Data fusion techniques integrate information from heterogeneous data sources to improve learning, generalization, and decision-making across data sciences. In causal inference, these methods leverage rich observational data to improve causal effect estimation, while maintaining the trustworthiness of randomized controlled trials. Existing approaches often relax the strong "no unobserved confounding" assumption by instead assuming exchangeability of counterfactual outcomes across data sources. However, when both assumptions simultaneously fail—a common scenario in practice—current methods cannot identify or estimate causal effects. We address this limitation by proposing a novel partial identification framework that enables researchers to answer key questions such as: *Is the causal effect positive/negative?* and *How severe must assumption violations be to overturn this conclusion?* Our approach introduces interpretable sensitivity parameters that quantify assumption violations and derives corresponding causal effect bounds. We develop doubly robust estimators for these bounds and operationalize breakdown frontier analysis to understand how causal conclusions change as assumption violations increase. We apply our framework to the Project STAR study, which investigates the effect of classroom size on students’ third-grade standardized test performance. Our analysis reveals that the Project STAR results are robust to simultaneous violations of key assumptions, both on average and across various subgroups of interest. This strengthens confidence in the study's conclusions despite potential unmeasured biases in the data.

After a person is arrested and charged with a crime, they may be released on bail and required to participate in a community supervision program while awaiting trial. These 'pre-trial programs' are common throughout the United States, but very little research has demonstrated their effectiveness. Researchers have emphasized the need for more rigorous program evaluation methods, which we introduce in this article. We describe a program evaluation pipeline that uses recent interpretable machine learning techniques for observational causal inference, and demonstrate these techniques in a study of a pre-trial program in Durham, North Carolina. Our findings show no evidence that the program either significantly increased or decreased the probability of new criminal charges. If these findings replicate, the criminal-legal system needs to either improve pre-trial programs or consider alternatives to them. The simplest option is to release low-risk individuals back into the community without subjecting them to any restrictions or conditions. Another option is to assign individuals to pre-trial programs that incentivize pro-social behavior. We believe that the techniques introduced here can provide researchers the rigorous tools they need to evaluate these programs.

Many modern causal questions ask how treatments affect complex outcomes that are measured using wearable devices and sensors. Current analysis approaches require summarizing these data into scalar statistics (e.g., the mean), but these summaries can be misleading. For example, disparate distributions can have the same means, variances, and other statistics. Researchers can overcome the loss in information by instead representing the data as distributions. We develop an interpretable method for distributional data analysis that ensures trustworthy and robust decision making: Analyzing Distributional Data via Matching After Learning to Stretch (ADD MALTS). We (i) provide analytical guarantees of the correctness of our estimation strategy, (ii) demonstrate via simulation that ADD MALTS outperforms other distributional data analysis methods at estimating treatment effects, and (iii) illustrate ADD MALTS’ ability to verify whether there is enough cohesion between treatment and control units within subpopulations to trustworthily estimate treatment effects. We demonstrate ADD MALTS’ utility by studying the effectiveness of continuous glucose monitors in mitigating diabetes risks.

Recent advancements in statistical and reinforcement learning methods have contributed to superior patient care strategies. However, these methods face substantial challenges in high-stakes contexts, including missing data, stochasticity, and the need for interpretability and patient safety. Our work operationalizes a safe and interpretable approach for optimizing treatment regimes by matching patients with similar medical and pharmacological profiles. This allows us to construct optimal policies via interpolation. Our comprehensive simulation study demonstrates our method’s effectiveness in complex scenarios. We use this approach to study seizure treatment in critically ill patients, advocating for personalized strategies based on medical history and pharmacological features. Our findings recommend reducing medication doses for mild, brief seizure episodes and adopting aggressive treatment strategies for severe cases, leading to improved outcomes.

Many populations defined by illegal or stigmatized behavior are difficult to sample using conventional survey methodology. Respondent Driven Sampling (RDS) is a participant referral process frequently employed in this context to collect information. This sampling methodology can be modeled as a stochastic process that explores the graph of a social network, generating a partially observed subgraph between study participants. The methods currently used to impute the missing edges in this subgraph exhibit biased downstream estimation. We leverage auxiliary participant information and concepts from indirect inference to ameliorate these issues and improve estimation of the hidden population size. These advances result in smaller bias and higher precision in the estimation of the study participant arrival rate, the sample subgraph, and the population size. Lastly, we use our method to estimate the number of People Who Inject Drugs (PWID) in the Kohtla-Jarve region of Estonia.

Most linear experimental design problems assume homogeneous variance, while the presence of heteroskedastic noise is present in many realistic settings. Let a learner have access to a finite set of measurement vectors $\mathcal{X}\subset \mathbb{R}^d$ that can be probed to receive noisy linear responses of the form $y=x^{\top}\theta^{\ast}+\eta$. Here $\theta^{\ast}\in \mathbb{R}^d$ is an unknown parameter vector, and $\eta$ is independent mean-zero $\sigma_x^2$-sub-Gaussian noise defined by a flexible heteroskedastic variance model, $\sigma_x^2 = x^{\top}\Sigma^{\ast}x$. Assuming that $\Sigma^{\ast}\in \mathbb{R}^{d\times d}$ is an unknown matrix, we propose, analyze and empirically evaluate a novel design for uniformly bounding estimation error of the variance parameters, $\sigma_x^2$. We demonstrate this method on two adaptive experimental design problems under heteroskedastic noise, fixed confidence transductive best-arm identification and level-set identification and prove the first instance-dependent lower bounds in these settings. Lastly, we construct near-optimal algorithms and demonstrate the large improvements in sample complexity gained from accounting for heteroskedastic variance in these designs empirically.

Our goal is to produce methods for observational causal inference that are auditable, easy to troubleshoot, yield accurate treatment effect estimates, and scalable to high-dimensional data. We describe a general framework called Model-to-Match that achieves these goals by (i) learning a distance metric via outcome modeling, (ii) creating matched groups using the distance metric, and (iii) using the matched groups to estimate treatment effects. Model-to-Match uses variable importance measurements to construct a distance metric, making it a flexible framework that can be adapted to various applications. Concentrating on the scalability of the problem in the number of potential confounders, we operationalize the Model-to-Match framework with LASSO. We derive performance guarantees for settings where LASSO outcome modeling consistently identifies all confounders (importantly without requiring the linear model to be correctly specified). We also provide experimental results demonstrating the auditability of matches, as well as extensions to more general nonparametric outcome modeling.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

A classical problem in causal inference is that of matching, where treatment units need to be matched to control units based on covariate information. In this work, we propose a method that computes high quality almost-exact matches for high-dimensional categorical datasets. This method, called FLAME (Fast Large-scale Almost Matching Exactly), learns a distance metric for matching using a hold-out training data set. In order to perform matching efficiently for large datasets, FLAME leverages techniques that are natural for query processing in the area of database management, and two implementations of FLAME are provided: the first uses SQL queries and the second uses bit-vector techniques. The algorithm starts by constructing matches of the highest quality (exact matches on all covariates), and successively eliminates variables in order to match exactly on as many variables as possible, while still maintaining interpretable high-quality matches and balance between treatment and control groups. We leverage these high quality matches to estimate conditional average treatment effects (CATEs). Our experiments show that FLAME scales to huge datasets with millions of observations where existing state-of-the-art methods fail, and that it achieves significantly better performance than other matching methods.

We propose a matching method that recovers direct treatment effects from randomized experiments where units are connected in an observed network, and units that share edges can potentially influence each others’ outcomes. Traditional treatment effect estimators for randomized experiments are biased and error prone in this setting. Our method matches units almost exactly on counts of unique subgraphs within their neighborhood graphs. The matches that we construct are interpretable and high-quality. Our method can be extended easily to accommodate additional unit-level covariate information. We show empirically that our method performs better than other existing methodologies for this problem, while producing meaningful, interpretable results.

We propose a matching method for observational data that matches units with others in unit-specific, hyper-box-shaped regions of the covariate space. These regions are large enough that many matches are created for each unit and small enough that the treatment effect is roughly constant throughout. The regions are found as either the solution to a mixed integer program, or using a (fast) approximation algorithm. The result is an interpretable and tailored estimate of the causal effect for each unit.

In this paper we propose a novel metric of basketball game success, derived from a team’s dynamic social network of game play. We combine ideas from random effects models for network links with taking a multi-resolution stochastic process approach to model passes between teammates. These passes can be viewed as directed dynamic relational links in a network. Multiplicative latent factors are introduced to study higher-order patterns in players’ interactions that distinguish a successful game from a loss. Parameters are estimated using a Markov chain Monte Carlo sampler. Results in simulation experiments suggest that the sampling scheme is effective in recovering the parameters. We also apply the model to the first high-resolution optical tracking data set collected in college basketball games. The learned latent factors demonstrate significant differences between players’ passing and receiving patterns in a loss, as opposed to a win. Our model is applicable to team sports other than basketball, as well as other time-varying network observations.

Matching methods are heavily used in the social and health sciences due to their interpretability. We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. The method proposed in this work aims to match units on a weighted Hamming distance, taking into account the relative importance of the covariates; the algorithm aims to match units on as many relevant variables as possible. To do this, the algorithm creates a hierarchy of covariate combinations on which to match (similar to downward closure), in the process solving an optimization problem for each unit in order to construct the optimal matches. The algorithm uses a single dynamic program to solve all of the units’ optimization problems simultaneously. Notable advantages of our method over existing matching procedures are its high-quality interpretable matches, versatility in handling different data distributions that may have irrelevant variables, and ability to handle missing data by matching on as many available covariates as possible.

The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow for variability in the sizes and behaviors of the different communities, and thus better reflect the behaviors observed in real-world networks. Our results show that the ability to detect communities can be described succinctly in terms of a matrix of effective signal-to-noise ratios that provides a geometrical representation of the relationships between the different communities. This characterization follows from a matrix version of the I-MMSE relationship and generalizes the concept of an effective scalar signal-to-noise ratio introduced in previous work. We provide explicit formulas for the asymptotic per-node mutual information and upper bounds on the minimum mean-squared error. The theoretical results are supported by numerical simulations.