Experimental data does not suffer from confounding but is usually limited in both scope and scale.

The joint probabilities of potential outcomes are fundamental components of causal inference in the sense that (i) if they are identifiable, then the causal risk is also identifiable, but not vise versa (Pearl, 2009; Tian and Pearl, 2000) and (ii) they enable us to evaluate the probabilistic aspects of sufficiency'', and ``necessity and sufficiency'', which are important concepts of successful explanation (Watson, et al., 2020). However, because they are not identifiable without any assumptions, various assumptions have been utilized to evaluate the joint probabilities of potential outcomes, e.g., the assumption of monotonicity (Pearl, 2009; Tian and Pearl, 2000), the independence between potential outcomes (Robins and Richardson, 2011), the condition of gain equality (Li and Pearl, 2019), and the specific functional relationships between cause and effect (Pearl, 2009). Unlike existing identification conditions, in order to evaluate the joint probabilities of potential outcomes without such assumptions, this paper proposes two types of novel identification conditions using covariate information. In addition, when the joint probabilities of potential outcomes are identifiable through the proposed conditions, the estimation problem of the joint probabilities of potential outcomes reduces to that of singular models and thus they can not be evaluated by standard statistical estimation methods. To solve the problem, this paper proposes a new statistical estimation method based on the augmented Lagrangian method and shows the asymptotic normality of the proposed estimators. Given space constraints, the proofs, the details on the statistical estimation method, some numerical experiments, and the case study are provided in the supplementary material.

Can democratized information gatekeepers and community note writers effectively decide what scientific information to amplify? Lacking domain expertise, such gatekeepers rely on automated reasoning agents that use RAG to ground evidence to cited sources. But such standard RAG systems validate summaries via semantic grounding and suffer from "methodological blindness," treating all cited evidence as equally valid regardless of rigor. To address this, we introduce VERIRAG, a post-retrieval auditing framework that shifts the task from classification to methodological vulnerability detection. Using private Small Language Models (SLMs), VERIRAG audits source papers against the Veritable taxonomy of statistical rigor. We contribute: (1) a benchmark of 1,730 summaries with realistic, non-obvious perturbations modeled after retracted papers; (2) the auditable Veritable taxonomy; and (3) an operational system that improves Macro F1 by at least 19 points over baselines using GPT-based SLMs, a result that replicates across MISTRAL and Gemma architectures. Given the complexity of detecting non-obvious flaws, we view VERIRAG as a "vulnerability-detection copilot," providing structured audit trails for human editors. In our experiments, individual human testers found over 80% of the generated audit trails useful for decision-making. We plan to release the dataset and code to support responsible science advocacy.

Matching is an effective strategy to tackle this problem.

Causal inference starts with a simple idea: compare groups that differ by treatment, not much else. Traditionally, similar groups are constructed using only observed covariates; however, it remains a long-standing challenge to incorporate available outcome data into the study design while preserving valid inference. In this paper, we study the general problem of covariate adjustment, effect estimation, and statistical inference when balancing features are constructed or selected with the aid of outcome information from the data. We propose cross-balancing, a method that uses sample splitting to separate the error in feature construction from the error in weight estimation. Our framework addresses two cases: one where the features are learned functions and one where they are selected from a potentially high-dimensional dictionary. In both cases, we establish mild and general conditions under which cross-balancing produces consistent, asymptotically normal, and efficient estimators. In the learned-function case, cross-balancing achieves finite-sample bias reduction relative to plug-in-type estimators, and is multiply robust when the learned features converge at slow rates. In the variable-selection case, cross-balancing only requires a product condition on how well the selected variables approximate true functions. We illustrate cross-balancing in extensive simulations and an observational study, showing that careful use of outcome information can substantially improve both estimation and inference while maintaining interpretability.