Synthetic Control

Enterprise customer journeys are shaped not only by product experiences and marketing, but also by recurring resource-allocation decisions. In B2B go-to-market (GTM) organizations, territory carving determines which accounts receive seller coverage, which seller-account relationships are preserved, and how limited field capacity is distributed. Yet the process often remains manual, making it difficult to compare opportunities, value continuity, and evaluate tradeoffs among growth, balance, capacity, and feasibility. We present a production decision system for tradeoff-aware customer-to-seller allocation in enterprise GTM planning. It integrates three components: a multidimensional account-value layer that combines predictive signals to score opportunity; an observational continuity-valuation layer that estimates the cost of breaking seller-account relationships using a synthetic-control-style counterfactual framework; and a multi-objective optimization layer that allocates coverage to high-value accounts while considering continuity, opportunity balance, and operational constraints. Deployed as a scenario-based decision-support system, the framework enables planners to inspect and compare allocation tradeoffs. Historical backtesting shows that optimizer-generated scenarios substantially improve assignment compliance while maintaining comparable seller-level opportunity distribution. In production planning, adopted scenarios improved both assignment compliance and opportunity balance relative to the previous baseline. Directing scarce seller capacity toward higher-value accounts also offers incremental revenue potential at enterprise scale. The key contribution is an integrated, inspectable framework that turns territory carving into a governable decision process.

Synthetic control methods estimate counterfactual outcomes by weighting untreated donor units to match a treated unit before treatment. In recent applications, however, the donor pool can be large, highly correlated, and short in pre-treatment history, yielding many near-equivalent solutions with unstable and difficult-to-interpret donor weights. We propose Graph-Regularized Synthetic Control (Graph-SC), a convex estimator that augments the classical pre-treatment matching objective with a graph Laplacian penalty. The graph encodes similarity among donor trajectories, encouraging coherent weights over structurally related donors while preserving the transparency of synthetic controls. We provide theoretical results characterizing the bias-variance tradeoff induced by graph regularization and establish efficient convergence guarantees with an accelerated proximal gradient method. Across a controlled simulation under donor redundancy, the California Proposition 99 benchmark, and observational counterfactual analyses on the Waymo Open Motion Dataset, Graph-SC improves weight stability, reduces sensitivity to redundant donor pools, and maintains competitive pre- and post-treatment accuracy relative to classical and regularized synthetic control baselines. Our results suggest that graph regularization is most valuable not as a universal accuracy booster, but as a principled mechanism for selecting stable and interpretable counterfactuals from near-equivalent synthetic controls with comparable pre-treatment fit.

We develop exponential family synthetic controls (EFSC), a distributional version of synthetic controls for a panel of datasets. Each cell of the panel corresponds to a dataset drawn from an exponential family whose natural parameters factorize probabilistically across units and times. We estimate the latent factors using black-box variational inference. This replaces the usual weighted-average view of synthetic controls with a flexible probabilistic model that operates on full distributions. We propose causal estimands based on divergences between pre- and post-intervention distributions induced by the posterior of the natural parameters, together with distributional placebo tests to support causal inference and assess the significance of the estimated effects. We validate the proposed framework on synthetic and real data. Across a variety of exponential-family distributions, EFSC accurately recovers causal effects induced by exponential tilts, together with the corresponding divergences between treated and counterfactual distributions. The framework also captures effects induced by structural perturbations of the latent factors and by heavy-tailed noise contamination. Finally, we apply EFSC to study the expansion of Medicaid under the Affordable Care Act (ACA) and its impact on the distribution of health insurance coverage across U.S. states. Code is available at https://github.com/blei-lab/efsc.

Synthetic control (SC) matches a treated unit's pre-treatment trajectory to a weighted combination of donor units. We study Spectral SC, which instead matches the treated unit in coordinates defined by the leading temporal singular vectors of the donor panel, and a hybrid estimator that places separately tunable weight on retained and discarded directions, nesting raw-path SC and truncated Spectral SC as endpoints. We prove that the family reduces exactly to raw-path SC at full rank, that exact balance on $K$ retained dimensions with $N_0$ donors is underdetermined whenever $N_0>K+1$, with an affine solution set of dimension $N_0-K-1$, and that spectral imbalance maps to treatment-effect bias through a finite-sample best-linear-predictor decomposition. We evaluate the estimators across eleven data-generating regimes, using $400$ replications per regime and donor-only placebo validation to select regularization and the mixing weight. Truncated Spectral SC has significantly higher RMSE than tuned raw-path SC in every regime, with paired differences equal to $4$ to $11$ Monte Carlo standard errors. The hybrid estimator selects raw-path matching in most replications and is statistically indistinguishable from tuned SC in most regimes. The result is highly sensitive to preprocessing. With raw inputs, the performance gap is large; after removing unit and time fixed effects before spectral decomposition, as suggested by the assumptions behind our bound, the gap nearly disappears and placebo validation begins to favor truncation. We interpret these findings diagnostically rather than as evidence that Spectral SC should replace raw-path SC. Basis-estimation noise, balancing underdetermination, and fixed-effects contamination determine when spectral matching can help.

Single-arm trials are an important study design for evaluating drug efficacy and safety without enrolling patients into a control arm. Although they do not provide the gold-standard evidence of randomized controlled trials, they are increasingly used in clinical development as they offer an efficient, ethical, and practical alternative. A wide variety of approaches can be used to construct control comparators and estimate treatment effects, from fixed comparators informed by clinical knowledge to data-based and model-based patient-level comparators, also known as synthetic controls. Powerful and flexible machine learning models can allow outcome-model-based synthetic controls to overcome key limitations of direct data-based approaches, yield more robust estimates of treatment effects, and provide a principled way to incorporate corrections or encode additional assumptions when external data are not directly comparable. In this work, we argue that outcome-model-based synthetic control arms are an important tool for single-arm trials. We focus on digital twins, personalized predictions of disease progression generated from machine learning models trained on historical datasets, which naturally leverage these flexible approaches. We review doubly robust estimators, present power and sample size formulas, and discuss trade-offs in selecting historical data for training and analysis. We also outline practical considerations for deploying digital twins within the framework of recent FDA draft guidance on the use of artificial intelligence in drug development. Finally, we reanalyze data from trials in amyotrophic lateral sclerosis and Huntington's disease to demonstrate the proposed methods.

Baseline estimation is critical to Demand Response (DR) settlement in electricity markets, yet existing machine learning methods remain limited in predictive performance, while methodologies from causal inference and counterfactual prediction are still underutilized in this domain. We introduce a Generalized Synthetic Control Method that builds on the classical Synthetic Control Method (SCM) from econometrics. While SCM provides a powerful framework for counterfactual estimation, classical SCM remains a static estimator: it fits the treated unit as a combination of contemporaneous donor units and therefore ignores predictable temporal structure in the residual error. We develop a generalized SCM framework that transforms baseline estimation into a dynamic counterfactual prediction problem by augmenting the donor representation with exogenous features, lagged treated load, and selected lagged donor signals. This enriched representation allows the estimator to capture autoregressive dependence, delayed donor-response patterns, and error-correction effects beyond the scope of standard SCM. The framework further accommodates nonlinear predictors when linear weighting is inadequate, with the greatest benefit arising in limited-data settings. Experiments on the Ausgrid smart-meter dataset show consistent improvements over classical SCM and strong benchmark methods, with the dominant performance gains driven by dynamic augmentation.

AI-based persona simulation -- often referred to as digital twin simulation -- is increasingly used for market research, recommender systems, and social sciences. Despite their flexibility, large language models (LLMs) often exhibit systematic bias and miscalibration relative to real human behavior, limiting their reliability. Inspired by synthetic control methods from causal inference, we propose SYN-DIGITS (SYNthetic Control Framework for Calibrated DIGItal Twin Simulation), a principled and lightweight calibration framework that learns latent structure from digital-twin responses and transfers it to align predictions with human ground truth. SYN-DIGITS operates as a post-processing layer on top of any LLM-based simulator and thus is model-agnostic. We develop a latent factor model that formalizes when and why calibration succeeds through latent space alignment conditions, and we systematically evaluate ten calibration methods across thirteen persona constructions, three LLMs, and two datasets. SYN-DIGITS supports both individual-level and distributional simulation for previously unseen questions and unobserved populations, with provable error guarantees. Experiments show that SYN-DIGITS achieves up to 50% relative improvements in individual-level correlation and 50--90% relative reductions in distributional discrepancy compared to uncalibrated baselines.

We propose a generalization of the synthetic control methods to the setting with dynamic treatment effects, in which each unit receives multiple treatments sequentially, according to an adaptive policy that depends on a latent, endogenously time-varying confounding state. Under a low-rank latent factor model assumption, which admits linear time-varying and time-invariant dynamic triangular systems as special cases, we develop an identification strategy for any unit-specific mean outcome under any sequence of interventions. Our method, which we term synthetic blips, is a backward induction process in which the blip effect of a treatment at each period for a target unit is recursively expressed as a linear combination of the blip effects of other units that received the designated treatment, avoiding the combinatorial donor requirements of naive synthetic control extensions. We provide easy-to-implement estimation algorithms that yield consistent estimators. Using unique Korean firm-level panel data, we estimate individualized dynamic treatment effects and optimal allocation rules in the context of financial support for exporting firms.