arXiv subjects

Zijian Guo

Publications and source records attributed to Zijian Guo.

At least 37 records · Page 2Linked to original sources

arXiv2026

Statistical Analysis of Conditional Group Distributionally Robust Optimization with Cross-Entropy Loss

In multi-source learning with discrete labels, distributional heterogeneity across domains poses a central challenge to developing predictive models that transfer reliably to unseen domains. We study multi-source unsupervised domain adaptation, where labeled data are available from multiple source domains and only unlabeled data are observed from the target domain. To address potential distribution shifts, we propose a novel Conditional Group Distributionally Robust Optimization (CG-DRO) framework that learns a classifier by minimizing the worst-case cross-entropy loss over the convex combinations of the conditional outcome distributions from sources domains. We develop an efficient Mirror Prox algorithm for solving the minimax problem and employ a double machine learning procedure to estimate the risk function, ensuring that errors in nuisance estimation contribute only at higher-order rates. We establish fast statistical convergence rates for the empirical CG-DRO estimator by constructing two surrogate minimax optimization problems that serve as theoretical bridges. A distinguishing challenge for CG-DRO is the emergence of nonstandard asymptotics: the empirical CG-DRO estimator may fail to converge to a standard limiting distribution due to boundary effects and system instability. To address this, we introduce a perturbation-based inference procedure that enables uniformly valid inference, including confidence interval construction and hypothesis testing.

stat.ME↗

arXiv2026

Adversarial Drift-Aware Predictive Transfer: Toward Durable Clinical AI

Clinical AI systems frequently suffer performance decay post-deployment due to temporal data shifts, such as evolving populations, diagnostic coding updates (e.g., ICD-9 to ICD-10), and systemic shocks like the COVID-19 pandemic. Addressing this ``aging'' effect via frequent retraining is often impractical due to computational costs and privacy constraints. To overcome these hurdles, we introduce Adversarial Drift-Aware Predictive Transfer (ADAPT), a novel framework designed to confer durability against temporal drift with minimal retraining. ADAPT innovatively constructs an uncertainty set of plausible future models by combining historical source models and limited current data. By optimizing worst-case performance over this set, it balances current accuracy with robustness against degradation due to future drifts. Crucially, ADAPT requires only summary-level model estimators from historical periods, preserving data privacy and ensuring operational simplicity. Validated on longitudinal suicide risk prediction using electronic health records from Mass General Brigham (2005--2021) and Duke University Health Systems, ADAPT demonstrated superior stability across coding transitions and pandemic-induced shifts. By minimizing annual performance decay without labeling or retraining future data, ADAPT offers a scalable pathway for sustaining reliable AI in high-stakes healthcare environments.

stat.AP↗

arXiv2026

Causal Invariance Learning via Efficient Nonconvex Optimization

Identifying the causal relationship among variables from observational data is an important yet challenging task. This work focuses on identifying the direct causes of an outcome and estimating their magnitude, i.e., learning the causal outcome model. Data from multiple environments provide valuable opportunities to uncover causality by exploiting the invariance principle that the causal outcome model holds across heterogeneous environments. Based on the invariance principle, we propose the Negative Weighted Distributionally Robust Optimization (NegDRO) framework to learn an invariant prediction model. NegDRO minimizes the worst-case combination of risks across multiple environments and enforces invariance by allowing potential negative weights. Under the additive interventions regime, we establish three major contributions: (i) On the statistical side, we provide sufficient and nearly necessary identification conditions under which the invariant prediction model coincides with the causal outcome model; (ii) On the optimization side, despite the nonconvexity of NegDRO, we establish its benign optimization landscape, where all stationary points lie close to the true causal outcome model; (iii) On the computational side, we develop a gradient-based algorithm that provably converges to the causal outcome model, with non-asymptotic convergence rates in both sample size and gradient-descent iterations. In particular, our method avoids exhaustive combinatorial searches over exponentially many subsets of covariates found in the literature, ensuring scalability even when the dimension of the covariates is large. To our knowledge, this is the first causal invariance learning method that finds the approximate global optimality for a nonconvex optimization problem efficiently.

stat.ME↗

arXiv2025

One Subgoal at a Time: Zero-Shot Generalization to Arbitrary Linear Temporal Logic Requirements in Multi-Task Reinforcement Learning

Generalizing to complex and temporally extended task objectives and safety constraints remains a critical challenge in reinforcement learning (RL). Linear temporal logic (LTL) offers a unified formalism to specify such requirements, yet existing methods are limited in their abilities to handle nested long-horizon tasks and safety constraints, and cannot identify situations when a subgoal is not satisfiable and an alternative should be sought. In this paper, we introduce GenZ-LTL, a method that enables zero-shot generalization to arbitrary LTL specifications. GenZ-LTL leverages the structure of Büchi automata to decompose an LTL task specification into sequences of reach-avoid subgoals. Contrary to the current state-of-the-art method that conditions on subgoal sequences, we show that it is more effective to achieve zero-shot generalization by solving these reach-avoid problems \textit{one subgoal at a time} through proper safe RL formulations. In addition, we introduce a novel subgoal-induced observation reduction technique that can mitigate the exponential complexity of subgoal-state combinations under realistic assumptions. Empirical results show that GenZ-LTL substantially outperforms existing methods in zero-shot generalization to unseen LTL specifications.

cs.AI↗

arXiv2025

Post-selection inference for causal effects after causal discovery

Algorithms for constraint-based causal discovery select graphical causal models among a space of possible candidates (e.g., all directed acyclic graphs) by executing a sequence of conditional independence tests. These may be used to inform the estimation of causal effects (e.g., average treatment effects) when there is uncertainty about which covariates ought to be adjusted for, or which variables act as confounders versus mediators. However, naively using the data twice, for model selection and estimation, would lead to invalid confidence intervals. Moreover, if the selected graph is incorrect, the inferential claims may apply to a selected functional that is distinct from the actual causal effect. We propose an approach to post-selection inference that is based on a resampling and screening procedure, which essentially performs causal discovery multiple times with randomly varying intermediate test statistics. Then, an estimate of the target causal effect and corresponding confidence sets are constructed from a union of individual graph-based estimates and intervals. We show that this construction has asymptotically correct coverage for the true causal effect parameter. Importantly, the guarantee holds for a fixed population-level effect, not a data-dependent or selection-dependent quantity. Most of our exposition focuses on the PC-algorithm for learning directed acyclic graphs and the multivariate Gaussian case for simplicity, but the approach is general and modular, so it may be used with other conditional independence based discovery algorithms and distributional families.

stat.ME↗

arXiv2025

Hierarchical Multi-Agent Reinforcement Learning with Control Barrier Functions for Safety-Critical Autonomous Systems

We address the problem of safe policy learning in multi-agent safety-critical autonomous systems. In such systems, it is necessary for each agent to meet the safety requirements at all times while also cooperating with other agents to accomplish the task. Toward this end, we propose a safe Hierarchical Multi-Agent Reinforcement Learning (HMARL) approach based on Control Barrier Functions (CBFs). Our proposed hierarchical approach decomposes the overall reinforcement learning problem into two levels learning joint cooperative behavior at the higher level and learning safe individual behavior at the lower or agent level conditioned on the high-level policy. Specifically, we propose a skill-based HMARL-CBF algorithm in which the higher level problem involves learning a joint policy over the skills for all the agents and the lower-level problem involves learning policies to execute the skills safely with CBFs. We validate our approach on challenging environment scenarios whereby a large number of agents have to safely navigate through conflicting road networks. Compared with existing state of the art methods, our approach significantly improves the safety achieving near perfect (within 5%) success/safety rate while also improving performance across all the environments.

cs.LG↗

arXiv2025

Testing High-Dimensional Mediation Effect with Arbitrary Exposure-Mediator Coefficients

In response to the unique challenge created by high-dimensional mediators in mediation analysis, this paper presents a novel procedure for testing the nullity of the mediation effect in the presence of high-dimensional mediators. The procedure incorporates two distinct features. Firstly, the test remains valid under all cases of the composite null hypothesis, including the challenging scenario where both exposure-mediator and mediator-outcome coefficients are zero. Secondly, it does not impose structural assumptions on the exposure-mediator coefficients, thereby allowing for an arbitrarily strong exposure-mediator relationship. To the best of our knowledge, the proposed test is the first of its kind to provably possess these two features in high-dimensional mediation analysis. The validity and consistency of the proposed test are established, and its numerical performance is showcased through simulation studies. The application of the proposed test is demonstrated by examining the mediation effect of DNA methylation between smoking status and lung cancer development.

stat.ME↗

arXiv2025

Domain Adaptation Optimized for Robustness in Mixture Populations

While domain adaptation methods address data shifts, most assume target populations align with at least one source population, neglecting mixtures that combine sources influenced by factors like demographics. Additional challenges in electronic health record (EHR)-based studies include unobserved outcomes and the need to explain population mixtures using broader clinical characteristics than those in standard risk models. To address these challenges under shifts in both covariate distributions and outcome models, we propose a novel framework: Domain Adaptation Optimized for Robustness in Mixture populations (DORM). Leveraging partially labeled source data, DORM constructs an initial target outcome model under a joint source-mixture assumption. To enhance generalizability to future target populations that may deviate from the joint source-mixture approximation, DORM incorporates a group adversarial learning step to derive a final estimate, optimizing its worst-case performance within a convex uncertainty set built around the initial target model. In addition, this robust domain adaptation procedure is assisted by high-dimensional surrogates that enhance transferability in EHR studies. When a small set of gold-standard or noisy labels is available from the target population, a tuning strategy is implemented to refine the uncertainty set, mitigating conservativeness and further improving performance for the specific target population. Statistical convergence and predictive accuracy of our method are quantified through asymptotic studies. Simulation and real-world studies demonstrate the out-performance of our method over existing approaches.

stat.ME↗

arXiv2025

Distributionally Robust Learning for Multi-source Unsupervised Domain Adaptation

Empirical risk minimization often performs poorly when the distribution of the target domain differs from those of source domains. To address such potential distribution shifts, we develop an unsupervised domain adaptation approach that leverages labeled data from multiple source domains and unlabeled data from the target domain. We introduce a distributionally robust model that optimizes an adversarial reward based on the explained variance across a class of target distributions, ensuring generalization to the target domain. We show that the proposed robust model is a weighted average of conditional outcome models from source domains. This formulation allows us to compute the robust model through the aggregation of source models, which can be estimated using various machine learning algorithms of the users' choice, such as random forests, boosting, and neural networks. Additionally, we introduce a bias-correction step to obtain a more accurate aggregation weight, which is effective for various machine learning algorithms. Our framework can be interpreted as a distributionally robust federated learning approach that satisfies privacy constraints while providing insights into the importance of each source for prediction on the target domain. The performance of our method is evaluated on both simulated and real data.

stat.ML↗

arXiv2025

Fundamental Computational Limits in Pursuing Invariant Causal Prediction and Invariance-Guided Regularization

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as ICP [Peters et al., 2016] and EILLS [Fan et al., 2024] that can attain sample-efficient estimation are based on exponential time algorithms. In this paper, we show that such a problem is intrinsically hard in computation: the decision problem, testing whether a non-trivial prediction-invariant solution exists across two environments, is NP-hard even for the linear causal relationship. In the world where P$\neq$NP, our results imply that the estimation error rate can be arbitrarily slow using any computationally efficient algorithm. This suggests that pursuing causality is fundamentally harder than detecting associations when no prior assumption is pre-offered. Given there is almost no hope of computational improvement under the worst case, this paper proposes a method capable of attaining both computationally and statistically efficient estimation under additional conditions. Furthermore, our estimator is a distributionally robust estimator with an ellipse-shaped uncertain set where more uncertainty is placed on spurious directions than invariant directions, resulting in a smooth interpolation between the most predictive solution and the causal solution by varying the invariance hyper-parameter. Non-asymptotic results and empirical applications support the claim.

math.ST↗

arXiv2025

Temporal Logic Specification-Conditioned Decision Transformer for Offline Safe Reinforcement Learning

Offline safe reinforcement learning (RL) aims to train a constraint satisfaction policy from a fixed dataset. Current state-of-the-art approaches are based on supervised learning with a conditioned policy. However, these approaches fall short in real-world applications that involve complex tasks with rich temporal and logical structures. In this paper, we propose temporal logic Specification-conditioned Decision Transformer (SDT), a novel framework that harnesses the expressive power of signal temporal logic (STL) to specify complex temporal rules that an agent should follow and the sequential modeling capability of Decision Transformer (DT). Empirical evaluations on the DSRL benchmarks demonstrate the better capacity of SDT in learning safe and high-reward policies compared with existing approaches. In addition, SDT shows good alignment with respect to different desired degrees of satisfaction of the STL specification that it is conditioned on.

cs.LG↗

arXiv2024

Multi-source Stable Variable Importance Measure via Adversarial Machine Learning

The quantification and inference of predictive importance for exposure covariates have recently gained significant attention in the context of interpretable machine learning. Contemporary scientific investigations often involve data originating from multiple sources with distributional heterogeneity. It is imperative to introduce a new notation of the variable importance measure that is stable across diverse environments. In this paper, we introduce MIMAL (Multi-source Importance Measure via Adversarial Learning), a novel statistical framework designed to quantify the importance of exposure variables by maximizing the worst-case predictive reward across source mixtures. The proposed framework is adaptable to a broad spectrum of machine learning methodologies for both confounding adjustment and exposure effect characterization. We establish the asymptotic normality of the data-dependent estimator of the multi-source variable importance measure under a general machine learning framework. Our framework requires the similar learning accuracy conditions compared to those required for single-source variable importance analysis. The finite-sample performance of MIMAL is demonstrated through extensive numerical studies encompassing diverse data generation scenarios and machine learning implementations. Furthermore, we illustrate the practical utility of our approach in a real-world case study of air pollution in Beijing, analyzing data collected from multiple locations.

stat.ME↗

arXiv2024

Spectral Deconfounding for High-Dimensional Sparse Additive Models

Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially extends previous work on spectral deconfounding for high-dimensional linear models to the nonlinear setting and with this, establishes a proof of concept that spectral deconfounding is valid for general nonlinear models. Concretely, we propose an algorithm to estimate high-dimensional sparse additive models in the presence of hidden dense confounding: arguably, this is a simple yet practically useful nonlinear scope. We prove consistency and convergence rates for our method and evaluate it on synthetic data and a genetic data set.

stat.ME↗

arXiv2024

Statistical Inference in High-dimensional Poisson Regression with Applications to Mediation Analysis

Large-scale datasets with count outcome variables are widely present in various applications, and the Poisson regression model is among the most popular models for handling count outcomes. This paper considers the high-dimensional sparse Poisson regression model and proposes bias-corrected estimators for both linear and quadratic transformations of high-dimensional regression vectors. We establish the asymptotic normality of the estimators, construct asymptotically valid confidence intervals, and conduct related hypothesis testing. We apply the devised methodology to high-dimensional mediation analysis with count outcome, with particular application of testing for the existence of interaction between the treatment variable and high-dimensional mediators. We demonstrate the proposed methods through extensive simulation studies and application to real-world epigenetic data.

stat.ME↗

arXiv2024

Identification and Inference with Invalid Instruments

Instrumental variables (IVs) are widely used to study the causal effect of an exposure on an outcome in the presence of unmeasured confounding. IVs require an instrument, a variable that is (A1) associated with the exposure, (A2) has no direct effect on the outcome except through the exposure, and (A3) is not related to unmeasured confounders. Unfortunately, finding variables that satisfy conditions (A2) or (A3) can be challenging in practice. This paper reviews works where instruments may not satisfy conditions (A2) or (A3), which we refer to as invalid instruments. We review identification and inference under different violations of (A2) or (A3), specifically under linear models, non-linear models, and heteroskedatic models. We conclude with an empirical comparison of various methods by re-analyzing the effect of body mass index on systolic blood pressure from the UK Biobank.

stat.ME↗

arXiv2024

Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity

Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the nonparametric treatment function, with a primary focus on an additive model that includes high-dimensional covariates. Using the control function approach for identification, we implement a regularized nonparametric estimation to obtain an initial estimator of the model. Such an initial estimator suffers from two biases: the bias in estimating the control function and the regularization bias for the high-dimensional outcome model. Our key innovation is to devise the double bias correction procedure that corrects these two biases simultaneously. Building on this debiased estimator, we further provide a confidence band of the marginal effect function. Simulations and an empirical study of air pollution and migration demonstrate the validity of our procedures.

econ.EM↗

arXiv2024

A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates

This paper proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and instruments to be larger than the sample size. The test is scale-invariant and is robust to heteroskedastic errors. To construct the final test statistic, we first introduce a test based on the maximum norm of multiple parameters that could be high-dimensional. The theoretical power based on the maximum norm is higher than that in the modified Cragg-Donald test (Kolesár, 2018), the only existing test allowing for large-dimensional covariates. Second, following the principle of power enhancement (Fan et al., 2015), we introduce the power-enhanced test, with an asymptotically zero component used to enhance the power to detect some extreme alternatives with many locally invalid instruments. Finally, an empirical example of the trade and economic growth nexus demonstrates the usefulness of the proposed test.

econ.EM↗

arXiv2024

STT: Stateful Tracking with Transformers for Autonomous Driving

Tracking objects in three-dimensional space is critical for autonomous driving. To ensure safety while driving, the tracker must be able to reliably track objects across frames and accurately estimate their states such as velocity and acceleration in the present. Existing works frequently focus on the association task while either neglecting the model performance on state estimation or deploying complex heuristics to predict the states. In this paper, we propose STT, a Stateful Tracking model built with Transformers, that can consistently track objects in the scenes while also predicting their states accurately. STT consumes rich appearance, geometry, and motion signals through long term history of detections and is jointly optimized for both data association and state estimation tasks. Since the standard tracking metrics like MOTA and MOTP do not capture the combined performance of the two tasks in the wider spectrum of object states, we extend them with new metrics called S-MOTA and MOTPS that address this limitation. STT achieves competitive real-time performance on the Waymo Open Dataset.

cs.RO↗