Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction between correlation and causation. While recent advances in causal machine learning and matching algorithms have improved estimation accuracy, these methods often face trade-offs between interpretability and computational efficiency. This paper proposes a novel approach that combines a tree-based discretization technique, tailored for causal inference, with an integer linear programming-based matching algorithm. The discretization ensures approximately linear relationships for control datasets within strata, enabling effective matching, while the optimization framework optimizes for global balance. The resulting algorithm yields computational efficiency and less biased ATT estimates compared to state-of-the-art algorithms. Empirical evaluations demonstrate the proposed method's practical advantages over existing techniques in causal inference scenarios.

We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A number of commonly used approaches fit this formulation, including the difference-inmeans estimator and a variety of synthetic-control techniques. We propose several methods for choosing the set of treated units in conjunction with the weights. Observing the NP-hardness of the problem, we introduce a mixed-integer programming formulation which selects both the treatment and control sets and unit weightings. We prove that these proposed approaches lead to qualitatively different experimental units being selected for treatment. We use simulations based on publicly available data from the USBureau of Labor Statistics that show improvements in terms of mean squared error and statistical power when compared to simple and commonly used alternatives such as randomized trials.

Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units.

The synthetic control method (SCM) estimates causal effects in panel data with a single-treated unit by constructing a counterfactual outcome as a weighted combination of untreated control units that matches the pre-treatment trajectory. In this paper, we introduce the targeted synthetic control (TSC) method, a new two-stage estimator that directly estimates the counterfactual outcome. Specifically, our TSC method (1) yields a targeted debiasing estimator, in the sense that the targeted updating refines the initial weights to produce more stable weights; and (2) ensures that the final counterfactual estimation is a convex combination of observed control outcomes to enable direct interpretation of the synthetic control weights. TSC is flexible and can be instantiated with arbitrary machine learning models. Methodologically, TSC starts from an initial set of synthetic-control weights via a one-dimensional targeted update through the weight-tilting submodel, which calibrates the weights to reduce bias of weights estimation arising from pre-treatment fit. Furthermore, TSC avoids key shortcomings of existing methods (e.g., the augmented SCM), which can produce unbounded counterfactual estimates. Across extensive synthetic and real-world experiments, TSC consistently improves estimation accuracy over state-of-the-art SCM baselines.

Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units. In such models, there may be so many free parameters that the model fits the training data perfectly. We first investigate high-dimensional linear regression for imputing wage data and estimating average treatment effects, where we find that models with many more covariates than sample size can outperform simple ones.

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions--how the timing of an event would change under a specified intervention--commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to estimate counterfactual hazard trajectories in a panel data setting where multiple units experience potentially different treatments over multiple periods. In such a setting, SSC estimates the counterfactual hazard trajectory for a unit of interest as a weighted combination of the observed trajectories from other units. To provide formal justification, we introduce a panel framework with a low-rank structure for causal survival analysis. Indeed, such a structure naturally arises under classical parametric survival models. Within this framework, for the causal estimand of interest, we establish identification and finite sample guarantees for SSC. We validate our approach using a multi-country clinical dataset of cancer treatment outcomes, where the staggered introduction of new therapies creates a quasi-experimental setting. Empirically, we find that access to novel treatments is associated with improved survival, as reflected by lower post-intervention hazard trajectories relative to their synthetic counterparts. Given the broad relevance of survival analysis across medicine, economics, and public policy, our framework offers a general and interpretable tool for counterfactual survival inference using observational data.

The Synthetic Control method (SC) has become a valuable tool for estimating causal effects. Originally designed for single-treated unit scenarios, it has recently found applications in high-dimensional disaggregated settings with multiple treated units. However, challenges in practical implementation and computational efficiency arise in such scenarios. To tackle these challenges, we propose a novel approach that integrates the Multivariate Square-root Lasso method into the synthetic control framework. We rigorously establish the estimation error bounds for fitting the Synthetic Control weights using Multivariate Square-root Lasso, accommodating high-dimensionality and time series dependencies. Additionally, we quantify the estimation error for the Average Treatment Effect on the Treated (ATT). Through simulation studies, we demonstrate that our method offers superior computational efficiency without compromising estimation accuracy. We apply our method to assess the causal impact of COVID-19 Stay-at-Home Orders on the monthly unemployment rate in the United States at the county level.

Event causality identification (ECI), a process that extracts causal relations between events from text, is crucial for distinguishing causation from correlation. Traditional approaches to ECI have primarily utilized linguistic patterns and multi-hop relational inference, risking false causality identification due to informal usage of causality and specious graphical inference. In this paper, we adopt the Rubin Causal Model to identify event causality: given two temporally ordered events, we see the first event as the treatment and the second one as the observed outcome. Determining their causality involves manipulating the treatment and estimating the resultant change in the likelihood of the outcome. Given that it is only possible to implement manipulation conceptually in the text domain, as a work-around, we try to find a'twin' for the protagonist from existing corpora. This'twin' should have identical life experiences with the protagonist before the treatment but undergoes an intervention of treatment. However, the practical difficulty of locating such a match limits its feasibility. Addressing this issue, we use the synthetic control method to generate such a'twin' from relevant historical data, leveraging text embedding synthesis and inversion techniques. This approach allows us to identify causal relations more robustly than previous methods, including GPT -4, which is demonstrated on a causality benchmark, COPES-hard.