Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Value Assumption (SUTVA), where a unit's outcome is influenced by its neighbors' treatment assignments. This interference biases naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness pairs the Horvitz-Thompson estimator of the ATE with a known exposure mapping, a function that identifies units in a given randomization unaffected by interference. For example, an exposure mapping may stipulate that a unit experiences no further interference if at least an $h$-fraction of its neighbors share its treatment status. However, selecting this threshold $h$ is challenging, requiring domain expertise; in its absence, fixed thresholds such as $h = 1$ are often used. In this work, we propose a data-adaptive method to select the $h$-fractional threshold that minimizes the mean-squared-error (MSE) of the Horvitz-Thompson estimator. Our approach estimates the bias and variance of the Horvitz-Thompson estimator paired with candidate thresholds by leveraging a first-order approximation, specifically, linear regression of potential outcomes on exposures. We present simulations illustrating that our method improves upon non-adaptive threshold choices, and an adapted Lepski's method. We further illustrate the performance of our estimator by running experiments with synthetic outcomes on a real village network dataset, and on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method remains robust to deviations from the linear potential outcomes model.

SUMMARY: ipd is an open-source R software package for the downstream modeling of an outcome and its associated features where a potentially sizable portion of the outcome data has been imputed by an artificial intelligence or machine learning prediction algorithm. The package implements several recent proposed methods for inference on predicted data with a single, user-friendly wrapper function, ipd. The package also provides custom print, summary, tidy, glance, and augment methods to facilitate easy model inspection. This document introduces the ipd software package and provides a demonstration of its basic usage. AVAILABILITY: ipd is freely available on CRAN or as a developer version at our GitHub page: github.com/ipd-tools/ipd. Full documentation, including detailed instructions and a usage 'vignette' are available at github.com/ipd-tools/ipd.

Instrumental variables (IV) are widely used in the social and health sciences in situations where a researcher would like to measure a causal effect but cannot perform an experiment. For valid causal inference in an IV model, there must be external (exogenous) variation that (i) has a sufficiently large impact on the variable of interest (called the relevance assumption) and where (ii) the only pathway through which the external variation impacts the outcome is via the variable of interest (called the exclusion restriction). For statistical inference, researchers must also make assumptions about the functional form of the relationship between the three variables. Current practice assumes (i) and (ii) are met, then postulates a functional form with limited input from the data. In this paper, we describe a framework that leverages machine learning to validate these typically unchecked but consequential assumptions in the IV framework, providing the researcher empirical evidence about the quality of the instrument given the data at hand. Central to the proposed approach is the idea of prediction validity. Prediction validity checks that error terms -- which should be independent from the instrument -- cannot be modeled with machine learning any better than a model that is identically zero. We use prediction validity to develop both one-stage and two-stage approaches for IV, and demonstrate their performance on an example relevant to climate change policy.

Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately modeling the residual dependencies among the relations. Frequently homogeneity assumptions are placed on the errors which are commonly incorrect and ignore critical natural clustering of the actors. In this work, we present a novel regression modeling framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability properties of the error distribution to obtain parsimonious standard errors for regression parameters.

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently and automatically with substantially smaller bias than would be induced by alternative regularization procedures. The performance of the proposed methods are demonstrated through simulation and two real data examples.