Reweighting a distribution to minimize a distance to a target distribution is a powerful and flexible strategy for estimating a wide range of causal effects, but can be challenging in practice because optimal weights typically depend on knowledge of the underlying data generating process. In this paper, we focus on design-based weights, which do not incorporate outcome information; prominent examples include prospective cohort studies, survey weighting, and the weighting portion of augmented weighting estimators. In such applications, we explore the central role of representation learning in finding desirable weights in practice. Unlike the common approach of assuming a well-specified representation, we highlight the error due to the choice of a representation and outline a general framework for finding suitable representations that minimize this error. Building on recent work that combines balancing weights and neural networks, we propose an end-to-end estimation procedure that learns a flexible representation, while retaining promising theoretical properties. We show that this approach is competitive in a range of common causal inference tasks.

The need for fair AI is increasingly clear in the era of general-purpose systems such as ChatGPT, Gemini, and other large language models (LLMs). However, the increasing complexity of human-AI interaction and its social impacts have raised questions of how fairness standards could be applied. Here, we review the technical frameworks that machine learning researchers have used to evaluate fairness, such as group fairness and fair representations, and find that their application to LLMs faces inherent limitations. We show that each framework either does not logically extend to LLMs or presents a notion of fairness that is intractable for LLMs, primarily due to the multitudes of populations affected, sensitive attributes, and use cases. To address these challenges, we develop guidelines for the more realistic goal of achieving fairness in particular use cases: the criticality of context, the responsibility of LLM developers, and the need for stakeholder participation in an iterative process of design and evaluation. Moreover, it may eventually be possible and even necessary to use the general-purpose capabilities of AI systems to address fairness challenges as a form of scalable AI-assisted alignment.

In many causal inference applications, the primary outcomes are missing for a non-trivial number of observations. For instance, in studies on long-term health effects of medical interventions, some measurements require expensive testing and a loss to follow-up is common (Hogan et al., 2004). In evaluating commercial online ad effectiveness, some individuals may drop out from the panel because they use multiple devices (Shankar et al., 2023), leading to missing revenue measures. In many of these studies, however, there often exist short-term outcomes that are easier and faster to measure, e.g., short-term health measures or an online ad's click-through rate, that are observed for a greater share of the sample. These outcomes, which are typically informative about the primary outcomes themselves, are refered to as surrogate outcomes or surrogates. There is a rich causal inference literature addressing missing outcome data. Simply restricting to data with observed primary outcomes may induce strong bias (Hernán and Robins, 2010). Ignoring unlabeled data also reduces the effective sample size for estimating the treatment effects and inflates the variance. Chakrabortty et al. (2022) considered the missing completely at random (MCAR) setting and showed that incorporating unlabeled data reduces variance.

We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning (AutoDML). These popular doubly robust or double machine learning estimators combine outcome modeling with balancing weights -- weights that achieve covariate balance directly in lieu of estimating and inverting the propensity score. When the outcome and weighting models are both linear in some (possibly infinite) basis, we show that the augmented estimator is equivalent to a single linear model with coefficients that combine the coefficients from the original outcome model coefficients and coefficients from an unpenalized ordinary least squares (OLS) fit on the same data; in many real-world applications the augmented estimator collapses to the OLS estimate alone. We then extend these results to specific choices of outcome and weighting models. We first show that the augmented estimator that uses (kernel) ridge regression for both outcome and weighting models is equivalent to a single, undersmoothed (kernel) ridge regression. This holds numerically in finite samples and lays the groundwork for a novel analysis of undersmoothing and asymptotic rates of convergence. When the weighting model is instead lasso-penalized regression, we give closed-form expressions for special cases and demonstrate a ``double selection'' property. Our framework opens the black box on this increasingly popular class of estimators, bridges the gap between existing results on the semiparametric efficiency of undersmoothed and doubly robust estimators, and provides new insights into the performance of augmented balancing weights.