Causality Elicitation from Large Language Models

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 candidate causal graphs using causal discovery methods. Our approach does not guarantee real-world causality. Rather, it provides a framework for presenting the set of causal hypotheses that LLMs can plausibly assume, as an inspectable set of variables and candidate graphs.

General Bayesian Policy Learning

This study proposes the General Bayes framework for policy learning. We consider decision problems in which a decision-maker chooses an action from an action set to maximize its expected welfare. Typical examples include treatment choice and portfolio selection. In such problems, the statistical target is a decision rule, and the prediction of each outcome $Y(a)$ is not necessarily of primary interest. We formulate this policy learning problem by loss-based Bayesian updating. Our main technical device is a squared-loss surrogate for welfare maximization. We show that maximizing empirical welfare over a policy class is equivalent to minimizing a scaled squared error in the outcome difference, up to a quadratic regularization controlled by a tuning parameter $ζ>0$. This rewriting yields a General Bayes posterior over decision rules that admits a Gaussian pseudo-likelihood interpretation. We clarify two Bayesian interpretations of the resulting generalized posterior, a working Gaussian view and a decision-theoretic loss-based view. As one implementation example, we introduce neural networks with tanh-squashed outputs. Finally, we provide theoretical guarantees in a PAC-Bayes style.

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

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 estimation as special cases. A key design principle of the package is automatic regressor balancing (ARB): given a Bregman generator $g$ and a representer model class, genriesz} automatically constructs a compatible link function so that the generalized Riesz regression estimator satisfies balancing (moment-matching) optimality conditions in a user-chosen basis. The package provides a modulr interface for specifying (i) the target linear functional via a black-box evaluation oracle, (ii) the representer model via basis functions (polynomial, RKHS approximations, random forest leaf encodings, neural embeddings, and a nearest-neighbor catchment basis), and (iii) the Bregman generator, with optional user-supplied derivatives. It returns regression adjustment (RA), Riesz weighting (RW), augmented Riesz weighting (ARW), and TMLE-style estimators with cross-fitting, confidence intervals, and $p$-values. We highlight representative workflows for estimation problems such as the average treatment effect (ATE), ATE on treated (ATT), and average marginal effect estimation. The Python package is available at https://github.com/MasaKat0/genriesz and on PyPI.

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

Estimating the Riesz representer is a central problem in debiased machine learning for causal and structural parameter estimation. Various methods for Riesz representer estimation have been proposed, including Riesz regression and covariate balancing. This study unifies these methods within a single framework. Our framework fits a Riesz representer model to the true Riesz representer under a Bregman divergence, which includes the squared loss and the Kullback--Leibler (KL) divergence as special cases. We show that the squared loss corresponds to Riesz regression, and the KL divergence corresponds to tailored loss minimization, where the dual solutions correspond to stable balancing weights and entropy balancing weights, respectively, under specific model specifications. We refer to our method as generalized Riesz regression, and we refer to the associated duality as automatic covariate balancing. Our framework also generalizes density ratio fitting under a Bregman divergence to Riesz representer estimation, and it includes various applications beyond density ratio estimation. We also provide a convergence analysis for both cases where the model class is a reproducing kernel Hilbert space (RKHS) and where it is a neural network.

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

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 policy value is equivalent to minimizing the mean squared error for the conditional average treatment effect (CATE) under $\{-1, 1\}$ restricted regression models. Based on this finding, we modify the causal forest, an end-to-end CATE estimation algorithm, for policy learning. We refer to our algorithm as the causal-policy forest. Our algorithm has three advantages. First, it is a simple modification of an existing, widely used CATE estimation method, therefore, it helps bridge the gap between policy learning and CATE estimation in practice. Second, while existing studies typically estimate nuisance parameters for policy learning as a separate task, our algorithm trains the policy in a more end-to-end manner. Third, as in standard decision trees and random forests, we train the models efficiently, avoiding computational intractability.

ScoreMatchingRiesz: Auto-DML with Infinitesimal Classification

This study proposes Riesz representer estimation methods based on score matching. The Riesz representer is a key component in debiased machine learning for constructing $\sqrt{n}$-consistent and efficient estimators in causal inference and structural parameter estimation. To estimate the Riesz representer, direct approaches have garnered attention, such as Riesz regression and the covariate balancing propensity score. These approaches can also be interpreted as variants of direct density ratio estimation (DRE) in several applications such as average treatment effect estimation. In DRE, it is well known that flexible models can easily overfit the observed data due to the estimand and the form of the loss function. To address this issue, recent work has proposed modeling the density ratio as a product of multiple intermediate density ratios and estimating it using score-matching techniques, which are often used in the diffusion model literature. We extend score-matching-based DRE methods to Riesz representer estimation. Our proposed method not only mitigates overfitting but also provides insights for causal inference by bridging marginal effects and average policy effects through time score functions.

Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice

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 allocation phase, where the experimenter allocates treatments to experimental subjects to gather observations. During this phase, the experimenter can adaptively update the allocation probabilities using the observations obtained in the experiment. After the allocation phase, the experimenter proceeds to the treatment choice phase, where one of the treatments is selected as the best. For this adaptive experimental procedure, we propose an adaptive experiment that splits the treatment allocation phase into two stages, where we first estimate the standard deviations and then allocate each treatment proportionally to its standard deviation. We show that this experiment, often referred to as Neyman allocation, is minimax and Bayes optimal in the sense that its regret upper bounds exactly match the lower bounds that we derive. To show this optimality, we derive minimax and Bayes lower bounds for the regret using change-of-measure arguments. Then, we evaluate the corresponding upper bounds using the central limit theorem and large deviation bounds.

Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates via Generalized Riesz Regression

This study investigates treatment effect estimation in the semi-supervised setting, where 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 processes: the one-sample setting and the two-sample setting. The one-sample setting considers the case where we can observe treatment indicators and outcomes for a part of the dataset, which is also called the censoring setting. In contrast, the two-sample setting considers two independent datasets with labeled and unlabeled data, which is also called the case-control setting or the stratified setting. In both settings, we find that by incorporating auxiliary covariates, we can lower the efficiency bound and obtain an estimator with an asymptotic variance smaller than that without such auxiliary covariates.

Riesz Regression As Direct Density Ratio Estimation

Riesz regression has garnered attention as a tool in debiased machine learning for causal and structural parameter estimation (Chernozhukov et al., 2021). This study shows that Riesz regression is closely related to direct density-ratio estimation (DRE) in important cases, including average treat- ment effect (ATE) estimation. Specifically, the idea and objective in Riesz regression coincide with the one in least-squares importance fitting (LSIF, Kanamori et al., 2009) in direct density-ratio estimation. While Riesz regression is general in the sense that it can be applied to Riesz representer estimation in a wide class of problems, the equivalence with DRE allows us to directly import exist- ing results in specific cases, including convergence-rate analyses, the selection of loss functions via Bregman-divergence minimization, and regularization techniques for flexible models, such as neural networks. Conversely, insights about the Riesz representer in debiased machine learning broaden the applications of direct density-ratio estimation methods. This paper consolidates our prior results in Kato (2025a) and Kato (2025b).

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

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 welfare. In contrast, the plug-in approach is based on regression, where one first estimates the conditional average treatment effect (CATE) and then recommends the treatment with the highest estimated outcome. This study bridges the gap between the two approaches by showing that both are based on essentially the same optimization problem. In particular, we prove an exact equivalence between EWM and least squares over a reparameterization of the policy class. As a consequence, the two approaches are interchangeable in several respects and share the same theoretical guarantees under common conditions. Leveraging this equivalence, we propose a novel regularization method for policy learning. Our findings yield a convex and computationally efficient training procedure that avoids the NP-hard combinatorial step typically required in EWM.