - personal decision theory - which instructs agents to maximize a subjective model of their own counterfactual utility. We introduce a formal performance metric based on hypothetical interventions that enforce a given decision theory across a population - such as might be achieved through education or policy -- and show that, under certain assumptions, personal decision theory is optimal with respect to this metric. Throughout, we use the smoking lesion problem as a running example and conclude with a formal analysis of Newcomb's problem. Our aim is to provide decision theory with a clearer modeling language and firmer evaluative ground, thereby enabling more rigorous comparisons and facilitating conceptual progress in the field.

Lifted inference exploits indistinguishabilities in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. In this article, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs (PCFGs) to incorporate causal knowledge in lifted models and give a formal semantics of interventions therein. We further present the Lifted Causal Inference (LCI) algorithm to compute causal effects on a lifted level, thereby drastically speeding up causal inference compared to propositional inference, e.g., in causal Bayesian networks. In addition, we present partially directed parametric causal factor graphs (PD-PCFGs) as a generalisation of PCFGs to handle partial causal knowledge and extend LCI to perform lifted causal inference in a PD-PCFG, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.

Causal inference provides a set of principles and tools that allow one to combine data and knowledge about an environment to reason with questions of counterfactual nature, i.e., what would have happened had reality been different, even when no data of this unrealized reality is currently available. Reinforcement learning provides methods to learn a policy that optimizes a specific measure (e.g., reward, regret) when the agent is deployed in an environment and pursues an exploratory, trial-and-error approach. These two disciplines have evolved independently and with virtually no interaction between them. We note that they operate over different aspects of the same building block, counterfactual relations, which makes them umbilically connected. Based on these observations, novel learning opportunities arise when this connection is explicitly acknowledged and mathematized. To realize this potential, we note that any environment where the RL agent is deployed can be decomposed as a collection of autonomous mechanisms with different causal invariances, parsimoniously modeled as a structural causal model; any standard RL setting implicitly encodes such a model. This formalization allows us to put under a unifying treatment different modes of learning, including online, off-policy, and causal calculus learning, which appear unrelated in the literature. However, these modalities are not exhaustive: we introduce several natural and pervasive classes of learning settings that entail novel dimensions of analysis. Specifically, we introduce and discuss through causal lenses generalized policy learning, where to intervene, imitation learning, and counterfactual learning. These tasks lead to a broader view of counterfactual learning and suggest great potential for studying causal inference and reinforcement learning side by side, which we call causal reinforcement learning (CRL).

Statistical matching combines partially overlapping datasets that share covariates $X$ but observe the target $Y$ and auxiliary variables $Z$ separately. Classical approaches typically invoke the conditional independence assumption (CIA), which makes the problem identifiable but fundamentally implies that the imported auxiliary variable provides no additional predictive power for $Y$ once $X$ is known. To capture this latent $Y$--$Z$ dependence, we propose a novel dependency-aware Schrödinger bridge for predictive statistical matching. Our approach couples the two separated databases by tilting the conservative CIA baseline with a transportation-based compatibility cost, recovering an informative joint distribution. The resulting statistical learning framework yields full probabilistic posterior rules for bidirectional imputation. Theoretically, we establish a sufficient condition under which the learned bridge strictly improves over the CIA baseline, alongside an exact joint recovery guarantee in the Gaussian setting under an appropriate cost. Across synthetic benchmarks and real-world datasets (CelebA and Adult), we demonstrate that our dependency-aware completion consistently improves downstream predictive utility, proving especially beneficial in settings like data recoding where the underlying population exhibits strong $Y$--$Z$ dependence.

The presence of confounding bias poses a key challenge in policy evaluation, as the target causal effects of actions are not identifiable (i.e., underdetermined) from observational data. On the other hand, existing confounding-robust evaluation strategies require detailed prior knowledge about the environment or apply only to discrete treatments and outcomes. This paper investigates causal effect evaluation over the continuous domain from confounded observations, while requiring only basic temporal ordering between the treatment and the outcome. We introduce a universal discretization of the exogenous domains that approximates the observational and interventional distributions of any causal model with arbitrary accuracy using a finite number of latent states. Building on this newfound universal approximation property, we develop a novel family of Causal Gaussian process (CGP) models that effectively approximate the observational and interventional distributions of any causal model with confounded observations.

There is a precise sense in which drawing causal inferences from observational data is hard, even when identifiability is assumed. In particular, Robins and Ritov (1997) and Robins et al. (2003) showed that causal effects can be discontinuous as a function of the data distribution: two arbitrarily close data distributions might correspond to different causal effects. This is a fact independent of the choice of estimator; however, not all estimators are equally unstable. Our contribution is to surface a second layer of instability that depends on the choice of estimator. We show that many standard point estimates can be read as point summaries of multimodal distributions over the space of structural causal models. As such, estimators can jump discontinuously in the data distribution. This defines a taxonomy of estimators that admits a decision-theoretic reading: stability depends on whether the implicit loss function an estimator optimizes is aligned with the causal effect itself. Specifically, inverse propensity weighted estimators and regression estimators are examples of discontinuous summaries, while explicit posterior means and medians are shown to be continuous.

Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on $\mathbb{R}$ and the reward is defined through a utility functional applied to the Wasserstein barycenter of induced outcome distributions. We establish statistical guarantees for the policy learning framework based on both Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators. By handling the challenging uniform deviation over the product of the combinatorial policy class and the infinite-dimensional quantile domain, we prove that the finite-sample regret has leading dependence $\widetilde{\mathcal{O}}(\sqrt{\mathrm{N\text{-}dim}(Π)/N})$. In the one-dimensional Wasserstein setting and under the stated regularity conditions, the leading regret rate is still governed by the policy-class complexity. Moreover, we provide a minimax lower bound establishing the sharpness of the leading dependence on $N$ and $\mathrm{N\text{-}dim}(Π)$.

The coupon incentive is one of the most common tools marketers use to court users to engage with a business at various stages of the customer life cycle. A variety of factors can affect the effectiveness of a coupon incentive on users, timing being one of them. We hypothesize that coupons can be more effective when delivered at critical times in the customer journey, right when a user is engaging with the platform. Verifying such a hypothesis would typically require real time event-triggered coupon distribution software that may be too expensive to implement. In this paper, we propose a framework in which we apply causal inference on "natural randomized control trial experiments" to measure the effectiveness of sending coupons at the right time to users without requiring a dedicated AB test. We demonstrate the usefulness of our framework in the case of a user onboarding coupon campaign held in our company and show how the results can lead to correct data-driven decisions for the business. Furthermore, in order to test the generalizability of our framework, and to make our research more reproducible, we apply our framework on a user retention campaign with a publicly available dataset.

Distinguishing causal adverse drug events (ADEs) from spurious correlations remains a central challenge in pharmacovigilance. The InferBERT framework integrates transformer models with Do-calculus, but its success hinges on the underlying classification model. This study evaluates the impact of model choice in InferBERT, assessing whether simpler models suffice, if domain-specific pre-training helps, whether scaling to LLMs improves causal detection, and the effect of post-hoc calibration. We performed a comparative study on two benchmarks: Analgesics-induced Acute Liver Failure (AILF) and Tramadol-related Mortalities (TRAM). Four models were evaluated-XGBoost (baseline), ALBERT (original InferBERT), BioBERT (biomedical transformer), and Med-LLaMA (medical LLM)-using 5-fold cross-validation repeated over 20 runs. We measured accuracy, Expected Calibration Error (ECE) pre- and post-isotonic regression, and Jaccard concordance of causal terms with PRR, ROR, and EBGM; significance was tested with paired t-tests. BioBERT achieved the highest accuracy on both datasets, while Med-LLaMA underperformed despite its size and parameter-efficient fine-tuning. Domain-specific pre-training was decisive. Calibration improved ECE but had mixed effects on accuracy and causal discovery. BioBERT's superiority also yielded the strongest concordance with traditional pharmacovigilance signals. These results show that domain-specific pre-training provides a clear advantage over simpler baselines and larger LLMs. Investing in manageable, domain-aware models is more effective for computational pharmacovigilance than simply scaling model size.

Synthetic and distilled student data are increasingly used to enable privacy-conscious learning analytics, yet their suitability for decision-facing institutional support remains uncertain. In dropout support, generated data must preserve not only predictive utility or distributional resemblance, but also the financial-status evidence used to guide advising, payment-plan assistance, and scholarship-related decisions. Method: This study introduces CaP-Eval, a decision-facing causal-privacy audit workflow for evaluating generated student data under a fixed estimand, timing-aware adjustment design, estimator set, and empirical privacy-governance screen. The workflow compares original, distilled, adversarial synthetic, statistical synthetic, and DPGNet privacy-oriented generated data on predictive utility, treatment-effect fidelity, robustness to alternative estimators, and local training-record proximity. Results: DPGNet and distilled data preserved the original financial-status treatment-effect structure more reliably than the adversarial and Gaussian Copula baselines. DPGNet preserved full direction and rank agreement across epsilon levels; epsilon = 10 produced the smallest non-original IPW and DML deviations, while epsilon = 1 and epsilon = 5 amplified several financial-status contrasts. Distilled data remained highly faithful but retained the strongest local training-record proximity signal. TabularGNet preserved qualitative directions with moderate attenuation, and Gaussian Copula compressed effect magnitudes. Conclusions: Predictive utility, privacy orientation, empirical disclosure signals, and causal fidelity diverged; generated student data require joint audits of direction, magnitude, overlap, and release-governance risk before decision use.

This study investigates semiparametric efficient estimation of causal and structural parameters in a semi-supervised setting. In our setting, unlabeled auxiliary regressors are available in addition to labeled observations consisting of outcomes and regressors. Our goal is to construct estimators of causal and structural parameters whose asymptotic variances are smaller than those of estimators constructed using only labeled data. We refer to this framework as prediction-powered causal inference (PPCI). We first derive the efficient influence function and the efficiency bound, which imply that the use of auxiliary regressors can attain a smaller asymptotic variance than the efficiency bound attainable from labeled observations alone. Then, by combining the efficient influence function with the debiased machine learning (DML) framework, we propose methods that we call DML-PPCI. If we construct an estimating-equation estimator, we refer to the method as EE-DML-PPCI; if we construct a targeted-learning estimator, we refer to the method as TMLE-DML-PPCI. The asymptotic variances of both estimators match our derived efficiency bound. In the construction of the estimators, estimation of the efficient influence function plays an important role. In our study, the efficient influence function is also a Neyman orthogonal score, which depends on the Riesz representer and the regression function. For Riesz representer estimation, we develop semi-supervised generalized Riesz regression with convergence rate guarantees.

Machine learning models often degrade when they are deployed on a target distribution that differs from the source distributions they were trained on. Recent work in causality-based domain generalization has shown how shared causal structure between domains can induce invariant predictors, e.g., models on a subset of features which have stable risk across structured domain shifts. However, the extent to which such population-level causal invariances can lead to gains in finite-sample settings remains underexplored. In particular, in practice we often have access to a few labeled target samples, a setting called supervised domain adaptation (sDA). In this paper, we explore when (full or partial) causal knowledge can provably improve supervised domain adaptation. As a first step, we study linear regression, where full or partial causal knowledge specifies a collection of invariant or possibly invariant feature subsets, each yielding a source-trained candidate predictor. We derive matching upper and lower bounds showing that finite-sample gains are governed by the target-risk margins separating the candidates, together with the finite-source estimation error. When these margins are sufficiently large relative to $n_Q$, an adaptive aggregation procedure can match the best candidate predictor while avoiding negative transfer relative to target-only learning. On the other hand, when the margins are too small, no algorithm can reliably exploit the candidate collection to obtain faster finite-sample rates. We further connect these margins to structural shift magnitude in linear SCMs and validate the theory on real-world causal benchmarks.

Transfer learning addresses the challenge of transfering knowledge from one domain to another. Traditional transfer learning focuses on adapting models trained on a source domain (with a lot of observations) to improve performance on a target domain (with few observations). In this work we consider the case of a model shift and we focus on the transfer learning applied to a causal forest namely HTERF. This causal forest aims to estimate the Conditional Average Treatment Effect (CATE). The approach considered is the offset method presented by Wang (2016) adapted to a causal context. This method relies on the use of intermediate models in order to estimate the offset between source and target distributions. Our main result is a bound on the CATE error of HTERF on target depending on the error of the intermediate models. Simulation studies show the good performances of this approach in different settings on simulations and on a real-world dataset.

Longitudinal treatment decisions from multivariate time-series data require predicting potential outcomes under future treatment sequences in the presence of time-varying confounding, heterogeneous patient dynamics, and limited domain-specific data. Existing longitudinal causal estimators typically address this problem by training a new model for each cohort or simulator. We introduce Causal Longitudinal Prior-Fitted Networks (CausalLongPFN), a prior-fitted network for time-series causal inference in longitudinal treatment-response data and zero-shot in-context counterfactual outcome prediction. The model is pretrained entirely on synthetic episodes sampled from a broad prior over temporal structural causal models, exposing it to treatment-confounder feedback, latent heterogeneity, nonlinear state evolution, delayed effects, and cumulative treatment responses. At test time, CausalLongPFN remains frozen and is used zero-shot: it conditions on support trajectories, a query history, and a planned future treatment sequence, and returns a predictive distribution over future outcomes without gradient updates or propensity-model fitting. Multi-step predictions are obtained by recursively applying the one-step predictor under the specified treatment sequence. We evaluate the model on branchable cancer, HIV, and warfarin benchmarks with ground-truth counterfactual labels, and on factual-only rolling-origin prediction in MIMIC-III ICU trajectories. CausalLongPFN is competitive with domain-trained longitudinal baselines on counterfactual benchmarks and performs strongly on factual MIMIC-III prediction, suggesting that broad synthetic causal pretraining can provide a frozen, amortized alternative for zero-shot longitudinal treatment-response prediction when repeated domain-specific training is costly or impractical.

Deep learning has enabled significant advances in time-series causal inference, yet progress remains constrained by the lack of realistic benchmarks with observable counterfactual outcomes. Existing datasets either rely on real-world observations without ground-truth counterfactuals or on simplified simulations that fail to capture complex causal dynamics. To address this gap, we develop a large-scale benchmark for counterfactual prediction in epidemic time series under dynamic interventions. Unlike existing benchmarks, it supports static and time-varying treatments, as well as both single-policy and multi-policy intervention settings, enabling evaluation of causal inference methods across a broad range of causal inference scenarios. Leveraging a calibrated agent-based model grounded in real-world demographic, mobility, epidemiological, and policy data, we generate realistic counterfactual trajectories across more than 150 U.S. counties. Using this benchmark, we evaluate widely used and state-of-the-art causal inference methods, revealing substantial performance differences and highlighting the challenges of realistic time-series causal reasoning.

Controlled experiments are the backbone of machine learning research, but at the scale of modern foundation models, they have become prohibitively expensive. Instead, the community increasingly relies on research strategies that approximate the ideal experiment at a fraction of the cost: proxy experiments and scaling laws, observational studies with publicly available models, and single-run designs that leverage variation within individual training runs. In this work, we argue that there is no free lunch when approximating large-scale experiments on a compute budget. Specifically, savings in compute come at the cost of validity threats -- hidden and sometimes untestable assumptions that, when violated, can invalidate research claims. To help navigate such threats, we propose an evaluation framework that casts foundation model research as a causal inference problem. Within this framework, we evaluate different research strategies through four types of validity adapted from the empirical social sciences -- statistical, internal, external, and construct validity. We find that each strategy comes with a characteristic validity profile: proxy experiments trade external and construct validity for statistical and internal validity; observational studies face confounding and effect heterogeneity; and single-run designs are strained by interference between treated units. This analysis reveals several validity threats that have received insufficient attention in the literature. Overall, our evaluation framework provides researchers with a practical toolkit for scrutinizing validity threats in foundation model research~designs.

Online reviews provide valuable insights into the perceived quality of facets of a product or service. While aspect-based sentiment analysis has focused on extracting these facets from reviews, there is less work understanding the impact of each aspect on overall perception. This is particularly challenging given correlations among aspects, making it difficult to isolate the effects of each. This paper introduces a methodology based on recent advances in text-based causal analysis, specifically CausalBERT, to disentangle the effect of each factor on overall review ratings. We enhance CausalBERT with three key improvements: temperature scaling for better calibrated treatment assignment estimates; hyperparameter optimization to reduce confound overadjustment; and interpretability methods to characterize discovered confounds. In this work, we treat the textual mentions in reviews as proxies for real-world attributes. We validate our approach on real and semi-synthetic data from over 600K reviews of U.S. K-12 schools. We find that the proposed enhancements result in more reliable estimates, and that perception of school administration and performance on benchmarks are significant drivers of overall school ratings.

Probabilistic models are typically trained using task-agnostic objectives like log-loss, which can lead to significant errors in downstream estimation. This disconnect is especially critical in Inverse Probability Weighting (IPW) for causal inference, where propensity score errors near $0$ and $1$ often lead to high bias and variance. We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric. We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping that can be readily integrated with any model like a neural network or a gradient boosting algorithm. Extensive evaluations on causal inference benchmarks demonstrate that our tailored objective consistently outperforms standard likelihood-based and covariate-balancing approaches.

Estimating the causal effect of time-varying treatments on survival outcomes in large observational studies is computationally demanding, particularly when outcomes are rare. While g-formula-based methods such as the iterative conditional expectation (ICE) estimator provide a principled framework for longitudinal causal inference, they become computationally expensive, especially when bootstrap-based variance estimation is required. In addition, outcome rarity at each time point induces severe class imbalance, leading to instability and convergence issues in logistic regression and related models. To address these challenges, we propose a principled subsampling and reweighting strategy for longitudinal survival data that can be applied to a range of existing causal effect estimators in this setting, including the ICE estimator. The proposed method substantially reduces computational burden while preserving consistency and improving estimation stability in rare-outcome settings. We evaluate the method through simulations and validate it using a large-scale EHR cohort study on social and behavioral determinants of health (SBDH) and suicide risk, demonstrating its effectiveness for modeling rare outcomes in longitudinal data.

Many interventions alter the structure of an outcome distribution rather than its mean: they can split a population into disconnected regimes, create loops or holes, generate branches, or reorganize an outcome cloud while leaving the average response nearly unchanged. In such settings, mean-based causal estimands such as the average treatment effect may miss important structural effects. We introduce topological-geometrical causal metrics based on summaries of interventional outcome laws, including density-superlevel Betti summaries, Euler signatures, and persistent-homology summaries. These metrics quantify structural differences between treated and untreated outcome laws beyond averages. We also study the assumptions needed for causal interpretation. We introduce topological ignorability, a topological analogue of conditional ignorability that requires invariance of the chosen structural feature rather than the full counterfactual distribution. When the chosen summary is injective, this condition coincides with weak ignorability; for noninjective summaries, it can identify the structural feature of interest without identifying the full interventional law. We define a covariate-standardized topological-geometrical causal effect and develop practical estimators. We validate the framework in two hidden-confounding benchmarks: a fully synthetic exact benchmark and a real-covariate semi-synthetic benchmark using Wisconsin breast-cancer covariates. In both, weak ignorability fails and balancing observed covariates nearly eliminates standardized mean differences, yet the coordinate-mean average treatment effect remains biased. By contrast, selected finite density-superlevel Betti and Euler contrasts remain stable across oracle, observational, and weighted analyses.

We introduce causal density functions: Radon-Nikodym derivatives that compare interventional laws to observational laws and therefore act as local density ratios for causal effects. Whereas many causal-strength measures compare whole distributions after graph surgery, causal density functions provide a pointwise change-of-measure object that can be estimated, calibrated, and used to score directed influence. The basic identity $$\mathbb{E}_{\mathrm{do}}[f(Y)] = \mathbb{E}_{\mathrm{obs}}\!\left[f(Y)ρ(X,Y)\right]$$ makes causal density directly testable: if the estimated density ratio is correct, observational expectations reweighted by $ρ$ reproduce interventional expectations. We derive practical estimators for do-curves and directed edge scores, relate the construction to Radon-Nikodym/Kan semantics for conditioning and intervention, and evaluate the resulting estimators on synthetic and real perturbation benchmarks.

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we observe $n$ units across $m$ times under unknown, non-uniform treatment assignments. The data in this setting is naturally represented as a matrix of all unit--time treatment effects. Estimating heterogeneous treatment effects can then be expressed as obtaining a good estimation of each row's average in this matrix. This allows us to formulate the problem as matrix completion, which can be solved under natural low-rankness assumptions. However, existing matrix-completion guarantees are not powerful enough to get meaningful bounds for the per-row guarantee required for estimating the heterogeneous treatment effect; roughly speaking, they are only useful for estimating average treatment effect bounds, as also illustrated in a recent line of work. We give a simple, computationally efficient estimator that, without knowledge of the propensities and under standard low-rankness and regularity assumptions, achieves a row-wise $\ell_2$ error of $\tilde{O}(\sqrt{\frac{1}{n} + \frac{n}{m^2}})$. Technically, our analysis establishes the first sharp row-wise $\ell_2$-perturbation bound for low-rank approximation, complementing existing spectral-, Frobenius-, and entrywise perturbation theory.

Randomized controlled trials are a cornerstone of medicine and the social sciences as they enable reliable estimates of causal effects. However, they are costly and time-consuming to conduct, motivating interest in predicting causal effects from existing experimental evidence. Recent advances in large language models (LLMs) have demonstrated strong performance on knowledge-intensive tasks, raising the question of whether these models can be used for forecasting causal effect sizes. To investigate this, we introduce Query2Effect, a new large-scale benchmark consisting of more than 72,000 natural language questions aligned with experiment descriptions, created to simulate realistic information-seeking scenarios by varying query specificity along dimensions of implicitness, abstraction, and ambiguity. We then propose a two-step framework that first generates a synthetic structured representation of a query before predicting effect size using a supervised encoder model. Experiments show that finetuning plays a crucial role in improving prediction performance, with absolute error reducing by -27% up to -71% compared to prompted out-of-the-box LLMs, and that our two-step framework is beneficial for out-of-domain generalization, highlighting the benefits of separating semantic interpretation from numerical effect estimation.

A central puzzle for the behavioural sciences and for human-facing artificial intelligence is the persistence of within-person variability. The same individual, presented with the same observable input, produces different outcomes on different occasions, and different individuals produce divergent outcomes that no observable covariate fully predicts. We argue that this variability belongs in the dynamic latent state of the person, and that human outcomes are controllable in a precise and operational sense through interventions that target the state and its weighting at the moment a decision is being formed. We define a state as the time-indexed weighting vector over the dimensions that govern how an individual's biology, physiology, and neuropsychology process the next event into a decision and an outcome. The relationship between state, decision, and outcome is causal rather than correlational. The weighting vector is dynamic at sub-daily timescales. The conscious channel through which outcomes are reportable is a narrow attentional bottleneck whose contents are themselves state-dependent. Taken together, these claims imply that the outcome of a given event is controllable, conditionally, on the state-trajectory at the time of intervention. We motivate the framework with six strands of established evidence (causal inference, predictive processing, allostasis, attentional bottleneck, chronobiology, computational psychiatry) and a 24-month observational base from a deployed behavioural platform spanning more than 200,000 consented users across four occupational personas (research period 2023 to 2026). We derive seven testable predictions, list six operational requirements for state-aware systems, and discuss implications for digital health, education, AI personalisation, and personal agency.

Estimating how an outcome responds to a continuous treatment (the Average Dose-Response Function, or ADRF) is a core causal-inference primitive. However, when outcomes possess heavy tails, standard robust double machine learning (DML) deliberately suppresses these extremes to stabilize the bulk average. In high-stakes settings, such as financial returns or climate losses, this omitted 1-in-1000 extreme event is the actual target quantity. Furthermore, current methods that read the tail from a model's residuals suffer from circular dependence, causing tail shape inferences to shift drastically based solely on whether the core estimator is switched between Huber and Welsch. The research proposes an ADRF estimator that emits a structured tail-shape output alongside the standard point estimate. Its tail diagnostic (PDHTE+JK) evaluates the per-treatment tail shape from the outcome centered by a pilot median, successfully breaking the circular dependence and rendering the diagnostic invariant to the choice of core method. The output encompasses four treatment-conditional quantities: tail shape $\hatξ(t)$, deep-tail return levels $\hat{Q}_α(t)$, conditional shortfalls $\hat{S}_α(t)$, the recovered mean ADRF, and an explicit refusal mechanism that declines extrapolation when extreme-value modeling is unsupported by the data. Compared to kernel-weighted quantile regression (QR), the proposed estimator reduces deep-tail ($α=0.001$) return-level MAE by 11% and conditional-shortfall MAE by 25.5% across a heavy-tailed panel. It also achieves a 20-29% MAE reduction in sample-scarce regimes ($n\le2000$). On freMTPL2 motor-insurance claims, it successfully triggered an explicit extrapolation refusal on the log-claim scale, which neither QR nor loss-only DML can produce.