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This paper investigates the accuracy of generative models and the impact of knowledge transfer on their generation precision. Specifically, we examine a generative model for a target task, fine-tuned using a pre-trained model from a source task. Building on the "Shared Embedding" concept, which bridges the source and target tasks, we introduce a novel framework for transfer learning under distribution metrics such as the Kullback-Leibler divergence. This framework underscores the importance of leveraging inherent similarities between diverse tasks despite their distinct data distributions. Our theory suggests that the shared structures can augment the generation accuracy for a target task, reliant on the capability of a source model to identify shared structures and effective knowledge transfer from source to target learning. To demonstrate the practical utility of this framework, we explore the theoretical implications for two specific generative models: diffusion and normalizing flows. The results show enhanced performance in both models over their non-transfer counterparts, indicating advancements for diffusion models and providing fresh insights into normalizing flows in transfer and non-transfer settings. These results highlight the significant contribution of knowledge transfer in boosting the generation capabilities of these models. 

Accurate uncertainty quantification is crucial for making reliable decisions in various supervised learning scenarios, particularly when dealing with complex, multimodal data such as images and text. Current approaches often face notable limitations, including rigid assumptions and limited generalizability, constraining their effectiveness across diverse supervised learning tasks. To overcome these limitations, we introduce Generative Score Inference (GSI), a flexible inference framework capable of constructing statistically valid and informative prediction and confidence sets across a wide range of multimodal learning problems. GSI utilizes synthetic samples generated by deep generative models to approximate conditional score distributions, facilitating precise uncertainty quantification without imposing restrictive assumptions about the data or tasks. We empirically validate GSI’s capabilities through two representative scenarios: hallucination detection in large language models and uncertainty estimation in image captioning. Our method achieves state-of-the-art performance in hallucination detection and robust predictive uncertainty in image captioning, and its performance is positively influenced by the quality of the underlying generative model. These findings underscore the potential of GSI as a versatile inference framework, significantly enhancing uncertainty quantification and trustworthiness in multimodal learning. 

Reliable causal inference is essential for making decisions in high-stakes areas like medicine, economics, and public policy. However, it remains unclear whether large language models (LLMs) can handle rigorous and trustworthy statistical causal inference. Current benchmarks usually involve simplified tasks. For example, these tasks might only ask LLMs to identify semantic causal relationships or draw conclusions directly from raw data. As a result, models may overlook important statistical pitfalls, such as Simpson’s paradox or selection bias. This oversight limits the applicability of LLMs in the real world. To address these limitations, we propose CausalPitfalls, a comprehensive benchmark designed to rigorously evaluate the capability of LLMs in overcoming common causal inference pitfalls. Our benchmark features structured challenges across multiple difficulty levels, each paired with grading rubrics. This approach allows us to quantitatively measure both causal reasoning capabilities and the reliability of LLMs’ responses. We evaluate models using two protocols: (1) direct prompting, which assesses intrinsic causal reasoning, and (2) code-assisted prompting, where models generate executable code for statistical analysis. Additionally, we validate the effectiveness of this judge by comparing its scoring with assessments from human experts. Our results reveal significant limitations in current LLMs when performing statistical causal inference. The CausalPitfalls benchmark provides essential guidance and quantitative metrics to advance the development of trustworthy causal reasoning systems. Our code is publicly available at CausalPitfalls. 

Not AvailableReliable machine learning and statistical analysis rely on diverse, well-distributed training data. However, real-world datasets are often limited in size and exhibit underrepresentation across key subpopulations, leading to biased predictions and reduced performance, particularly in supervised tasks such as classification. To address these challenges, we propose Conditional Data Synthesis Augmentation (CoDSA), a novel framework that leverages generative models, such as diffusion models, to synthesize high-fidelity data for improving model performance across multimodal domains, including tabular, textual, and image data. CoDSA generates synthetic samples that faithfully capture the conditional distributions of the original data, with a focus on under-sampled or high-interest regions. Through transfer learning, CoDSA fine-tunes pre-trained generative models to enhance the realism of synthetic data and increase sample density in sparse areas. This process preserves inter-modal relationships, mitigates data imbalance, improves domain adaptation, and boosts generalization. We also introduce a theoretical framework that quantifies the statistical accuracy improvements enabled by CoDSA as a function of synthetic sample volume and targeted region allocation, providing formal guarantees of its effectiveness. Extensive experiments demonstrate that CoDSA consistently outperforms non-adaptive augmentation strategies and state-of-the-art baselines in both supervised and unsupervised settings. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. 

Atrial fibrillation (AF), a cardiac arrhythmia characterized by an abnormal and rapid heartbeat, has the potential to develop into stroke, heart failure, and, ultimately, mortality. The electrocardiogram (ECG) is a pivotal tool in the diagnosis of AF, offering a quick, cost‐effective, and non‐invasive mean to record the heart's electrical activity. Recent studies are increasingly engaged in the implementation of deep learning techniques for ECG feature extraction for AF prediction. In addition, the application of Mendelian randomization (MR) methodologies has been investigated to identify causal associations between genetically imputed pre‐defined ECG characteristics and cardiovascular diseases, such as AF. DeepFEIVR, a non‐linear extension of the classical instrumental variable (IV) regression model, was designed with the objective of extracting disease‐associated causal features from high‐dimensional data, such as neuroimaging data. In this article, we applied DeepFEIVR as well as its variant (with residual inclusion), DeepFEIVR‐RI, to the large UK Biobank dataset. The application of DeepFEIVR and DeepFEIVR‐RI showed that the genetic components in ECGs could contribute to the development of AF statistically significantly (pvalues < ). Another contribution of this article is an extension to both DeepFEIVR and DeepFEIVR‐RI to accommodate a large number of IVs. A comparison of results from DeepFEIVR and DeepFEIVR‐RI, based on various choices of IVs, was conducted. Furthermore, we applied a recent algorithm called dnn‐loc, enabling a visual examination on specific ECG components as extracted causal features for AF, thus advancing the understanding of the etiology of AF. 

Not AvailableThis paper addresses critical data-sharing issues encountered when disseminating individual-level data across multiple sites, particularly under stringent privacy constraints and site heterogeneity. In many multi-site clinical trials, for example, privacy concerns restrict sharing to site-specific summary statistics rather than raw data, complicating the analysis of global effects relative to individual or site-specific effects. Our contribution offers a robust distributed framework for high-dimensional, heterogeneous data analysis that overcomes these limitations. We develop a heterogeneous model that integrates both global and sitespecific effects, employing nonconvex regularization via difference of convex programming under an ℓ0 constraint to ensure selection consistency. Although the underlying optimization problem is worst-case NP-hard, our method converges to the global minimizer in polynomial time with high probability under realistic conditions. Moreover, by applying ℓ0 penalization exclusively to nuisance parameters while leaving hypothesized parameters unpenalized, our approach yields valid statistical inference. This work not only advances methodological research but also directly addresses the challenges of data sharing in distributed data environments.