处理效应

Conditional average treatment effect (CATE) estimation is the de facto gold standard for targeting a treatment to a heterogeneous population. The method estimates treatment effects up to an error $\epsilon > 0$ in each of $M$ different strata of the population, targeting individuals in decreasing order of estimated treatment effect until the budget runs out. In general, this method requires $O(M/\epsilon^2)$ samples. This is best possible if the goal is to estimate all treatment effects up to an $\epsilon$ error. In this work, we show how to achieve the same total treatment effect as CATE with only $O(M/\epsilon)$ samples for natural distributions of treatment effects. The key insight is that coarse estimates suffice for near-optimal treatment allocations. In addition, we show that budget flexibility can further reduce the sample complexity of allocation. Finally, we evaluate our algorithm on various real-world RCT datasets. In all cases, it finds nearly optimal treatment allocations with surprisingly few samples. Our work highlights the fundamental distinction between treatment effect estimation and treatment allocation: the latter requires far fewer samples.

We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made public). The demand function of each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. We propose a dynamic pricing policy that uses semi-parametric least-squares estimation and show that when the sellers employ our policy, their prices converge at a rate of $O(T^{-1/7})$ to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of $O(T^{5/7})$ relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of $s$-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making.

Estimating heterogeneous treatment effects (HTEs) from right-censored survival data is critical in high-stakes applications such as precision medicine and individualized policy-making. Yet, the survival analysis setting poses unique challenges for HTE estimation due to censoring, unobserved counterfactuals, and complex identification assumptions. Despite recent advances, from causal survival forests to survival meta-learners and outcome imputation approaches, evaluation practices remain fragmented and inconsistent. We introduce SurvHTE‐Bench, the first comprehensive benchmark for HTE estimation with censored outcomes. The benchmark spans (i) a modular suite of synthetic datasets with known ground truth, systematically varying causal assumptions and survival dynamics, (ii) semi-synthetic datasets that pair real-world covariates with simulated treatments and outcomes, and (iii) real-world datasets from a twin study (with known ground truth) and from an HIV clinical trial. Across synthetic, semi-synthetic, and real-world settings, we provide the first rigorous comparison of survival HTE methods under diverse conditions and realistic assumption violations. SurvHTE‐Bench establishes a foundation for fair, reproducible, and extensible evaluation of causal survival methods.

In heterogeneous treatment effect estimation from observational data, the fundamental challenge is that only the factual outcome under the received treatment is observable, while the potential outcomes under other treatments or no treatment can never be observed. As a simple and effective approach, matching aims to predict counterfactual outcomes of the target treatment by leveraging the nearest neighbors within the target group. However, due to limited observational data and the distribution shifts between groups, one cannot always find sufficiently close neighbors in the target group, resulting in inaccurate counterfactual prediction because of the manifold structure of data. To address this, we remove group barriers and propose a matching method that selects neighbors from all samples, not just the target group. This helps find closer neighbors and improves counterfactual prediction. Specifically, we analyze the effect estimation error in matching, which motivates us to propose a self optimal transport model for matching. Based on this, we employ an outcome propagation mechanism via the transport plan for counterfactual prediction, and exploit factual outcomes to learn a distance as the transport cost. The experiments are conducted on both binary and multiple treatment settings to evaluate our method.

Large Language Models (LLM) have gained significant attention. KV cache, stored to avoid quadratic complexity of attention, becomes a bottleneck due to the demands for long-context. Sparse attention (SA) has been proposed to address this by only selecting critical KVs for attention, which may degrade model quality in less sparse scenarios. To improve quality, rather than selecting more KVs, this paper reveals another perspective by estimating the contributions of remaining KVs, called Residual Estimation. We find that attention logits (before softmax) exhibit substantial redundancy due to its inherent low-rank nature. We perform Singular Value Decomposition (SVD) on logits matrix in prefilling and find the spectral dominance of principal singular value and its linearly scaling property with sequence length. These imply that increasing sequence length leads to replication-like logits growth with significant redundancy. However, it is impossible to perform SVD at each decoding step in practice due to its heavy costs. To this end, we propose RESA, a training-free framework compensating SA's output with an estimated low-rank prior of logits. RESA introduces (i) a Prior Estimator that derives a prior distribution from a typical query as a rank-1 approximation at the end of prefilling, and (ii) an Online Aggregator that fuses the prior with SA at each decoding step via lightweight scaling and merging. Besides, we further show that RESA's effect comes from priors being used as attention bias for knowledge injection. Extensive experiments show that without extra overheads, RESA improves model quality by up to 26\% across various tasks with the same KV budget compared to state-of-the-art. Moreover, RESA maintains the same quality with up to 33.2\% KV budget reduction and 1.23$\times$ attention throughput improvement.

While significant progress has been made in heterogeneous treatment effect (HTE) estimation, the evaluation of HTE estimators remains underdeveloped. In this article, we propose a robust evaluation framework based on relative error, which quantifies performance differences between two HTE estimators. We first derive the key theoretical conditions on the nuisance parameters that are necessary to achieve a robust estimator of relative error. Building on these conditions, we introduce novel loss functions and design a neural network architecture to estimate nuisance parameters, thereby obtaining a robust estimation of relative error. We provide large sample properties of the proposed relative error estimator. Furthermore, beyond evaluation, we propose a new learning algorithm for HTE that leverages both the previously HTE estimators and the nuisance parameters learned through our neural network architecture. Extensive experiments demonstrate that our evaluation framework supports reliable comparisons across HTE estimators, and the proposed learning algorithm for HTE exhibits desirable performance.

Prior-data fitted networks (PFNs) have recently been proposed as a promising way to train tabular foundation models. PFNs are transformers that are pre-trained on synthetic data generated from a prespecified prior distribution and that enable Bayesian inference through in-context learning. In this paper, we introduce CausalFM, a comprehensive framework for training PFN-based foundation models in various causal inference settings. First, we formalize the construction of Bayesian priors for causal inference based on structural causal models (SCMs) in a principled way and derive necessary criteria for the validity of such priors. Building on this, we propose a novel family of prior distributions using causality-inspired Bayesian neural networks that enable CausalFM to perform Bayesian causal inference in various settings, including back-door, front-door, and instrumental variable adjustment. Finally, we instantiate CausalFM and train our foundation models for estimating conditional average treatment effects (CATEs) for different settings. We show that CausalFM performs competitively for CATE estimation using various synthetic and semi-synthetic benchmarks. In sum, our framework can be used as a general recipe to train foundation models for various causal inference settings. In contrast to the current state-of-the-art in causal inference, CausalFM offers a novel paradigm with the potential to fundamentally change how practitioners perform causal inference in medicine, economics, and other disciplines.

Estimating potential outcomes for treatments over time based on observational data is important for personalized decision-making in medicine. However, many existing methods for this task fail to properly adjust for time-varying confounding and thus yield biased estimates. There are only a few neural methods with proper adjustments, but these have inherent limitations (e.g., division by propensity scores that are often close to zero), which result in poor performance. As a remedy, we introduce the iterative G-computation network (IGC-Net). Our IGC-Net is a novel, neural end-to-end model which adjusts for time-varying confounding in order to estimate conditional average potential outcomes (CAPOs) over time. Specifically, our IGC-Net is the first neural model to perform fully regression-based iterative G-computation for CAPOs in the time-varying setting. We evaluate the effectiveness of our IGC-Net across various experiments. In sum, this work represents a significant step towards personalized decision-making from electronic health records.

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of transformers, with particular emphasis on the role of the number of attention heads. Our analysis begins with the introduction of a generalized $D$-retrieval task, which we prove to be dense in the space of continuous functions, thereby providing the basis for our theoretical framework. We then establish both upper and lower bounds on the parameter complexity required for $\epsilon$-approximation. Specifically, we show that transformers with sufficiently many heads admit efficient approximation, whereas with too few heads, the number of parameters must scale at least as $O(1/\epsilon^{cT})$, for some constant $c$ and sequence length $T$. To the best of our knowledge, this constitutes the first rigorous lower bound of this type in a nonlinear and practically relevant setting. We further examine the single-head case and demonstrate that an embedding dimension of order $O(T)$ allows complete memorization of the input, resulting in the approximation entirely achieved by the feed-forward block. Finally, we validate our theoretical findings with experiments on both synthetic data and real-world tasks, illustrating the practical relevance of our results.

AI-assisted programming is rapidly reshaping software development, with large language models (LLMs) enabling new paradigms such as vibe coding and agentic coding. While prior works have focused on prompt design and code generation quality, the broader impact of LLM-driven development on the iterative dynamics of software engineering remains underexplored. In this paper, we conduct large-scale experiments on thousands of algorithmic programming tasks and hundreds of framework selection tasks to systematically investigate how AI-assisted programming interacts with the software ecosystem. Our analysis quantifies a substantial performance asymmetry: mainstream languages and frameworks achieve significantly higher success rates than niche ones. This disparity suggests a feedback loop consistent with the Matthew Effect, where data-rich ecosystems gain superior AI support. While not the sole driver of adoption, current models introduce a non-negligible productivity friction for niche technologies, representing a hidden bias in software evolution.

Deep learning has achieved remarkable success across many domains, but it has also created a growing demand for interpretability in model predictions. Although many explainable machine learning methods have been proposed, post-hoc explanations lack guaranteed fidelity and are sensitive to hyperparameter choices, highlighting the appeal of inherently interpretable models. For example, linear regression provides clear feature effects through its coefficients. However, such models are often outperformed by more complex neural networks (NNs) that usually lack inherent interpretability. To address this dilemma, we introduce NIMO, a framework that combines inherent interpretability with the expressive power of neural networks. Building on the simple linear regression, NIMO is able to provide flexible and intelligible feature effects. Relevantly, we develop an optimization method based on parameter elimination, that allows for optimizing the NN parameters and linear coefficients effectively and efficiently. By relying on adaptive ridge regression we can easily incorporate sparsity as well. We show empirically that our model can provide faithful and intelligible feature effects while maintaining good predictive performance.

Score-based diffusion models have achieved remarkable progress in various domains with the ability to generate new data samples that do not exist in the training set. In this work, we study the hypothesis that such creativity arises from an interpolation effect caused by a smoothing of the empirical score function. Focusing on settings where the training set lies uniformly in a one-dimensional subspace, we probe the interplay between score smoothing and the denoising dynamics with analytical solutions and numerical experiments. In particular, we demonstrate how a smoothed score function can lead to the generation of samples that interpolate among the training data within their subspace while avoiding full memorization. Moreover, we present theoretical and empirical evidence that learning score functions with regularized neural networks can have a similar effect as score smoothing, including in simple nonlinear settings.

The conditional average treatment effect (CATE) is widely used in personalized medicine to inform therapeutic decisions. However, state-of-the-art methods for CATE estimation (so-called meta-learners) often perform poorly in the presence of low overlap. In this work, we introduce a new approach to tackle this issue and improve the performance of existing meta-learners in the low-overlap regions. Specifically, we introduce Overlap-Adaptive Regularization (OAR) that regularizes target models proportionally to overlap weights so that, informally, the regularization is higher in regions with low overlap. To the best of our knowledge, our OAR is the first approach to leverage overlap weights in the regularization terms of the meta-learners. Our OAR approach is flexible and works with any existing CATE meta-learner: we demonstrate how OAR can be applied to both parametric and non-parametric second-stage models. Furthermore, we propose debiased versions of our OAR that preserve the Neyman-orthogonality of existing meta-learners and thus ensure more robust inference. Through a series of (semi-)synthetic experiments, we demonstrate that our OAR significantly improves CATE estimation in low-overlap settings in comparison to constant regularization.

Within heterogeneous treatment effect (HTE) analysis, various estimands have been proposed to capture the effect of a treatment conditional on covariates. Recently, the conditional quantile comparator (CQC) has emerged as a promising estimand, offering quantile-level summaries akin to the conditional quantile treatment effect (CQTE) while preserving some interpretability of the conditional average treatment effect (CATE). It achieves this by summarising the treated response conditional on both the covariates and the untreated response. Despite these desirable properties, the CQC's current estimation is limited by the need to first estimate the difference in conditional cumulative distribution functions and then invert it. This inversion obscures the CQC estimate, hampering our ability to both model and interpret it. To address this, we propose the first direct estimator of the CQC, allowing for explicit modelling and parameterisation. This explicit parameterisation enables better interpretation of our estimate while also providing a means to constrain and inform the model. We show, both theoretically and empirically, that our estimation error depends directly on the complexity of the CQC itself, improving upon the existing estimation procedure. Furthermore, it retains the desirable double robustness property with respect to nuisance parameter estimation. We further show our method to outperform existing procedures in estimation accuracy across multiple data scenarios while varying sample size and nuisance error. Finally, we apply it to real-world data from an employment scheme, uncovering a reduced range of potential earnings improvement as participant age increases.

In recent years, estimating causal effects of treatment on the outcome variable in network environments has attracted growing interest. The intrinsic interconnectedness of network and the attendant violation of the SUTVA assumption have prompted a wave of treatment effect estimation methods tailored to network settings, yielding considerable progress such as capturing hidden confounders by leveraging auxiliary network structure. Nevertheless, despite these advances, the existing methods: (i) mainly focus on the static network, overlooking the dynamic nature of many real-world networks and confounders that evolve over time; (ii) assume the absence of dynamic network interference where one unit’s treatment can affect its neighbors’ outcomes. To address these two limitations, we first define a new estimand of treatment effects accounting for interference in a dynamic network environment, i.e., CATE-ID, and establish its identifiability under such an environment. Then we accordingly propose DSPNET, a framework tailored specifically for treatment effect estimation in dynamic network environment, that leverages historical information and network structure to capture time-varying confounders and model dynamic interference. Extensive experiments demonstrate the superiority of our proposed method compared to state-of-the-art approaches.

Estimating causal quantities (CQs) typically requires large datasets, which can be expensive to obtain, especially when measuring individual outcomes is costly. This challenge highlights the importance of sample-efficient active learning strategies. To address the narrow focus of prior work on the conditional average treatment effect, we formalize the broader task of Actively estimating Causal Quantities (ActiveCQ) and propose a unified framework for this general problem. Built upon the insight that many CQs are integrals of regression functions, our framework models the regression function with a Gaussian Process. For the distribution component, we explore both a baseline using explicit density estimators and a more integrated method using conditional mean embeddings in a reproducing kernel Hilbert space. This latter approach offers key advantages: it bypasses explicit density estimation, operates within the same function space as the GP, and adaptively refines the distributional model after each update. Our framework enables the principled derivation of acquisition strategies from the CQ's posterior uncertainty; we instantiate this principle with two utility functions based on information gain and total variance reduction. A range of simulated and semi-synthetic experiments demonstrate that our principled framework significantly outperforms relevant baselines, achieving substantial gains in sample efficiency across a variety of CQs.

In many applications, treatment and outcome are confounded by unobservables, yet mediators remain unconfounded. The front‑door (FD) adjustment identifies causal effects through mediators even with unmeasured confounding. However, most estimators focus on *average treatment effects*, and work on *heterogeneous treatment effect* (HTE) estimation remain scarce. We address this gap with two *debiased* learners for heterogeneous FD effects: *FD‑DR‑Learner* and *FD‑R‑Learner*. Both attain fast, quasi-oracle rates (i.e., performance comparable to an oracle that knows the nuisances) even when nuisance functions converge as slowly as $n^{-1/4}$. Beyond theory, we demonstrate fast convergence and debiasedness in synthetic and real-world evaluations. Our results show that the proposed learners deliver robust and debiased HTE estimates under the FD scenario.

Estimating heterogeneous treatment effects (HTEs) in time-varying settings is particularly challenging, as the probability of observing certain treatment sequences decreases exponentially with longer prediction horizons. Thus, the observed data contain little support for many plausible treatment sequences, which creates severe overlap problems. Existing meta-learners for the time-varying setting typically assume adequate treatment overlap, and thus suffer from exploding estimation variance when the overlap is low. To address this problem, we introduce a novel overlap-weighted orthogonal WO meta-learner for estimating HTEs that targets regions in the observed data with high probability of receiving the interventional treatment sequences. This offers a fully data-driven approach through which our WO-learner can counteract instabilities as in existing meta-learners and thus obtain more reliable HTE estimates. Methodologically, we develop a novel Neyman-orthogonal population risk function that minimizes the overlap-weighted oracle risk. We show that our WO-learner has the favorable property of Neyman-orthogonality, meaning that it is robust against misspecification in the nuisance functions. Further, our WO-learner is fully model-agnostic and can be applied to any machine learning model. Through extensive experiments with both transformer and LSTM backbones, we demonstrate the benefits of our novel WO-learner.