arXiv subjects

Debarghya Mukherjee

Publications and source records attributed to Debarghya Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysis

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.

stat.ME↗

arXiv2026

Self-Distillation is Optimal Among Spectral Shrinkage Estimators in Spiked Covariance Models

Self-distillation has emerged as a promising technique for improving model performance in modern machine learning systems. We develop the statistical foundations of self-distillation in spiked covariance models, by introducing and analyzing a broad class of estimators, namely spectral shrinkage estimators. We establish that for spiked covariance matrices with $s$ spikes, $s$-step self-distillation achieves optimal performance among spectral shrinkage estimators, outperforming well-known estimators in statistics and machine learning. Moreover, we show that $s$ steps are necessary for optimality: any $(s-k)$-step distilled estimator is strictly suboptimal for $1 \leq k \leq s$. For the special subclass of isotropic covariances, we show that optimally tuned Ridge regression performs best among spectral shrinkage estimators. We also study a federated approach where multiple data centers share spectral shrinkage estimators and a common server seeks to aggregate them to achieve optimal performance. In this case, we find that the best local rule again takes the form of self-distillation, though it differs from the optimal rule when data are hosted centrally on a single server. Together, our results elucidate why self-distillation improves predictive performance and provide a broader statistical framework connecting it with classical shrinkage-based methods.

math.ST↗

arXiv2026

Towards General Preference Alignment: Diffusion Models at Nash Equilibrium

Reinforcement learning from human feedback (RLHF) has been popular for aligning text-to-image (T2I) diffusion models with human preferences. As a mainstream branch of RLHF, Direct Preference Optimization (DPO) offers a computationally efficient alternative that avoids explicit reward modeling and has been widely adopted in diffusion alignment. However, existing preference-based methods for diffusion alignment still rely on reward-induced preference signals and typically assume that human preferences can be adequately modeled by the Bradley--Terry (BT) model, which may fail to capture the full complexity of human preferences. In this paper, we formulate diffusion alignment from a game-theoretic perspective. We propose Diffusion Nash Preference Optimization (Diff.-NPO), an intuitive general preference framework for diffusion alignment. Diff.-NPO encourages the current policy to play against itself to achieve self improvement and lead to a better alignment. Empirically, we demonstrate the effectiveness of Diff.-NPO on the text-to-image generation task via various metrics. Diff.-NPO consistently outperforms existing preference-based diffusion alignment methods.

cs.LG↗

arXiv2026

Adaptive Estimation and Inference in Semi-parametric Heterogeneous Clustered Multitask Learning via Neyman Orthogonality

We study clustered multitask learning in a semiparametric setting where tasks share a latent cluster structure in their target parameters but exhibit heterogeneous, potentially infinite-dimensional nuisance components. Such heterogeneity poses a major challenge for existing multitask learning methods, which typically rely on aligned feature spaces or homogeneous task structures. To address this challenge, we propose an adaptive fused orthogonal estimator that integrates Neyman-orthogonal losses with data-driven pairwise fusion penalties. Our framework leverages task-specific pilot estimates to calibrate the fusion penalties and combines adaptive aggregation with orthogonalization to mitigate the impact of nuisance-parameter estimation error. Theoretically, we show that the proposed estimator achieves exact recovery of the latent clustering with high probability and attains pooled parametric convergence rates proportional to cluster size. Moreover, we establish asymptotic normality and show that, asymptotically, our estimator matches the performance of an oracle procedure that knows the true clustering in advance. Empirically, we show that the proposed method consistently outperforms strong baselines in various simulation setups. A real-world application to U.S. residential energy consumption demonstrates the effectiveness of our approach in uncovering meaningful regional clustering in electricity price elasticity, showcasing the efficacy of our method.

stat.ML↗

arXiv2026

Minimax optimal adaptive structured transfer learning through semi-parametric domain-varying coefficient model

Transfer learning aims to improve inference in a target domain by leveraging information from related source domains, but its effectiveness critically depends on how cross-domain heterogeneity is modeled and controlled. When the conditional mechanism linking covariates and responses varies across domains, indiscriminate information pooling can lead to negative transfer, degrading performance relative to target-only estimation. We study a multi-source, single-target transfer learning problem under conditional distributional drift and propose a semiparametric domain-varying coefficient model (DVCM), in which domain-relatedness is encoded through an observable domain identifier. This framework generalizes classical varying-coefficient models to structured transfer learning and interpolates between invariant and fully heterogeneous regimes. Building on this model, we develop an adaptive transfer learning estimator that selectively borrows strength from informative source domains while provably safeguarding against negative transfer. Our estimator is computationally efficient and easy to implement; we also show that it is minimax rate-optimal and derive its asymptotic distribution, enabling valid uncertainty quantification and hypothesis testing despite data-adaptive pooling and shrinkage. Our results precisely characterize the interplay among domain heterogeneity, the smoothness of the underlying mean function, and the number of source domains and are corroborated by comprehensive numerical experiments and two real-data applications.

math.ST↗

arXiv2025

Transfer Learning on Edge Connecting Probability Estimation under Graphon Model

Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

cs.LG↗

arXiv2025

CINDES: Classification induced neural density estimator and simulator

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator that is (i) straightforward to implement and (ii) provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application.

stat.ML↗

arXiv2025

Optimal Nuisance Function Tuning for Estimating a Doubly Robust Functional under Proportional Asymptotics

In this paper, we explore the asymptotically optimal tuning parameter choice in ridge regression for estimating nuisance functions of a statistical functional that has recently gained prominence in conditional independence testing and causal inference. Given a sample of size $n$, we study estimators of the Expected Conditional Covariance (ECC) between variables $Y$ and $A$ given a high-dimensional covariate $X \in \mathbb{R}^p$. Under linear regression models for $Y$ and $A$ on $X$ and the proportional asymptotic regime $p/n \to c \in (0, \infty)$, we evaluate three existing ECC estimators and two sample splitting strategies for estimating the required nuisance functions. Since no consistent estimator of the nuisance functions exists in the proportional asymptotic regime without imposing further structure on the problem, we first derive debiased versions of the ECC estimators that utilize the ridge regression nuisance function estimators. We show that our bias correction strategy yields $\sqrt{n}$-consistent estimators of the ECC across different sample splitting strategies and estimator choices. We then derive the asymptotic variances of these debiased estimators to illustrate the nuanced interplay between the sample splitting strategy, estimator choice, and tuning parameters of the nuisance function estimators for optimally estimating the ECC. Our analysis reveals that prediction-optimal tuning parameters (i.e., those that optimally estimate the nuisance functions) may not lead to the lowest asymptotic variance of the ECC estimator -- thereby demonstrating the need to be careful in selecting tuning parameters based on the final goal of inference. Finally, we verify our theoretical results through extensive numerical experiments.

math.ST↗

arXiv2025

CCFC: Core & Core-Full-Core Dual-Track Defense for LLM Jailbreak Protection

Jailbreak attacks pose a serious challenge to the safe deployment of large language models (LLMs). We introduce CCFC (Core & Core-Full-Core), a dual-track, prompt-level defense framework designed to mitigate LLMs' vulnerabilities from prompt injection and structure-aware jailbreak attacks. CCFC operates by first isolating the semantic core of a user query via few-shot prompting, and then evaluating the query using two complementary tracks: a core-only track to ignore adversarial distractions (e.g., toxic suffixes or prefix injections), and a core-full-core (CFC) track to disrupt the structural patterns exploited by gradient-based or edit-based attacks. The final response is selected based on a safety consistency check across both tracks, ensuring robustness without compromising on response quality. We demonstrate that CCFC cuts attack success rates by 50-75% versus state-of-the-art defenses against strong adversaries (e.g., DeepInception, GCG), without sacrificing fidelity on benign queries. Our method consistently outperforms state-of-the-art prompt-level defenses, offering a practical and effective solution for safer LLM deployment.

cs.CR↗

arXiv2025

Phase Transition in Nonparametric Minimax Rates for Covariate Shifts on Approximate Manifolds

We study nonparametric regression under covariate shift with structured data, where a small amount of labeled target data is supplemented by a large labeled source dataset. In many real-world settings, the covariates in the target domain lie near a low-dimensional manifold within the support of the source, e.g., personalized handwritten digits (target) within a large, high-dimensional image repository (source). Since density ratios may not exist in these settings, standard transfer learning techniques often fail to leverage such structure. This necessitates the development of methods that exploit both the size of the source dataset and the structured nature of the target. Motivated by this, we establish new minimax rates under covariate shift for estimating a regression function in a general H\"older class, assuming the target distribution lies near -- but not exactly on -- a smooth submanifold of the source. General smoothness helps reduce the curse of dimensionality when the target function is highly regular, while approximate manifolds capture realistic, noisy data. We identify a phase transition in the minimax rate of estimation governed by the distance to the manifold, source and target sample sizes, function smoothness, and intrinsic versus ambient dimensions. We propose a local polynomial regression estimator that achieves optimal rates on either side of the phase transition boundary. Additionally, we construct a fully adaptive procedure that adjusts to unknown smoothness and intrinsic dimension, and attains nearly optimal rates. Our results unify and extend key threads in covariate shift, manifold learning, and adaptive nonparametric inference.

math.ST↗

arXiv2025

DRO-Augment Framework: Robustness by Synergizing Wasserstein Distributionally Robust Optimization and Data Augmentation

In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image classification tasks that encounter various input perturbations. While data augmentation techniques have been widely adopted to enhance the resilience of a trained model against such perturbations, there remains significant room for improvement in robustness against corrupted data and adversarial attacks simultaneously. To address this challenge, we introduce DRO-Augment, a novel framework that integrates Wasserstein Distributionally Robust Optimization (W-DRO) with various data augmentation strategies to improve the robustness of the models significantly across a broad spectrum of corruptions. Our method outperforms existing augmentation methods under severe data perturbations and adversarial attack scenarios while maintaining the accuracy on the clean datasets on a range of benchmark datasets, including but not limited to CIFAR-10-C, CIFAR-100-C, MNIST, and Fashion-MNIST. On the theoretical side, we establish novel generalization error bounds for neural networks trained using a computationally efficient, variation-regularized loss function closely related to the W-DRO problem.

stat.ML↗

arXiv2025

Transfer Learning Under High-Dimensional Network Convolutional Regression Model

Transfer learning enhances model performance by utilizing knowledge from related domains, particularly when labeled data is scarce. While existing research addresses transfer learning under various distribution shifts in independent settings, handling dependencies in networked data remains challenging. To address this challenge, we propose a high-dimensional transfer learning framework based on network convolutional regression (NCR), inspired by the success of graph convolutional networks (GCNs). The NCR model incorporates random network structure by allowing each node's response to depend on its features and the aggregated features of its neighbors, capturing local dependencies effectively. Our methodology includes a two-step transfer learning algorithm that addresses domain shift between source and target networks, along with a source detection mechanism to identify informative domains. Theoretically, we analyze the lasso estimator in the context of a random graph based on the Erdos-Renyi model assumption, demonstrating that transfer learning improves convergence rates when informative sources are present. Empirical evaluations, including simulations and a real-world application using Sina Weibo data, demonstrate substantial improvements in prediction accuracy, particularly when labeled data in the target domain is limited.

cs.LG↗

arXiv2025

Estimation and Inference for the Average Treatment Effect in a Score-Explained Heterogeneous Treatment Effect Model

In many practical situations, randomly assigning treatments to subjects is uncommon due to feasibility constraints. For example, economic aid programs and merit-based scholarships are often restricted to those meeting specific income or exam score thresholds. In these scenarios, traditional approaches to estimating treatment effects typically focus solely on observations near the cutoff point, thereby excluding a significant portion of the sample and potentially leading to information loss. Moreover, these methods generally achieve a non-parametric convergence rate. While some approaches, e.g., Mukherjee et al. (2021), attempt to tackle these issues, they commonly assume that treatment effects are constant across individuals, an assumption that is often unrealistic in practice. In this study, we propose a differencing and matching-based estimator of the average treatment effect on the treated (ATT) in the presence of heterogeneous treatment effects, utilizing all available observations. We establish the asymptotic normality of our estimator and illustrate its effectiveness through various synthetic and real data analyses. Additionally, we demonstrate that our method yields non-parametric estimates of the conditional average treatment effect (CATE) and individual treatment effect (ITE) as a byproduct.

stat.ME↗

arXiv2024

Debiased Causal Mediation Analysis in Ultra-High-Dimensional Settings in the Presence of Interaction Effects

Mediation analysis is a crucial tool for uncovering the mechanisms through which a treatment affects an outcome, providing deeper causal insights and guiding effective interventions. Despite substantial advances in mediation analysis with fixed- or low-dimensional mediators and covariates, estimation and inference for mediation functionals remain limited when both mediators and covariates are ultra-high-dimensional. In this paper, we propose an estimator for the mediation functional in a high-dimensional setting that accommodates the treatment--covariate interactions in the mediator model, as well as treatment--covariate and treatment--mediator interactions in the outcome model. As the parameter of interest involves high-dimensional components from different treatment arms and regression equations, existing debiasing approaches are not directly applicable, motivating our multi-step debiasing technique for handling such structurally complex functionals. We establish that the proposed estimator is $\sqrt{n}$-consistent and asymptotically normal, enabling valid inference for natural direct and indirect effects. We evaluate our proposed methodology through extensive simulation studies and apply it to the TCGA lung cancer dataset to estimate the effect of smoking, mediated by DNA methylation, on the survival time of lung cancer patients.

stat.ME↗

arXiv2024

UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

Uncertainty quantification in prediction presents a compelling challenge with vast applications across various domains, including biomedical science, economics, and weather forecasting. There exists a wide array of methods for constructing prediction intervals, such as quantile regression and conformal prediction. However, practitioners often face the challenge of selecting the most suitable method for a specific real-world data problem. In response to this dilemma, we introduce a novel and universally applicable strategy called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). This technique excels in efficiently aggregating multiple prediction intervals while maintaining a small average width of the prediction band and ensuring coverage. UTOPIA is grounded in linear or convex programming, making it straightforward to train and implement. In the specific case where the prediction methods are elementary basis functions, as in kernel and spline bases, our method becomes the construction of a prediction band. Our proposed methodologies are supported by theoretical guarantees on the coverage probability and the average width of the aggregated prediction interval, which are detailed in this paper. The practicality and effectiveness of UTOPIA are further validated through its application to synthetic data and two real-world datasets in finance and macroeconomics.

stat.ME↗

arXiv2024

On the estimation rate of Bayesian PINN for inverse problems

Solving partial differential equations (PDEs) and their inverse problems using Physics-informed neural networks (PINNs) is a rapidly growing approach in the physics and machine learning community. Although several architectures exist for PINNs that work remarkably in practice, our theoretical understanding of their performances is somewhat limited. In this work, we study the behavior of a Bayesian PINN estimator of the solution of a PDE from $n$ independent noisy measurement of the solution. We focus on a class of equations that are linear in their parameters (with unknown coefficients $θ_\star$). We show that when the partial differential equation admits a classical solution (say $u_\star$), differentiable to order $β$, the mean square error of the Bayesian posterior mean is at least of order $n^{-2β/(2β+ d)}$. Furthermore, we establish a convergence rate of the linear coefficients of $θ_\star$ depending on the order of the underlying differential operator. Last but not least, our theoretical results are validated through extensive simulations.

math.ST↗

arXiv2024

Transfer Learning Under High-Dimensional Graph Convolutional Regression Model for Node Classification

Node classification is a fundamental task, but obtaining node classification labels can be challenging and expensive in many real-world scenarios. Transfer learning has emerged as a promising solution to address this challenge by leveraging knowledge from source domains to enhance learning in a target domain. Existing transfer learning methods for node classification primarily focus on integrating Graph Convolutional Networks (GCNs) with various transfer learning techniques. While these approaches have shown promising results, they often suffer from a lack of theoretical guarantees, restrictive conditions, and high sensitivity to hyperparameter choices. To overcome these limitations, we propose a Graph Convolutional Multinomial Logistic Regression (GCR) model and a transfer learning method based on the GCR model, called Trans-GCR. We provide theoretical guarantees of the estimate obtained under GCR model in high-dimensional settings. Moreover, Trans-GCR demonstrates superior empirical performance, has a low computational cost, and requires fewer hyperparameters than existing methods.

stat.ML↗

arXiv2024

Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift

As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating process changes, leading to a deviation in the model's performance. The prediction interval, which captures the range of likely outcomes for a given prediction, serves as a crucial tool for characterizing uncertainties induced by their underlying distribution. In this paper, we propose methodologies for aggregating prediction intervals to obtain one with minimal width and adequate coverage on the target domain under unsupervised domain shift, under which we have labeled samples from a related source domain and unlabeled covariates from the target domain. Our analysis encompasses scenarios where the source and the target domain are related via i) a bounded density ratio, and ii) a measure-preserving transformation. Our proposed methodologies are computationally efficient and easy to implement. Beyond illustrating the performance of our method through real-world datasets, we also delve into the theoretical details. This includes establishing rigorous theoretical guarantees, coupled with finite sample bounds, regarding the coverage and width of our prediction intervals. Our approach excels in practical applications and is underpinned by a solid theoretical framework, ensuring its reliability and effectiveness across diverse contexts.

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