Treatment Effect

Density ratio estimation is fundamental to tasks involving f-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports --- the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design $\textbf{D}^3\textbf{RE}$, a unified framework for robust, stable and efficient density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schr{\"o}dinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schr{\"o}dinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.

*In silico* modeling of transcriptional responses to perturbations is crucial for advancing our understanding of cellular processes and disease mechanisms. We present PertEval-scFM, a standardized framework designed to evaluate models for perturbation effect prediction. We apply PertEval-scFM to benchmark zero-shot single-cell foundation model (scFM) embeddings against baseline models to assess whether these contextualized representations enhance perturbation effect prediction. Our results show that scFM embeddings offer limited improvement over simple baseline models in the zero-shot setting, particularly under distribution shift. Overall, this study provides a systematic evaluation of zero-shot scFM embeddings for perturbation effect prediction, highlighting the challenges of this task and the limitations of current-generation scFMs. Our findings underscore the need for specialized models and high-quality datasets that capture a broader range of cellular states. Source code and documentation can be found at: https://github.com/aaronwtr/PertEval.

Designing experiments for causal effect estimation remains an enduring topic in both machine learning and statistics. While much of the existing statistical literature focuses on using central limit theorems to analyze asymptotic properties of estimators, a parallel line of research has emerged around theoretical tools that provide finite-sample error bounds, offering performance on par with—or superior to—the asymptotic approaches. These finite-sample results are especially relevant in active sampling settings where the sample size is limited (for instance, under privacy or cost constraints). In this paper, we develop a finite-sample estimator with sample complexity analysis and extend its applicability to social networks. Through simulations and real-world experiments, we show that our method achieves higher estimation accuracy with fewer samples than traditional estimators endowed with asymptotic normality and other estimators backed by finite-sample guarantees.

Reliable estimation of treatment effects from observational data is important in many disciplines such as medicine. However, estimation is challenging when unconfoundedness as a standard assumption in the causal inference literature is violated. In this work, we leverage arbitrary (potentially high-dimensional) instruments to estimate bounds on the conditional average treatment effect (CATE). Our contributions are three-fold: (1) We propose a novel approach for partial identification through a mapping of instruments to a discrete representation space so that we yield valid bounds on the CATE. This is crucial for reliable decision-making in real-world applications. (2) We derive a two-step procedure that learns tight bounds using a tailored neural partitioning of the latent instrument space. As a result, we avoid instability issues due to numerical approximations or adversarial training. Furthermore, our procedure aims to reduce the estimation variance in finite-sample settings to yield more reliable estimates. (3) We show theoretically that our procedure obtains valid bounds while reducing estimation variance. We further perform extensive experiments to demonstrate the effectiveness across various settings. Overall, our procedure offers a novel path for practitioners to make use of potentially high-dimensional instruments (e.g., as in Mendelian randomization).

Randomized controlled trials (RCTs) generate guarantees for treatment effects. However, RCTs often spend unnecessary resources exploring sub-optimal treatments, which can reduce the power of treatment guarantees. To address this, we propose a two-stage RCT design. In the first stage, a data-driven screening procedure prunes low-impact treatments, while the second stage focuses on developing high-probability lower bounds for the best-performing treatment effect. Unlike existing adaptive RCT frameworks, our method is simple enough to be implemented in scenarios with limited adaptivity. We derive optimal designs for two-stage RCTs and demonstrate how such designs can be implemented through sample splitting. Empirically, we demonstrate that two-stage designs improve upon single-stage approaches, especially for scenarios where domain knowledge is available through a prior. Our work is thus, a simple yet effective design for RCTs, optimizing for the ability to certify with high probability the largest possible treatment effect for at least one of the arms studied.

This paper focuses on the estimation of distributional treatment effects in randomized experiments that use covariate-adaptive randomization (CAR). These include designs such as Efron's biased-coin design and stratified block randomization, where participants are first grouped into strata based on baseline covariates and assigned treatments within each stratum to ensure balance across groups. In practice, datasets often contain additional covariates beyond the strata indicators. We propose a flexible distribution regression framework that leverages off-the-shelf machine learning methods to incorporate these additional covariates, enhancing the precision of distributional treatment effect estimates. We establish the asymptotic distribution of the proposed estimator and introduce a valid inference procedure. Furthermore, we derive the semiparametric efficiency bound for distributional treatment effects under CAR and demonstrate that our regression-adjusted estimator attains this bound. Simulation studies and analyses of real-world datasets highlight the practical advantages of our method.

Estimating causal effects of joint interventions on multiple variables is crucial in many domains, but obtaining data from such simultaneous interventions can be challenging. Our study explores how to learn joint interventional effects using only observational data and single-variable interventions. We present an identifiability result for this problem, showing that for a class of nonlinear additive outcome mechanisms, joint effects can be inferred without access to joint interventional data. We propose a practical estimator that decomposes the causal effect into confounded and unconfounded contributions for each intervention variable. Experiments on synthetic data demonstrate that our method achieves performance comparable to models trained directly on joint interventional data, outperforming a purely observational estimator.

We study the design of adaptive, sequential experiments for unbiased average treatment effect (ATE) estimation in the design-based potential outcomes setting. Our goal is to develop adaptive designs offering *sublinear Neyman regret*, meaning their efficiency must approach that of the hindsight-optimal nonadaptive design. Recent work [Dai et al, 2023] introduced ClipOGD, the first method achieving $\widetilde{O}(\sqrt{T})$ expected Neyman regret under mild conditions. In this work, we propose adaptive designs with substantially stronger Neyman regret guarantees. In particular, we modify ClipOGD to obtain anytime $\widetilde{O}(\log T)$ Neyman regret under natural boundedness assumptions. Further, in the setting where experimental units have pre-treatment covariates, we introduce and study a class of contextual ``multigroup'' Neyman regret guarantees: Given a set of possibly overlapping groups based on the covariates, the adaptive design outperforms each group's best non-adaptive designs. In particular, we develop a contextual adaptive design with $\widetilde{O}(\sqrt{T})$ anytime multigroup Neyman regret. We empirically validate the proposed designs through an array of experiments.

Bivariate structural causal models (SCM) are often used to infer causal direction by examining their goodness-of-fit under restricted model classes. In this paper, we describe a parametrization of bivariate SCMs in terms of a *causal velocity* by viewing the cause variable as time in a dynamical system. The velocity implicitly defines counterfactual curves via the solution of initial value problems where the observation specifies the initial condition. Using tools from measure transport, we obtain a unique correspondence between SCMs and the score function of the generated distribution via its causal velocity. Based on this, we derive an objective function that directly regresses the velocity against the score function, the latter of which can be estimated non-parametrically from observational data. We use this to develop a method for bivariate causal discovery that extends beyond known model classes such as additive or location-scale noise, and that requires no assumptions on the noise distributions. When the score is estimated well, the objective is also useful for detecting model non–identifiability and misspecification. We present positive results in simulation and benchmark experiments where many existing methods fail, and perform ablation studies to examine the method's sensitivity to accurate score estimation.

Causal inference seeks to estimate the effect given a treatment such as a medicine or the dosage of a medication. To reduce the confounding bias caused by the non-randomized treatment assignment, most existing methods reduce the shift between subpopulations receiving different treatments. However, these methods split limited training samples into smaller groups, which cuts down the number of samples in each group, while precise distribution estimation and alignment highly rely on a sufficient number of training samples. In this paper, we propose a distribution alignment paradigm without data splitting, which can be naturally applied in the settings of binary and continuous treatments. To this end, we characterize the confounding bias by considering different probability measures of the same set including all the training samples, and exploit the optimal transport theory to analyze the confounding bias and outcome estimation error. Based on this, we propose to learn balanced representations by reducing the bias between the marginal distribution and the conditional distribution of a treatment. As a result, data reduction caused by splitting is avoided, and the outcome prediction model trained on one treatment group can be generalized to the entire population. The experiments on both binary and continuous treatment settings demonstrate the effectiveness of our method.

We address the problem of estimating heterogeneous treatment effects in panel data, adopting the popular Difference-in-Differences (DiD) framework under the conditional parallel trends assumption. We propose a novel doubly robust meta-learner for the Conditional Average Treatment Effect on the Treated (CATT), reducing the estimation to a convex risk minimization problem involving a set of auxiliary models. Our framework allows for the flexible estimation of the CATT, when conditioning on any subset of variables of interest using generic machine learning. Leveraging Neyman orthogonality, our proposed approach is robust to estimation errors in the auxiliary models. As a generalization to our main result, we develop a meta-learning approach for the estimation of general conditional functionals under covariate shift. We also provide an extension to the instrumented DiD setting with non-compliance. Empirical results demonstrate the superiority of our approach over existing baselines.

Generalizing causal effects from Randomized Controlled Trials (RCTs) to target populations across diverse environments is of significant practical importance, as RCTs are often costly and logistically complex to conduct. A key challenge is environmental shift, defined as changes in the distribution and availability of covariates between source and target environments. A common approach addressing this challenge is to identify a separating set--covariates that govern both treatment effect heterogeneity and environmental differences--and combine RCT samples with target populations matched on this set. However, this approach assumes that the separating set is fully observed and shared across datasets, an assumption often violated in practice. We propose a novel Two-Stage Doubly Robust (2SDR) method that relaxes this assumption by allowing the separating set to be observed in only one of the two datasets. 2SDR leverages shadow variables to impute missing components of the separating set and generalize treatment effects across environments in a two-stage procedure. We show the identification of causal effects in target environments under 2SDR and demonstrate its effectiveness through extensive experiments on both synthetic and real-world datasets.

The real world naturally has dimensions of time and space. Therefore, estimating the counterfactual outcomes with spatial-temporal attributes is a crucial problem. However, previous methods are based on classical statistical models, which still have limitations in performance and generalization. This paper proposes a novel framework for estimating counterfactual outcomes with spatial-temporal attributes using the Transformer, exhibiting stronger estimation ability. Under mild assumptions, the proposed estimator within this framework is consistent and asymptotically normal. To validate the effectiveness of our approach, we conduct simulation experiments and real data experiments. Simulation experiments show that our estimator has a stronger estimation capability than baseline methods. Real data experiments provide a valuable conclusion to the causal effect of conflicts on forest loss in Colombia. The source code is available at this [URL](https://github.com/lihe-maxsize/DeppSTCI_Release_Version-master).

This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning unnormalized distributions, which have been independently proposed and studied in separate research communities, through the lens of NCE. This unified view offers new insights into existing estimators. Specifically, for exponential families, we establish the finite-sample convergence rates of the proposed estimators under a set of regularity assumptions, most of which are new.

Estimating Individual Treatment Effects (ITE) from observational data is challenging due to covariate shift and counterfactual absence. While existing methods attempt to balance distributions globally, they often lack fine-grained sample-level alignment, especially in scenarios with significant individual heterogeneity. To address these issues, we reconsider counterfactual as a proxy to emulate balanced randomization. Furthermore, we derive a theoretical bound that links the expected ITE estimation error to both factual prediction errors and representation distances between factuals and counterfactuals. Building on this theoretical foundation, we propose FCCL, a novel method designed to effectively capture the nuances of potential outcomes under different treatments by (i) generating diffeomorphic counterfactuals that adhere to the data manifold while maintaining high semantic similarity to their factual counterparts, and (ii) mitigating distribution shift via sample-level alignment grounded in our derived generalization-error bound, which considers factual-counterfactual similarity and category consistency. Extensive evaluations on benchmark datasets demonstrate that FCCL outperforms 13 state-of-the-art methods, particularly in capturing individual-level heterogeneity and handling sparse boundary samples.

Estimating causal effects is crucial in domains like healthcare, economics, and education. Despite advances in machine learning (ML) for estimating conditional average treatment effects (CATE), the practical adoption of these methods remains limited, due to the complexities of implementing, tuning, and validating them. To address these challenges, we formalize the search for an optimal ML pipeline for CATE estimation as a counterfactual Combined Algorithm Selection and Hyperparameter (CASH) optimization. We introduce AutoCATE, the first end-to-end, automated solution for CATE estimation. Unlike prior approaches that address only parts of this problem, AutoCATE integrates evaluation, estimation, and ensembling in a unified framework. AutoCATE enables comprehensive comparisons of different protocols, yielding novel insights into CATE estimation and a final configuration that outperforms commonly used strategies. To facilitate broad adoption and further research, we release AutoCATE as an open-source software package.

Contrastive Language-Image Pre-Training (CLIP) is highly instrumental in machine learning applications within a large variety of domains. We investigate the geometry of this embedding, which is still not well understood, and show that text and image reside on linearly separable ellipsoid shells, not centered at the origin. We explain the benefits of having this structure, allowing to better embed instances according to their uncertainty during contrastive training. Frequent concepts in the dataset yield more false negatives, inducing greater uncertainty. A new notion of conformity is introduced, which measures the average cosine similarity of an instance to any other instance within a representative data set. We show this measure can be accurately estimated by simply computing the cosine similarity to the modality mean vector. Furthermore, we find that CLIP's modality gap optimizes the matching of the conformity distributions of image and text.

Tailoring treatments to individual needs is a central goal in fields such as medicine. A key step toward this goal is estimating Heterogeneous Treatment Effects (HTE)—the way treatments impact different subgroups. While crucial, HTE estimation is challenging with survival data, where time until an event (e.g., death) is key. Existing methods often assume complete observation, an assumption violated in survival data due to right-censoring, leading to bias and inefficiency. Cui et al. (2023) proposed a doubly-robust method for HTE estimation in survival data under no hidden confounders, combining a causal survival forest with an augmented inverse-censoring weighting estimator. However, we find it struggles under heavy censoring, which is common in rare-outcome problems such as Amyotrophic lateral sclerosis (ALS). Moreover, most current methods cannot handle instrumental variables, which are a crucial tool in the causal inference arsenal. We introduce Multiple Imputation for Survival Treatment Response (MISTR), a novel, general, and non-parametric method for estimating HTE in survival data. MISTR uses recursively imputed survival trees to handle censoring without directly modeling the censoring mechanism. Through extensive simulations and analysis of two real-world datasets—the AIDS Clinical Trials Group Protocol 175 and the Illinois unemployment dataset we show that MISTR outperforms prior methods under heavy censoring in the no-hidden-confounders setting, and extends to the instrumental variable setting. To our knowledge, MISTR is the first non-parametric approach for HTE estimation with unobserved confounders via instrumental variables.

Although numerous complex algorithms for treatment effect estimation have been developed in recent years, their effectiveness remains limited when handling insufficiently labeled training sets due to the high cost of labeling the post-treatment effect, e.g., the expensive tumor imaging or biopsy procedures needed to evaluate treatment effects. Therefore, it becomes essential to actively incorporate more high-quality labeled data, all while adhering to a constrained labeling budget. To enable data-efficient treatment effect estimation, we formalize the problem through rigorous theoretical analysis within the active learning context, where the derived key measures -- factual and counterfactual covering radii determine the risk upper bound. To reduce the bound, we propose a greedy radius reduction algorithm, which excels under an idealized, balanced data distribution. To generalize to more realistic data distributions, we further propose FCCM, which transforms the optimization objective into the Factual and Counterfactual Coverage Maximization to ensure effective radius reduction during data acquisition. Furthermore, benchmarking FCCM against other baselines demonstrates its superiority across both fully synthetic and semi-synthetic datasets. Code: https://github.com/uqhwen2/FCCM.

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) $L^2$ distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) $L^2$ and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.