Federated prognostics enable clients (e.g., companies, factories, and production lines) to collaboratively develop a failure time prediction model while keeping each client's data local and confidential. However, traditional federated models often assume homogeneity in the degradation processes across clients, an assumption that may not hold in many industrial settings. To overcome this, this paper proposes a personalized federated prognostic model designed to accommodate clients with heterogeneous degradation processes, allowing them to build tailored prognostic models. The prognostic model iteratively facilitates the underlying pairwise collaborations between clients with similar degradation patterns, which enhances the performance of personalized federated learning. To estimate parameters jointly using decentralized datasets, we develop a federated parameter estimation algorithm based on proximal gradient descent. The proposed approach addresses the limitations of existing federated prognostic models by simultaneously achieving model personalization, preserving data privacy, and providing comprehensive failure time distributions. The superiority of the proposed model is validated through extensive simulation studies and a case study using the turbofan engine degradation dataset from the NASA repository.

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive specialization can induce negative transfer. We formulate adaptive pooling as a statistical decision problem and propose a validation-driven framework that determines when and how specialization should be applied. Rather than grouping series based on representation similarity, we define partitions through out-of-sample predictive performance, thereby aligning data organization with predictive risk, defined as expected out-of-sample loss and approximated via validation error. Cluster assignments are iteratively updated using validation losses for both point (Huber) and probabilistic (pinball) forecasting, improving robustness to heavy-tailed errors and local anomalies. To ensure reliability, we introduce a leakage-free fallback mechanism that reverts to a global model whenever specialization fails to improve validation performance, providing a safeguard against performance degradation under a strict training-validation-test protocol. Experiments on large-scale traffic datasets demonstrate consistent improvements over strong baselines while avoiding degradation when heterogeneity is weak. Overall, the proposed framework provides a principled and practically reliable approach to adaptive pooling in high-dimensional forecasting problems.

Large language models (LLMs) can generate survey responses at low cost, but their reliability varies substantially across questions and is unknown before data collection. Deploying LLMs in surveys still requires costly human responses for verification and correction. How should a limited human-labeling budget be allocated across questions in real time? We propose an adaptive allocation algorithm that learns which questions are hardest for the LLM while simultaneously collecting human responses. Each human label serves a dual role: it improves the estimate for that question and reveals how well the LLM predicts human responses on it. The algorithm directs more budget to questions where the LLM is least reliable, without requiring any prior knowledge of question-level LLM accuracy. We prove that the allocation gap relative to the best possible allocation vanishes as the budget grows, and validate the approach on both synthetic data and a real survey dataset with 68 questions and over 2000 respondents. On real survey data, the standard practice of allocating human labels uniformly across questions wastes 10--12% of the budget relative to the optimal; our algorithm reduces this waste to 2--6%, and the advantage grows as questions become more heterogeneous in LLM prediction quality. The algorithm achieves the same estimation quality as traditional uniform sampling with fewer human samples, requires no pilot study, and is backed by formal performance guarantees validated on real survey data. More broadly, the framework applies whenever scarce human oversight must be allocated across tasks where LLM reliability is unknown.

We study mean estimation of a random vector $X$ in a distributed parameter-server-worker setup. Worker $i$ observes samples of $a_i^\top X$, where $a_i^\top$ is the $i$th row of a known sensing matrix $A$. The key challenges are adversarial measurements and asynchrony: a fixed subset of workers may transmit corrupted measurements, and workers are activated asynchronously--only one is active at any time. In our previous work, we proposed a two-timescale $\ell_1$-minimization algorithm and established asymptotic recovery under a null-space-property-like condition on $A$. In this work, we establish tight non-asymptotic convergence rates under the same null-space-property-like condition. We also identify relaxed conditions on $A$ under which exact recovery may fail but recovery of a projected component of $\mathbb{E}[X]$ remains possible. Overall, our results provide a unified finite-time characterization of robustness, identifiability, and statistical efficiency in distributed linear estimation with adversarial workers, with implications for network tomography and related distributed sensing problems.

We study identification and inference in nonlinear dynamic systems defined on unknown interaction networks. The system evolves through an unobserved dependence matrix governing cross-sectional shock propagation via a nonlinear operator. We show that the network structure is not generically identified, and that identification requires sufficient spectral heterogeneity. In particular, identification arises when the network induces non-exchangeable covariance patterns through heterogeneous amplification of eigenmodes. When the spectrum is concentrated, dependence becomes observationally equivalent to common shocks or scalar heterogeneity, leading to non-identification. We provide necessary and sufficient conditions for identification, characterize observational equivalence classes, and propose a semiparametric estimator with asymptotic theory. We also develop tests for network dependence whose power depends on spectral properties of the interaction matrix. The results apply to a broad class of economic models, including production networks, contagion models, and dynamic interaction systems.

In many modern applications, a carefully designed primary study provides individual-level data for interpretable modeling, while summary-level external information is available through black-box, efficient, and nonparametric machine-learning predictions. Although summary-level external information has been studied in the data integration literature, there is limited methodology for leveraging external nonparametric machine-learning predictions to improve statistical inference in the primary study. We propose a general empirical-likelihood framework that incorporates external predictions through moment constraints. An advantage of nonparametric machine-learning prediction is that it induces a rich class of valid moment restrictions that remain robust to covariate shift under a mild overlap condition without requiring explicit density-ratio modeling. We focus on multinomial logistic regression as the primary model and address common data-quality issues in external sources, including coarsened outcomes, partially observed covariates, covariate shift, and heterogeneity in generating mechanisms known as concept shift. We establish large-sample properties of the resulting fused estimator, including consistency and asymptotic normality under regularity conditions. Moreover, we provide mild sufficient conditions under which incorporating external predictions delivers a strict efficiency gain relative to the primary-only estimator. Simulation studies and an application to the National Health and Nutrition Examination Survey on multiclass blood-pressure classification.

In recent years, there has been growing interest in causal machine learning estimators for quantifying subject-specific effects of a binary treatment on time-to-event outcomes. Estimation approaches have been proposed which attenuate the inherent regularisation bias in machine learning predictions, with each of these estimators addressing measured confounding, right censoring, and in some cases, left truncation. However, the existing approaches are found to exhibit suboptimal finite-sample performance, with none of the existing estimators fully leveraging the temporal structure of the data, yielding non-smooth treatment effects over time. We address these limitations by introducing surv-iTMLE, a targeted learning procedure for estimating the difference in the conditional survival probabilities under two treatments. Unlike existing estimators, surv-iTMLE accommodates both left truncation and right censoring while enforcing smoothness and boundedness of the estimated treatment effect curve over time. Through extensive simulation studies under both right censoring and left truncation scenarios, we demonstrate that surv-iTMLE outperforms existing methods in terms of bias and smoothness of time-varying effect estimates in finite samples. We then illustrate surv-iTMLE's practical utility by exploring heterogeneity in the effects of immunotherapy on survival among non-small cell lung cancer (NSCLC) patients, revealing clinically meaningful temporal patterns that existing estimators may obscure.

We propose a novel class of network models for temporal dyadic interaction data. Our objective is to capture important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We use mutually-exciting Hawkes processes to model the interactions between each (directed) pair of individuals. The intensity of each process allows interactions to arise as responses to opposite interactions (reciprocity), or due to shared interests between individuals (community structure). For sparsity and degree heterogeneity, we build the non time dependent part of the intensity function on compound random measures following Todeschini et al., 2016. We conduct experiments on real-world temporal interaction data and show that the proposed model outperforms competing approaches for link prediction, and leads to interpretable parameters.

Thisworkdiscusses howtoachieveworst-case Out-Of-Distribution(OOD) generalization for avariety of distributions based on arelatively small labeling cost.

It is regarded as a promising distributed and privacy-preserving method.