arXiv subjects

Jelena Bradic

Publications and source records attributed to Jelena Bradic.

At least 19 recordsLinked to original sources

arXiv2026

Surrogate-powered Causal Inference with Censored Outcomes

Clinical trials with survival endpoints lose information when participants are censored before death is observed. We develop target-preserving estimators that use posttreatment disease history, such as recurrence or progression, to recover information lost to censoring for marginal survival and restricted mean survival effects. The difficulty is that the intermediate event is downstream of treatment: naive adjustment can change the causal estimand, and the useful information enters only through the observed coarsening. We derive observed-data influence functions with and without recurrence history and obtain an exact gain identity. The identity shows that efficiency improvement is driven by the censoring hazard, the split of the alive risk set into recurrence states, and the residual-survival separation between those states. In the no-covariate illness-death model, the Aalen-Johansen estimator realizes the recurrence-augmented efficient score after standardization to the marginal target. With covariates, correctly specified Cox-Breslow transition hazards provide a root-N plug-in benchmark, while a hazard-induced one-step estimator gives rate robustness and, under primitive transition and censoring learner rates, canonical inference with a second-order product remainder. A semi-synthetic metastatic breast cancer study calibrated from digitized progression-free survival and overall survival curves illustrates the gain identity. The framework applies broadly to censored time-to-event studies with informative intermediate histories.

math.ST↗

arXiv2026

High-dimensional semi-supervised learning: in search for optimal inference of the mean

A fundamental challenge in semi-supervised learning lies in the observed data's disproportional size when compared with the size of the data collected with missing outcomes. An implicit understanding is that the dataset with missing outcomes, being significantly larger, ought to improve estimation and inference. However, it is unclear to what extent this is correct. We illustrate one clear benefit: root-n inference of the outcome's mean is possible while only requiring a consistent estimation of the outcome, possibly at a rate slower than root n. This is achieved by a novel k-fold, cross-fitted, double robust estimator. We discuss both linear and nonlinear outcomes. Such an estimator is particularly suited for models that naturally do not admit root-n consistency, such as high-dimensional, nonparametric or semiparametric models. We apply our methods to estimating heterogeneous treatment effects.

stat.ME↗

arXiv2026

Multi-environment Invariance Learning with Missing Data

Learning models that can handle distribution shifts is a key challenge in domain generalization. Invariance learning, an approach that focuses on identifying features invariant across environments, improves model generalization by capturing stable relationships, which may represent causal effects when the data distribution is encoded within a structural equation model (SEM) and satisfies modularity conditions. This has led to a growing body of work that builds on invariance learning, leveraging the inherent heterogeneity across environments to develop methods that provide causal explanations while enhancing robust prediction. However, in many practical scenarios, obtaining complete outcome data from each environment is challenging due to the high cost or complexity of data collection. This limitation in available data hinders the development of models that fully leverage environmental heterogeneity, making it crucial to address missing outcomes to improve both causal insights and robust prediction. In this work, we derive an estimator from the invariance objective under missing outcomes. We establish non-asymptotic guarantees on variable selection property and $\ell_2$ error convergence rates, which are influenced by the proportion of missing data and the quality of imputation models across environments. We evaluate the performance of the new estimator through extensive simulations and demonstrate its application using the UCI Bike Sharing dataset to predict the count of bike rentals. The results show that despite relying on a biased imputation model, the estimator is efficient and achieves lower prediction error, provided the bias is within a reasonable range.

stat.ML↗

arXiv2026

When Symbol Names Should Not Matter: A Logistic Theory of Fresh-Symbol Classification

Template tasks have emerged as a clean testbed for asking whether transformers reason with abstract symbols rather than concrete token names. We study the fixed-label classification version of this problem, where train and test examples share latent templates but may use disjoint vocabularies. Unlike next-token prediction, the model need not emit unseen symbols; it must learn a decision rule invariant to symbol renaming. We analyze regularized kernel logistic classification in the transformer-kernel regime. Our main result decomposes the learned predictor into an ideal template-level classifier and a finite-sample perturbation caused by accidental token overlaps in the training data. We encode these overlaps by a colored collision graph and prove high-probability margin-transfer guarantees for fresh-symbol classification. This perspective extends template-based analyses to logistic classification and refines scalar diversity conditions: vocabulary size controls the average rate of collisions, but collision geometry controls whether the ideal classification margin is preserved. More broadly, the same perturbation framework applies to abstraction-augmented inputs, yielding a general margin-versus-collision criterion for identifying when prompting strategies improve fresh-symbol generalization. Synthetic template experiments illustrate the predicted roles of regularization, sample size, and transformer-kernel structure.

cs.LG↗

arXiv2026

Dynamic covariate balancing: estimating treatment effects over time with potential local projections

This paper studies the estimation and inference of treatment effects in panel data settings when treatments change dynamically over time. We propose a balancing method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes, and treatments; (ii) outcomes and time-varying covariates to depend on the trajectory of all past treatments; (iii) heterogeneity of treatment effects. Our approach recursively projects potential outcomes' expectations on past histories. It then controls the bias arising from the non-experimental and sequential nature of this setting by balancing dynamically observable characteristics over time. We establish inferential guarantees of the proposed method even when the number of observable characteristics significantly exceeds the sample size. We study numerical properties of the estimator and illustrate the benefits of the procedure in an empirical application.

econ.EM↗

arXiv2025

Minimax Semiparametric Learning With Approximate Sparsity

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of parameters are precisely non-zero. This excludes models where linear formulations only approximate the underlying data distribution, such as nonparametric regression methods that use basis expansion such as splines, kernel methods or polynomial regressions. Many recent methods for root-$n$ estimation have been proposed, but the implications of exact model sparsity remain largely unexplored. In particular, minimax optimality for models that are not exactly sparse has not yet been developed. This paper formalizes the concept of approximate sparsity through classical semi-parametric theory. We derive minimax rates under this formulation for a regression slope and an average derivative, finding these bounds to be substantially larger than those in low-dimensional, semi-parametric settings. We identify several new phenomena. We discover new regimes where rate double robustness does not hold, yet root-$n$ estimation is still possible. In these settings, we propose an estimator that achieves minimax optimal rates. Our findings further reveal distinct optimality boundaries for ordered versus unordered nonparametric regression estimation.

math.ST↗

arXiv2025

The Decaying Missing-at-Random Framework: Model Doubly Robust Causal Inference with Partially Labeled Data

In modern large-scale observational studies, data collection constraints often result in partially labeled datasets, posing challenges for reliable causal inference, especially due to potential labeling bias and relatively small size of the labeled data. This paper introduces a decaying missing-at-random (decaying MAR) framework and associated approaches for doubly robust causal inference on treatment effects in such semi-supervised (SS) settings. This simultaneously addresses selection bias in the labeling mechanism and the extreme imbalance between labeled and unlabeled groups, bridging the gap between the standard SS and missing data literatures, while throughout allowing for confounded treatment assignment and high-dimensional confounders under appropriate sparsity conditions. To ensure robust causal conclusions, we propose a bias-reduced SS (BRSS) estimator for the average treatment effect, a type of 'model doubly robust' estimator appropriate for such settings, establishing asymptotic normality at the appropriate rate under decaying labeling propensity scores, provided that at least one nuisance model is correctly specified. Our approach also relaxes sparsity conditions beyond those required in existing methods, including standard supervised approaches. Recognizing the asymmetry between labeling and treatment mechanisms, we further introduce a de-coupled BRSS (DC-BRSS) estimator, which integrates inverse probability weighting (IPW) with bias-reducing techniques in nuisance estimation. This refinement further weakens model specification and sparsity requirements. Numerical experiments confirm the effectiveness and adaptability of our estimators in addressing labeling bias and model misspecification.

stat.ME↗

arXiv2025

Dynamic treatment effects: high-dimensional inference under model misspecification

Estimating dynamic treatment effects is crucial across various disciplines, providing insights into the time-dependent causal impact of interventions. However, this estimation poses challenges due to time-varying confounding, leading to potentially biased estimates. Furthermore, accurately specifying the growing number of treatment assignments and outcome models with multiple exposures appears increasingly challenging to accomplish. Double robustness, which permits model misspecification, holds great value in addressing these challenges. This paper introduces a novel "sequential model doubly robust" estimator. We develop novel moment-targeting estimates to account for confounding effects and establish that root-$N$ inference can be achieved as long as at least one nuisance model is correctly specified at each exposure time, despite the presence of high-dimensional covariates. Although the nuisance estimates themselves do not achieve root-$N$ rates, the carefully designed loss functions in our framework ensure final root-$N$ inference for the causal parameter of interest. Unlike off-the-shelf high-dimensional methods, which fail to deliver robust inference under model misspecification even within the doubly robust framework, our newly developed loss functions address this limitation effectively.

stat.ME↗

arXiv2024

Estimating Treatment Effect under Additive Hazards Models with High-dimensional Covariates

Estimating causal effects for survival outcomes in the high-dimensional setting is an extremely important topic for many biomedical applications as well as areas of social sciences. We propose a new orthogonal score method for treatment effect estimation and inference that results in asymptotically valid confidence intervals assuming only good estimation properties of the hazard outcome model and the conditional probability of treatment. This guarantee allows us to provide valid inference for the conditional treatment effect under the high-dimensional additive hazards model under considerably more generality than existing approaches. In addition, we develop a new Hazards Difference (HDi), estimator. We showcase that our approach has double-robustness properties in high dimensions: with cross-fitting, the HDi estimate is consistent under a wide variety of treatment assignment models; the HDi estimate is also consistent when the hazards model is misspecified and instead the true data generating mechanism follows a partially linear additive hazards model. We further develop a novel sparsity doubly robust result, where either the outcome or the treatment model can be a fully dense high-dimensional model. We apply our methods to study the treatment effect of radical prostatectomy versus conservative management for prostate cancer patients using the SEER-Medicare Linked Data.

stat.ME↗

arXiv2024

Adaptive Split Balancing for Optimal Random Forest

In this paper, we propose a new random forest algorithm that constructs the trees using a novel adaptive split-balancing method. Rather than relying on the widely-used random feature selection, we propose a permutation-based balanced splitting criterion. The adaptive split balancing forest (ASBF), achieves minimax optimality under the Lipschitz class. Its localized version, which fits local regressions at the leaf level, attains the minimax rate under the broad Hölder class $\mathcal{H}^{q,β}$ of problems for any $q\in\mathbb{N}$ and $β\in(0,1]$. We identify that over-reliance on auxiliary randomness in tree construction may compromise the approximation power of trees, leading to suboptimal results. Conversely, the proposed less random, permutation-based approach demonstrates optimality over a wide range of models. Although random forests are known to perform well empirically, their theoretical convergence rates are slow. Simplified versions that construct trees without data dependence offer faster rates but lack adaptability during tree growth. Our proposed method achieves optimality in simple, smooth scenarios while adaptively learning the tree structure from the data. Additionally, we establish uniform upper bounds and demonstrate that ASBF improves dimensionality dependence in average treatment effect estimation problems. Simulation studies and real-world applications demonstrate our methods' superior performance over existing random forests.

stat.ML↗

arXiv2024

Causal inference through multi-stage learning and doubly robust deep neural networks

Deep neural networks (DNNs) have demonstrated remarkable empirical performance in large-scale supervised learning problems, particularly in scenarios where both the sample size $n$ and the dimension of covariates $p$ are large. This study delves into the application of DNNs across a wide spectrum of intricate causal inference tasks, where direct estimation falls short and necessitates multi-stage learning. Examples include estimating the conditional average treatment effect and dynamic treatment effect. In this framework, DNNs are constructed sequentially, with subsequent stages building upon preceding ones. To mitigate the impact of estimation errors from early stages on subsequent ones, we integrate DNNs in a doubly robust manner. In contrast to previous research, our study offers theoretical assurances regarding the effectiveness of DNNs in settings where the dimensionality $p$ expands with the sample size. These findings are significant independently and extend to degenerate single-stage learning problems.

stat.ML↗

arXiv2024

Semiparametrically Efficient Score for the Survival Odds Ratio

We consider a general proportional odds model for survival data under binary treatment, where the functional form of the covariates is left unspecified. We derive the efficient score for the conditional survival odds ratio given the covariates using modern semiparametric theory. The efficient score may be useful in the development of doubly robust estimators, although computational challenges remain.

stat.ME↗

arXiv2023

Doubly Robust Estimation under Possibly Misspecified Marginal Structural Cox Model

In this paper we address the challenges posed by non-proportional hazards and informative censoring, offering a path toward more meaningful causal inference conclusions. We start from the marginal structural Cox model, which has been widely used for analyzing observational studies with survival outcomes, and typically relies on the inverse probability weighting method. The latter hinges upon a propensity score model for the treatment assignment, and a censoring model which incorporates both the treatment and the covariates. In such settings, model misspecification can occur quite effortlessly, and the Cox regression model's non-collapsibility has historically posed challenges when striving to guard against model misspecification through augmentation. We introduce an augmented inverse probability weighted estimator which, enriched with doubly robust properties, paves the way for integrating machine learning and a plethora of nonparametric methods, effectively overcoming the challenges of non-collapsibility. The estimator extends naturally to estimating a time-average treatment effect when the proportional hazards assumption fails. We closely examine its theoretical and practical performance, showing that it satisfies both the assumption-lean and the well-specification criteria discussed in the recent literature. Finally, its application to a dataset reveals insights into the impact of mid-life alcohol consumption on mortality in later life.

stat.ME↗

arXiv2023

Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap

Semi-supervised (SS) inference has received much attention in recent years. Apart from a moderate-sized labeled data, L, the SS setting is characterized by an additional, much larger sized, unlabeled data, U. The setting of |U| >> |L|, makes SS inference unique and different from the standard missing data problems, owing to natural violation of the so-called "positivity" or "overlap" assumption. However, most of the SS literature implicitly assumes L and U to be equally distributed, i.e., no selection bias in the labeling. Inferential challenges in missing at random (MAR) type labeling allowing for selection bias, are inevitably exacerbated by the decaying nature of the propensity score (PS). We address this gap for a prototype problem, the estimation of the response's mean. We propose a double robust SS (DRSS) mean estimator and give a complete characterization of its asymptotic properties. The proposed estimator is consistent as long as either the outcome or the PS model is correctly specified. When both models are correctly specified, we provide inference results with a non-standard consistency rate that depends on the smaller size |L|. The results are also extended to causal inference with imbalanced treatment groups. Further, we provide several novel choices of models and estimators of the decaying PS, including a novel offset logistic model and a stratified labeling model. We present their properties under both high and low dimensional settings. These may be of independent interest. Lastly, we present extensive simulations and also a real data application.

stat.ME↗

arXiv2023

High-dimensional Inference for Dynamic Treatment Effects

Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects due to their flexibility. However, we showcase that the traditional DR approaches that only focus on the DR representation of the expected outcomes may fall short of delivering optimal results. In this paper, we propose a novel DR representation for intermediate conditional outcome models that leads to superior robustness guarantees. The proposed method achieves consistency even with high-dimensional confounders, as long as at least one nuisance function is appropriately parametrized for each exposure time and treatment path. Our results represent a significant step forward as they provide new robustness guarantees. The key to achieving these results is our new DR representation, which offers superior inferential performance while requiring weaker assumptions. Lastly, we confirm our findings in practice through simulations and a real data application.

stat.ME↗

arXiv2022

Synthetic learner: model-free inference on treatments over time

Understanding the effect of a particular treatment or a policy pertains to many areas of interest, ranging from political economics, marketing to healthcare. In this paper, we develop a non-parametric algorithm for detecting the effects of treatment over time in the context of Synthetic Controls. The method builds on counterfactual predictions from many algorithms without necessarily assuming that the algorithms correctly capture the model. We introduce an inferential procedure for detecting treatment effects and show that the testing procedure is asymptotically valid for stationary, beta mixing processes without imposing any restriction on the set of base algorithms under consideration. We discuss consistency guarantees for average treatment effect estimates and derive regret bounds for the proposed methodology. The class of algorithms may include Random Forest, Lasso, or any other machine-learning estimator. Numerical studies and an application illustrate the advantages of the method.

stat.ME↗

arXiv2022

Fair Policy Targeting

One of the major concerns of targeting interventions on individuals in social welfare programs is discrimination: individualized treatments may induce disparities across sensitive attributes such as age, gender, or race. This paper addresses the question of the design of fair and efficient treatment allocation rules. We adopt the non-maleficence perspective of first do no harm: we select the fairest allocation within the Pareto frontier. We cast the optimization into a mixed-integer linear program formulation, which can be solved using off-the-shelf algorithms. We derive regret bounds on the unfairness of the estimated policy function and small sample guarantees on the Pareto frontier under general notions of fairness. Finally, we illustrate our method using an application from education economics.

econ.EM↗

arXiv2021

Learning to Combat Noisy Labels via Classification Margins

A deep neural network trained on noisy labels is known to quickly lose its power to discriminate clean instances from noisy ones. After the early learning phase has ended, the network memorizes the noisy instances, which leads to a significant degradation in its generalization performance. To resolve this issue, we propose MARVEL (MARgins Via Early Learning), a new robust learning method where the memorization of the noisy instances is curbed. We propose a new test statistic that tracks the goodness of "fit" of every instance based on the epoch-history of its classification margins. If its classification margin is small in a sequence of consecutive learning epochs, that instance is declared noisy and the network abandons learning on it. Consequently, the network first flags a possibly noisy instance, and then waits to see if learning on that instance can be improved and if not, the network learns with confidence that this instance can be safely abandoned. We also propose MARVEL+, where arduous instances can be upweighted, enabling the network to focus and improve its learning on them and consequently its generalization. Experimental results on benchmark datasets with synthetic label noise and real-world datasets show that MARVEL outperforms other baselines consistently across different noise levels, with a significantly larger margin under asymmetric noise.

cs.LG↗