A Deep Latent Variable Framework for Jointly Modeling Missingness, Measurement Error, and Heterogeneity

Missing data, measurement error, and population heterogeneity are pervasive challenges in analyzing data arising from modern observational studies and machine learning applications. Although these problems frequently coexist and interact, they are often treated separately in existing works. We propose a unified probabilistic framework that jointly addresses these issues utilizing deep latent variable representation. The proposed method integrates a novel hierarchical tree-routed variational autoencoder with pattern-aware latent representations and calibration-based denoising. The framework accommodates missing data mechanisms, including MCAR, MAR, and MNAR, while simultaneously learning subgroup-specific and globally shared latent structure. The introduced reconvergent routing mechanism enables selective parameters to be shared across related subpopulations, which offers flexibility as well as improved statistical efficiency. Simulation studies demonstrate substantial improvements over existing deep generative imputation approaches under complex heterogeneous missingness and measurement-error settings. The proposed framework provides a principled approach for learning from noisy and incomplete data in modern healthcare and other high-dimensional applications.

Toward Machine Learning with the Unit as a Primitive: Learning from Unit-Linked Events

Machine learning is usually formalized through samples, while the persistent individual to which multiple observed or possible events refer often remains implicit. We propose the \emph{unit} as an explicit primitive at the level of task semantics. A learning task first declares a population of persistent referents and a sameness criterion; the realized value $u$ denotes the selected referent. Supervised learning is the main formal specialization. Its semantic object is a family of unit-conditioned response laws. Homogeneity is the special case in which those laws coincide; a sample-only conditional is silent as to whether the world is homogeneous or the observed law is only the marginal of a heterogeneous family. What is learned from data is a pair $(T_φ,R_θ)$: a tokenizer that produces a contextual unit token and one shared response-law form that reads it. The structured class takes that form to be a simple relation in the token; a linear predictor is the running instance. The token is the learner-side representation through which the task-side unit affects prediction, while a learner specification that omits unit information is unit-insensitive; homogeneity remains a property of the world-side response family. When identity is unresolved, the world-side law mixes unit-conditioned targets, while the learner composes its shared form with a token. A trusted resolver may fix the unit and supply a lookup token; otherwise \emph{unit abduction} forms a token of the same type from factual evidence. Unlinked single-row observations can fail to distinguish a heterogeneous unit world from a homogeneous pooled world; trusted same-unit pairs separate a restricted witness. The formal results concern this supervised specialization.

Coordination on a Budget: Federated Active Learning with Few Labels

Federated Active Learning (FAL) addresses the dual challenges of data privacy and label scarcity, where the absence of a global data view introduces additional hurdles for coordinated query selection. We study cross-silo FAL in the low-budget regime, where annotation decisions are most critical. We characterize, both theoretically and empirically, a heterogeneity reversal: in low-budget settings, homogeneous (IID) data requires stronger coordination to avoid redundant queries, whereas heterogeneous data naturally promotes diversity; this trend reverses at higher budgets. Thus, in contrast to the standard federated learning (FL) narrative where heterogeneity is a primary challenge, we show that IID settings are more challenging for query selection in FAL. Motivated by these findings, we propose a new FAL framework that utilizes federated representation learning to align client data in a shared embedding space. This enables the server to perform globally coordinated active selection over optionally obfuscated client embeddings, while annotation remains local to each client. Although our framework operates in the more challenging low-budget regime, it achieves performance that surpasses existing FAL methods even when they are given substantially larger annotation budgets, demonstrating the value of centralized coordination under privacy constraints.

UniFed-VLM: Federated Instruction Tuning for Vision-Language Models with Multiple Heterogeneity

Vision-Language Models (VLMs) have demonstrated strong performance in multimodal understanding and generation. However, fine-tuning of VLMs typically relies on centralized data, which raises privacy concerns in certain domains (e.g. healthcare). Federated Learning (FL) provides a natural solution by enabling model training without sharing raw data. However, applying FL to VLM instruction tuning is highly challenging. VLMs have substantial parameter scales, and in real-world scenarios, clients exhibit significant heterogeneity in tasks, modalities, and model architectures. Existing methods mainly focus on simplified settings and are unable to handle such multi-dimensional heterogeneous scenarios. In this work, we study federated instruction tuning under joint heterogeneity in tasks, modalities, and model architectures. We propose UniFed-VLM, a unified federated instruction tuning framework for VLMs that addresses multiple types of heterogeneity. It consists of two key components: 1) Federated Compensated Subspace Aggregation (FedCSA), which performs subspace-aligned aggregation of parameter-efficient adapters with dynamic weighting and compensation to mitigate heterogeneity-induced conflicts; 2) Two-stage Collaborative Distillation (TCoD), which enables effective knowledge transfer across heterogeneous models via a Mutual Distillation Adapter (MDA) and a mixture-of-experts-based distillation strategy. We conduct experiments on multiple benchmark datasets, and the results show that UniFed-VLM achieves stronger average performance across diverse tasks compared with existing FL methods. The source code is available at: https://github.com/wangpengyu2004/UniFed-VLM.

Distinguishing case-mix from context heterogeneity in prognostic regression model synthesis settings

Prognostic regression models often synthesize data from multiple sites, whether within a multi-site study, across federated settings, or in individual participant data meta-analysis. Here, a site is any data source, such as a hospital, registry, trial, or study, and need not be a physical center. Analysts must then decide whether one regression model represents all sites or whether site-specific models are needed. Established measures such as coefficient-level tau^2 quantify heterogeneity but do not distinguish its source. We focus on diagnosing whether coefficient heterogeneity reflects case-mix or site-specific context effects. Case-mix heterogeneity can arise when linear regression terms approximate multivariable non-linear relationships in populations with different covariate distributions. Contextual heterogeneity arises when comparable patients require different regression relationships across sites. We do this by fitting site-specific local regressions in a dimension-reduced space and partitioning the smoothed coefficient surfaces into a cross-site reference and site-specific deviations. An autoencoder and custom loss structure the latent space around local prognostic relationships. We then project this partition onto the outcome scale to derive observation- and site-level summaries. We demonstrate the approach on a COPD trial with two sites. In the three leading latent slope coordinates, coefficient-surface variation was predominantly contextual. The derived observation-level outcome-scale variance partition was case-mix-leading, whereas its between-site aggregation was concentrated in contextual differences rather than case-mix shifts. A permuted-site negative control assesses whether the contextual summary can arise when site labels carry no signal. This diagnostic distinction can inform whether joint or site-specific regression models should be evaluated.

Towards Effective Federated Multimodal Graph Learning via Navigating Multifaceted Heterogeneity

Multimodal-attributed graphs (MAGs), where nodes carry heterogeneous semantic content across multiple modalities while edges encode relational dependencies, have been widely adopted across diverse domains. Federated multimodal graph learning (FMGL) extends federated graph learning (FGL) to MAGs, enabling collaborative optimization across decentralized MAGs without exposing raw data. However, naively applying existing FGL methods to FMGL is insufficient, as they fail to navigate the multifaceted heterogeneity inherent in decentralized MAGs, including task heterogeneity across diverse client objectives, modality heterogeneity from discrepant modality quality and semantic domains, and topology heterogeneity arising from divergent topological patterns with low cross-modality correlation. To address these challenges, we propose Federated multimodal graph learning with Topology-aware Cross-modal Routing (FedTCR), the first systematic algorithm designed for FMGL. To handle task heterogeneity, FedTCR employs a two-stage paradigm that comprises federated task-agnostic pre-training followed by isolated task-oriented fine-tuning. To jointly address modality and topology heterogeneity, FedTCR introduces a topology-aware cross-modal routing mechanism. Concretely, each client distills modality-specific knowledge into compact prototypes via topology-aware importance-weighted aggregation informed by graph structure; the server then evaluates cross-client cross-modal relationships among these structure-informed prototypes and routes informative ones as contrastive references, driving a tri-level cross-modal contrastive learning scheme that jointly aligns cross-client modalities while preserving discrimination. Experiments across 7 domains demonstrate that FedTCR outperforms state-of-the-art baselines on both graph-centric and modality-centric tasks.

Dementia Etiology Diagnosis via Collaborative Meta Knowledge Enhancement

Although artificial intelligence (AI) has shown promising performance in several medical tasks, accurate dementia etiology diagnosis with AI remains challenging due to complex overlapping symptoms among diseases. Scaling up the dataset size by combining the cross-center samples may bring a gain in the pursuit of performance, while the inherent data heterogeneity across centers or populations induces the conflict. Conventional multi-task learning paradigms offer a promising framework; however, they fail to consider critical meta information (e.g., site-specific acquisition and modality availability) to combat the heterogeneity. To address this challenge, we propose a Collaborative Meta Knowledge Enhancement (COME) framework for dementia etiology diagnosis, which injects multi-center acquisition semantics, source identifiers, and modality indicators as heterogeneity-aware embeddings into a unified Transformer architecture for scale-up training, enabling explicit modeling of heterogeneity. Besides, a trust-region constrained optimization scheme is designed to regularize the model from spurious correlations during training through a reference model. Across seven independent cohorts, our method achieves state-of-the-art in-domain performance with a mean macro-averaged AUC of 85.62% and a 4.29-point gain over the strongest baseline, while maintaining superior out-of-domain generalization under both cross-center and cross-sequence evaluations. Extensive validation also confirms the alignment between model predictions and established biomarkers (amyloid, tau) and clinical severity, highlighting the potential of COME to enable robust and interpretable dementia diagnostics in real-world settings.

What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity

Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm. Although Local SGD often outperforms alternatives such as Mini-batch SGD in practice, theory still only partially explains when and why local updates help under realistic data heterogeneity. Recent work by [Patel et al., 2025] shows that a bounded second-order heterogeneity assumption captures the efficiency of Local SGD for strongly convex objectives, and conjectures that the same principle extends to the general convex setting. In this paper, we prove this conjecture by establishing an improved convergence guarantee for Local SGD on general convex objectives under bounded second-order heterogeneity. We also improve the best-known lower bounds for Local SGD in this setting, showing that our upper bounds are nearly tight. Together, these results provide a sharper, more fine-grained convergence theory for Local SGD. As a further application of our techniques, we provide a lower bound for serial SGD with replacement, showing how second-order heterogeneity captures the impact of rare high-curvature clients.

Tabular Foundation Models for Discrete Choice Estimation

Tabular foundation models (TFMs) generate predictions on structured data via in-context learning, without task-specific estimation. We ask whether TFMs can be effectively applied to discrete choice, a central demand estimation framework in marketing and operations, and find that directly applying TFMs yields limited performance. The gap is structural: TFMs assume row-independent observations, whereas discrete choice is inherently set-valued and subject to persistent consumer preference heterogeneity. We propose a reformulation that encodes both choice-set dependence and individual heterogeneity within a row-based learning framework. Evaluated on a yogurt scanner panel, individual-level heterogeneity encoding is the dominant driver of predictive accuracy. The best reformulation outperforms hierarchical Bayesian estimation on both holdout log-likelihood and hit rate, running 16 times faster, a practical advantage for large-scale demand estimation. The advantage is largest in the medium-data regime (10--40 purchase occasions per consumer), where parametric Bayesian shrinkage most distorts estimates for atypical consumers. Fine-tuning on population choice data provides additional gains for consumers with shallow purchase histories, where in-context learning has limited individual-specific signal to condition on. These results establish a principled approach for applying foundation models to consumer choice problems more broadly.

FedSPM: Routing-Enabled Federated Learning under Dual Heterogeneity via Semiparametric Mixture

Routing-prediction federated learning has emerged as a new paradigm that reframes inter-client heterogeneity as a resource for system-level intelligence: at inference time, the server routes each external query to the best-matched client for prediction. Existing approaches, however, typically treat each client as internally homogeneous, overlooking latent subpopulations within local data. For example, patients with the same diagnosis at one hospital may exhibit morphologically distinct disease subtypes. The coexistence of inter-client and intra-client heterogeneity, which we call dual heterogeneity, can impair both routing and prediction. To address this challenge, we propose FedSPM, a routing-enabled semiparametric mixture framework that represents each client using client-specific latent components. Each component combines a predictive distribution for classification with a feature distribution for routing. To flexibly model feature distributions while effectively sharing information across clients, FedSPM models their density ratios relative to a common nonparametric measure estimated via empirical likelihood. We develop a federated expectation-maximization algorithm that optimizes a tractable surrogate and prove convergence of the exact profiled objective at the standard $\mathcal{O}(1/\sqrt{T})$ rate when the surrogate errors are properly controlled. Experiments on controlled benchmarks and real-world medical data demonstrate consistent improvements in routing and prediction under dual heterogeneity. Code is available at https://github.com/zijianwang0510/FedSPM.

HERO: A Heterogeneity-Aware Benchmark Library for Federated Continual Learning

Federated continual learning (FCL) evaluates how distributed clients learn from changing data streams while retaining previously learned knowledge. Existing evaluations are difficult to compare because they often change datasets, task splits, client data splits, task orders, backbones, memory assumptions, and reporting rules simultaneously. We introduce \textbf{HERO}, a heterogeneity-aware benchmark library for FCL. HERO builds benchmark streams by separating three choices that are often coupled, namely the task split, the client data split, and the client task sequence. In HERO-Core, the main comparable benchmark, $α$ controls client data skew and $ρ$ controls task-order mismatch. We evaluate representative FCL methods on CIFAR-100 and TinyImageNet using final average accuracy, average forgetting, and bottom-10\% client accuracy. We also include a graph-based Domain-IL portability case study on OGB-MolPCBA, where scaffold-domain granularity changes the input distribution while the prediction task remains fixed. Our results show that method behavior changes across easy and heterogeneous settings, that average accuracy can hide weak bottom-client performance, that task-order mismatch favors different strategies from synchronized evaluation, and that the same HERO interface can expose domain-shift difficulty beyond image-based FCIL. HERO releases benchmark streams, configurations, method implementations, and reporting scripts to support reproducible and setting-aware FCL evaluation.

Hierarchical Federated Learning with Dynamic Clustering and Adaptive Regularization for Robust Infrastructure Inspection

The deployment of data-driven computer vision models for structural health monitoring (SHM) is heavily constrained by the data silo dilemma due to stringent privacy and security regulations. While federated learning (FL) offers a privacy-preserving collaborative alternative, its application to nationwide infrastructure networks is severely hindered by the challenge of ``double heterogeneity'': macro-level physical divergence across disparate structural types and micro-level statistical imbalances within local datasets. To overcome this challenge, this paper proposes a novel hierarchical federated learning framework. The framework orchestrates a synergistic two-tier optimization strategy. At the macro-level, a dynamic gradient-based clustering mechanism autonomously aggregates distributed clients into specialized expert groups based on their structural degradation trajectories, circumventing the need for prior geographical metadata. Concurrently, at the micro-level, an intra-cluster Dynamic Region-Adaptive Proximal Regularization (DRAPR) module computes a real-time statistical Non-IID Intensity Score for each client. By adaptively modulating a proximal penalty based on local label skewness and gradient divergence, DRAPR effectively calibrates local updates, mitigates client drift, and prevents the catastrophic forgetting of minority damage classes. Comprehensive evaluations on a large-scale, real-world structural inspection dataset demonstrate that the hierarchical integration of macro-clustering and micro-regularization successfully neutralizes dual-level heterogeneity, yielding highly robust and specialized diagnostic models for complex infrastructure inspection.

FedPLT: Scalable, Resource-Efficient, and Heterogeneity-Aware Federated Learning via Partial Layer Training

Federated Learning (FL) has gained significant attention in distributed machine learning by enabling collaborative model training across decentralized system while preserving data privacy. Although extensive research has addressed statistical data heterogeneity, FL still faces several challenges, including high communication and computation overheads and severe device heterogeneity, which require further investigation. Prior work has addressed these issues through sub-model training and partial parameter training. However, such methods often suffer from inconsistent parameter distributions across clients, inaccurate global loss estimation, and increased bias and variance. Guided by our empirical analysis, we propose FedPLT (Federated Learning with Partial Layer Training), an innovative and structured partial parameter training approach that exhibits training behavior similar to full model training while assigning client-specific portions of the model according to their communication and computational capabilities. In addition, we evaluate the performance of FedPLT when combined with optimal client sampling under communication constraints. We show that this integration improves FL performance by reducing sampling variance under the same communication budget. Through extensive experiments, we demonstrate that FedPLT achieves performance comparable to, or even surpassing, that of full-model training (i.e., FedAvg), while requiring significantly fewer trainable parameters per client. Moreover, FedPLT outperforms existing methods in highly heterogeneous environments, effectively adapts to client resource constraints, and reduces the number of straggling clients. In particular, FedPLT reduces the number of trainable parameters by 71%-82% while achieving performance on par with full-model training.