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Generative Marketing Mix Modeling: A Causal Inference Framework Linking GEO and GEM to Business Impact

生成式营销组合建模:连接生成引擎优化、营销与业务影响

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.…

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Generalized Riesz Regression: A Unified Framework for Debiased Machine Learning with Riesz Representer Fitting under Bregman Divergence

广义 Riesz 回归:基于 Bregman 散度拟合的去偏机器学习统一框架

Estimating the Riesz representer is central to debiased machine learning, yet the generator and representer model determine which regression directions their first-order conditions protect. We introduce generalized Riesz regression, which minimizes a Bregman divergence made observable by the Riesz identity. Squared and Kullback--Leibler-type choices recover Riesz regression, tailored loss minimization, and density-ratio objectives. For any twice-differentiable generator and…

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General Bayesian Policy Learning

广义贝叶斯政策学习

This study proposes a General Bayes framework for policy learning. We consider decision problems in which a decision-maker chooses an action from a given set to maximize expected welfare. Typical examples include treatment choice and portfolio optimization. In such problems, the statistical target is a decision rule, and predicting each potential outcome is not necessarily of primary interest. We formulate this policy-learning problem through loss-based Bayesian updating.…

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Vector Search As Nearest Neighbor Matching: RAG-based Policy Learning in Causal Inference

向量检索作为最近邻匹配:因果推断中的 RAG 政策学习

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…

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Prediction-Powered Causal Inference by Automatic Debiased Machine Learning and Semi-Supervised Riesz Regression

通过自动去偏机器学习与半监督 Riesz 回归实现预测辅助因果推断

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…

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Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning

去偏机器学习中的协变量平衡与 Riesz 回归应由 Neyman 正交得分指导

This position paper argues that, in debiased machine learning, balancing functions should be derived from the Neyman orthogonal score, not chosen only as functions of covariates. Covariate balancing is effective when the regression error entering the score can be represented by functions of covariates alone, and it is the natural finite-dimensional approximation for targets such as ATT counterfactual means. For ATE estimation under treatment effect heterogeneity, however,…

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Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference

利用无标签协变量的半监督处理效应估计与预测驱动因果推断

This study investigates treatment effect estimation in the semi-supervised setting, also can be interpreted as prediction-powered inference. In our setting, we can use not only the standard triple of covariates, treatment indicator, and outcome, but also unlabeled auxiliary covariates. For this problem, we develop efficiency bounds and efficient estimators whose asymptotic variance aligns with the efficiency bound. In the analysis, we introduce two different data-generating…

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Conformal Prediction for Nonparametric Instrumental Regression

非参数工具变量回归的共形预测

We propose a method for constructing distribution-free prediction intervals in nonparametric instrumental variable regression (NPIV), with finite-sample coverage guarantees. Building on the conditional guarantee framework in conformal inference, we reformulate conditional coverage as marginal coverage over a class of IV shifts $\mathcal{F}$. Our method can be combined with any NPIV estimator, including sieve 2SLS and other machine-learning-based NPIV methods such as neural…

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Riesz Regression As Direct Density Ratio Estimation

将 Riesz 回归理解为直接密度比估计

This study clarifies the relationship between Riesz regression [Chernozhukov et al., 2021] and density ratio estimation (DRE) in causal inference problems, such as average treatment effect estimation. We first show that the Riesz representer can be written as a signed density ratio and then demonstrate that the Riesz regression objective coincides with the least-squares importance fitting criterion [Kanamori et al., 2009]. Although Riesz regression applies to a broad class…

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Causality Elicitation from Large Language Models

从大语言模型中提取因果关系假说

Large language models (LLMs) are trained on enormous amounts of data and encode knowledge in their parameters. We propose a pipeline to elicit causal relationships from LLMs. Specifically, (i) we sample many documents from LLMs on a given topic, (ii) we extract an event list from from each document, (iii) we group events that appear across documents into canonical events, (iv) we construct a binary indicator vector for each document over canonical events, and (v) we estimate…

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genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression

genriesz:基于广义 Riesz 回归的自动去偏机器学习 Python 包

Efficient estimation of causal and structural parameters can be automated using the Riesz representation theorem and debiased machine learning (DML). We present genriesz, an open-source Python package that implements automatic DML and generalized Riesz regression, a unified framework for estimating Riesz representers by minimizing empirical Bregman divergences. This framework includes covariate balancing, nearest-neighbor matching, calibrated estimation, and density ratio…

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Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation

平均处理效应估计中偏差校正项的直接估计

This study considers the estimation of the direct bias-correction term for estimating the average treatment effect (ATE). Let $\{(X_i, D_i, Y_i)\}_{i=1}^{n}$ be the observations, where $X_i$ denotes $K$-dimensional covariates, $D_i \in \{0, 1\}$ denotes a binary treatment assignment indicator, and $Y_i$ denotes an outcome. In ATE estimation, $h_0(D_i, X_i) = \frac{1[D_i = 1]}{e_0(X_i)} - \frac{1[D_i = 0]}{1 - e_0(X_i)}$ is called the bias-correction term, where $e_0(X_i)$ is…

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ScoreMatchingRiesz: Score Matching for Debiased Machine Learning and Policy Path Estimation

ScoreMatchingRiesz:用于去偏机器学习与政策路径估计的得分匹配

We propose ScoreMatchingRiesz, a family of Riesz representer estimators based on score matching. The Riesz representer is a key nuisance component in debiased machine learning, enabling $\sqrt{n}$-consistent and asymptotically efficient estimation of causal and structural targets via Neyman-orthogonal scores. We formulate Riesz representer estimation as a score estimation problem. This perspective stabilizes representer estimation by allowing us to leverage denoising score…

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Causal-Policy Forest for End-to-End Policy Learning

用于端到端政策学习的因果政策森林

This study proposes an end-to-end algorithm for policy learning in causal inference. We observe data consisting of covariates, treatment assignments, and outcomes, where only the outcome corresponding to the assigned treatment is observed. The goal of policy learning is to train a policy from the observed data, where a policy is a function that recommends an optimal treatment for each individual, to maximize the policy value. In this study, we first show that maximizing the…

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Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice

面向处理选择的极小极大与贝叶斯最优自适应实验设计

We consider an adaptive experiment for treatment choice and design a minimax and Bayes optimal adaptive experiment with respect to regret. Given binary treatments, the experimenter's goal is to choose the treatment with the highest expected outcome through an adaptive experiment, in order to maximize welfare. We consider adaptive experiments that consist of two phases, the treatment allocation phase and the treatment choice phase. The experiment starts with the treatment…

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Asymptotically Unbiased Synthetic Control Methods by Moment Matching

基于矩匹配的渐近无偏合成控制方法

Synthetic Control Methods (SCMs) have become a fundamental tool for comparative case studies. The core idea behind SCMs is to estimate treatment effects by predicting counterfactual outcomes for a treated unit using a weighted combination of observed outcomes from untreated units. The accuracy of these predictions is crucial for evaluating the treatment effect of a policy intervention. Subsequent research has therefore focused on estimating SC weights. In this study, we…

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Bridging the Gap between Empirical Welfare Maximization and Conditional Average Treatment Effect Estimation in Policy Learning

连接政策学习中的经验福利最大化与条件平均处理效应估计

The goal of policy learning is to train a policy function that recommends a treatment given covariates to maximize population welfare. There are two major approaches in policy learning: the empirical welfare maximization (EWM) approach and the plug-in approach. The EWM approach is analogous to a classification problem, where one first builds an estimator of the population welfare, which is a functional of policy functions, and then trains a policy by maximizing the estimated…

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A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression

因果推断的统一理论:通过 Bregman-Riesz 回归实现直接去偏机器学习

This note introduces a unified theory for causal inference that integrates Riesz regression, covariate balancing, density-ratio estimation (DRE), targeted maximum likelihood estimation (TMLE), and the matching estimator in average treatment effect (ATE) estimation. In ATE estimation, the balancing weights and the regression functions of the outcome play important roles, where the balancing weights are referred to as the Riesz representer, bias-correction term, and clever…

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Direct Debiased Machine Learning via Bregman Divergence Minimization

通过最小化 Bregman 散度实现直接去偏机器学习

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate balancing, targeted maximum likelihood estimation (TMLE), and density-ratio estimation. In many problems involving causal effects or structural models, the parameters of interest depend on regression functions. Plugging regression functions estimated by machine…

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Adaptive Experimental Design for Policy Learning

用于政策学习的自适应实验设计

This study investigates the contextual best arm identification (BAI) problem, aiming to design an adaptive experiment to identify the best treatment arm conditioned on contextual information (covariates). We consider a decision-maker who assigns treatment arms to experimental units during an experiment and recommends the estimated best treatment arm based on the contexts at the end of the experiment. The decision-maker uses a policy for recommendations, which is a function…

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PUATE: Efficient Average Treatment Effect Estimation from Treated (Positive) and Unlabeled Units

PUATE:处理组与未标记个体的高效平均处理效应估计

The estimation of average treatment effects (ATEs), defined as the difference in expected outcomes between treatment and control groups, is a central topic in causal inference. This study develops semiparametric efficient estimators for ATE in a setting where only a treatment group and an unlabeled group, consisting of units whose treatment status is unknown, are observed. This scenario constitutes a variant of learning from positive and unlabeled data (PU learning) and can…

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A Note on Doubly Robust Estimator in Regression Discontinuity Designs

关于回归不连续设计中双重稳健估计量的说明

This note introduces a doubly robust (DR) estimator for regression discontinuity (RD) designs. RD designs provide a quasi-experimental framework for estimating treatment effects, where treatment assignment depends on whether a running variable surpasses a predefined cutoff. A common approach in RD estimation is the use of nonparametric regression methods, such as local linear regression. However, the validity of these methods still relies on the consistency of the…

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Minimax Optimal Simple Regret in Two-Armed Best-Arm Identification

双臂最优臂识别中简单遗憾的极小极大最优性

This study investigates an asymptotically minimax optimal algorithm in the two-armed fixed-budget best-arm identification (BAI) problem. Given two treatment arms, the objective is to identify the arm with the highest expected outcome through an adaptive experiment. We focus on the Neyman allocation, where treatment arms are allocated following the ratio of their outcome standard deviations. Our primary contribution is to prove the minimax optimality of the Neyman allocation…

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Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices

可选择协变量的主动自适应处理效应实验设计

This study designs an adaptive experiment for efficiently estimating average treatment effects (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed…

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