Papers

Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient alternative, but their development is hindered by the cost of generating sufficient training data from numerical solvers. In this paper, we present a novel framework for active learning in PDE surrogate modeling that reduces this cost. Unlike the existing AL methods for PDEs that always acquire entire PDE trajectories, our approach, STAP (**S**elective **T**ime-Step **A**cquisition for **P**DEs), strategically generates only the most important time steps with the numerical solver, while employing the surrogate model to approximate the remaining steps. This reduces the cost incurred by each trajectory and thus allows the active learning algorithm to try out a more diverse set of trajectories given the same budget. To accommodate this novel framework, we develop an acquisition function that estimates the utility of a set of time steps by approximating its resulting variance reduction. We demonstrate the effectiveness of our method on several benchmark PDEs.

We develop a convex framework for spatially varying coefficient quantile regression that, for each predictor, separates a location-invariant global effect from a spatial deviation. An adaptive group penalty selects whether a predictor varies over space, while a graph\textendash Laplacian quadratic promotes spatial continuity of the deviations on irregular networks. The formulation is identifiable via degree-weighted centering and scales with sparse linear algebra. We provide two practical solvers\textemdash an ADMM algorithm with closed-form proximal maps for the check loss and a smoothed proximal-gradient scheme based on the Moreau envelope\textemdash together with implementation guidance (projection for identifiability, stopping diagnostics, and preconditioning). Under mild conditions on the sampling design, covariates, error density, and graph geometry, we establish selection consistency for the deviation groups, mean-squared error bounds that balance Laplacian bias and stochastic variability, and root-\(n\) asymptotic normality for the global coefficients with an oracle property. Simulations mimicking air-pollution applications demonstrate accurate recovery of global vs.\ local effects and competitive predictive performance under heteroskedastic, heavy-tailed noise. We discuss graph construction, spatially blocked cross-validation (to prevent leakage), and options for robust standard errors under spatial dependence.

Background: Non-inferiority studies based on non-randomised data are increasingly used in clinical research but remain prone to unmeasured confounding. The classical E-value offers a simple way to quantify such bias but has been applied almost exclusively with respect to the statistical null. We reformulated the E-value framework to make explicit its applicability to predefined clinical margins, thereby extending its utility to non-inferiority analyses. Development: Using the bias-factor formulation by Ding and VanderWeele, we defined the non-inferiority E-value as the minimum strength of association that an unmeasured confounder would need with both treatment and outcome, on the risk-ratio scale, to move the 95% confidence-limit estimate to the prespecified non-inferiority margin. Application: This approach was applied to three observational studies and one single-arm trial with external controls to illustrate interpretation and range. The resulting non-inferiority E-values for the confidence limits varied from about one to three, depending on design and findings. In the single-arm trial, a large gap between the confidence-limit and point-estimate NIEs reflected small sample size and wide confidence intervals, highlighting that both should be reported for a balanced assessment of robustness. Conclusion: This study reformulates the E-value to focus on clinically meaningful margins rather than the statistical null, enabling its application to non-inferiority analyses. Although the non-inferiority E-value inherits the limitations of the original method and cannot address all bias sources, it offers a transparent framework for interpreting non-randomised evidence and for generating insights that inform the design of future, more definitive randomised controlled trials.

Out-of-Bag (OOB) estimation is the standard internal diagnostic for bootstrap-aggregated tree ensembles. Under the classical multinomial bootstrap, the number of distinct training observations in each replicate, $U_b$, is itself random, but its contribution to OOB-based variability has rarely been isolated empirically. We use Sequential Bootstrap (SB) – a resampling scheme that holds $U_b$ at a fixed target $k_n = \lfloor 0.632 n\rfloor$ – as a controlled perturbation of the bootstrap mechanism, and ask whether stabilizing $U_b$ produces any measurable change in OOB-based diagnostics. We reproduce Breiman's five OOB experimental families on twelve synthetic and real datasets, but unlike the three-seed presentation common in this literature, we run 100 independent random seeds with 50 internal replications per seed, enabling formal paired statistical comparison (Wilcoxon signed-rank, paired-$t$, Pitman–Morgan variance test). We report three findings. First, OOB means are essentially insensitive to stabilization of $U_b$: of 57 (experiment, dataset, metric) cells under 100 seeds, only 6 reach $p<0.05$ on the paired mean comparison, and 4 of those 6 point in the opposite direction from what a 3-seed reading would suggest. Second, a narrow but reproducible effect survives at the variance level: SB reduces the cross-seed standard deviation of node-level classification diagnostics on real datasets while slightly increasing it on synthetic ones (permutation $p=0.026$); the Vehicle dataset exhibits a 21% cross-seed sd reduction (Pitman–Morgan $p=0.017$). Third, several directional claims that appear stable across three seeds flip sign under 100-seed replication, illustrating the cost of underpowered replication protocols. We therefore treat SB as a diagnostic tool for probing the distinct-sample-count term in the variance of OOB estimators, not as an alternative to the classical bootstrap.

Wasserstein-Fisher-Rao (WFR) gradient flows have been recently proposed as a powerful sampling tool that combines the advantages of pure Wasserstein (W) and pure Fisher-Rao (FR) gradient flows. Existing algorithmic developments implicitly make use of operator splitting techniques to numerically approximate the WFR partial differential equation, whereby the W flow is evaluated over a given step size and then the FR flow (or vice versa). This works investigates the impact of the order in which the W and FR operator are evaluated and aims to provide a quantitative analysis. Somewhat surprisingly, we show that with a judicious choice of step size and operator ordering, the split scheme can converge to the target distribution faster than the exact WFR flow (in terms of model time). We obtain variational formulae describing the evolution over one time step of both splitting schemes and investigate in which settings the W-FR split should be preferred to the FR-W split. As a step towards this goal we show that the WFR gradient flow preserves log-concavity and obtain the first sharp decay bound for WFR flow.

Hierarchical clustering seeks to uncover nested structures in data by constructing a tree of clusters, where deeper levels reveal finer-grained relationships. Traditional methods, including linkage approaches, face three major limitations: (i) they always return a hierarchy, even if none exists, (ii) they are restricted to binary trees, even if the true hierarchy is non-binary, and (iii) they are highly sensitive to the choice of linkage function. In this paper, we address these issues by introducing the notion of a valid hierarchy and defining a partial order over the set of valid hierarchies. We prove the existence of a finest valid hierarchy, that is, the hierarchy that encodes the maximum information consistent with the similarity structure of the data set. In particular, the finest valid hierarchy is not constrained to binary structures and, when no hierarchical relationships exist, collapses to a star tree. We propose a simple two-step algorithm that first constructs a binary tree via a linkage method and then prunes it to enforce validity. We establish necessary and sufficient conditions on the linkage function under which this procedure exactly recovers the finest valid hierarchy, and we show that all linkage functions satisfying these conditions yield the same hierarchy after pruning. Notably, classical linkage rules such as single, complete, and average satisfy these conditions, whereas Ward's linkage fails to do so.

This paper presents a real time, data driven decision support framework for epidemic control. We combine a compartmental epidemic model with sequential Bayesian inference and reinforcement learning (RL) controllers that adaptively choose intervention levels to balance disease burden, such as intensive care unit (ICU) load, against socio economic costs. We construct a context specific cost function using empirical experiments and expert feedback. We study two RL policies: an ICU threshold rule computed via Monte Carlo grid search, and a policy based on a posterior averaged Q learning agent. We validate the framework by fitting the epidemic model to publicly available ICU occupancy data from the COVID 19 pandemic in England and then generating counterfactual roll out scenarios under each RL controller, which allows us to compare the RL policies to the historical government strategy. Over a 300 day period and for a range of cost parameters, both controllers substantially reduce ICU burden relative to the observed interventions, illustrating how Bayesian sequential learning combined with RL can support the design of epidemic control policies.

Many biomarker pipelines require patient-level decisions aggregated from instance-level (cell/patch) scores. Thresholds tuned on pooled instances often fail across sites due to hierarchical dependence, prevalence shift, and score-scale mismatch. We present a selection-honest framework for hierarchical thresholding that makes patient-level decisions reproducible and more defensible. At its core is a risk decomposition theorem for selection-honest thresholds. The theorem separates contributions from (i) internal fit and patient-level generalization, (ii) operating-point shift reflecting prevalence and shape changes, and (iii) a stability term that penalizes sensitivity to threshold perturbations. The stability component is computable via patient-block bootstraps mapped through a monotone modulus of risk. This framework is model-agnostic, reconciles heterogeneous decision rules on a quantile scale, and yields monotone-invariant ensembles and reportable diagnostics (e.g. flip-rate, operating-point shift).

We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training.

Clustering in stationary and nonstationary settings, where data distributions remain static or evolve over time, requires models that can adapt to distributional shifts while preserving previously learned cluster structures. This paper proposes an Adaptive Resonance Theory (ART)-based topological clustering algorithm that autonomously adjusts its recalculation interval and vigilance threshold through a diversity-driven adaptation mechanism. This mechanism enables hyperparameter-free learning that maintains cluster stability and continuity in dynamic environments. Experiments on 24 real-world datasets demonstrate that the proposed algorithm outperforms state-of-the-art methods in both clustering performance and continual learning capability. These results highlight the effectiveness of the proposed parameter adaptation in mitigating catastrophic forgetting and maintaining consistent clustering in evolving data streams. Source code is available at https://github.com/Masuyama-lab/IDAT

We develop a divergence-minimization (DM) framework for robust and efficient inference in latent-mixture models. By optimizing a residual-adjusted divergence, the DM approach recovers EM as a special case and yields robust alternatives through different divergence choices. We establish that the sample objective decreases monotonically along the iterates, leading the DM sequence to stationary points under standard conditions, and that at the population level the operator exhibits local contractivity near the minimizer. Additionally, we verify consistency and $\sqrt{n}$-asymptotic normality of minimum-divergence estimators and of finitely many DM iterations, showing that under correct specification their limiting covariance matches the Fisher information. Robustness is analyzed via the residual-adjustment function, yielding bounded influence functions and a strictly positive breakdown bound for bounded-RAF divergences, and we contrast this with the non-robust behaviour of KL/EM. Next, we address the challenge of determining the number of mixture components by proposing a penalized divergence criterion combined with repeated sample splitting, which delivers consistent order selection and valid post-selection inference. Empirically, DM instantiations based on Hellinger and negative exponential divergences deliver accurate inference and remain stable under contamination in mixture and image-segmentation tasks. The results clarify connections to MM and proximal-point methods and offer practical defaults, making DM a drop-in alternative to EM for robust latent-structure inference.

Intelligent agents equipped with causal knowledge can optimize their action spaces to avoid unnecessary exploration. The structural causal bandit framework provides a graphical characterization for identifying actions that are unable to maximize rewards by leveraging prior knowledge of the underlying causal structure. While such knowledge enables an agent to estimate the expected rewards of certain actions based on others in online interactions, there has been little guidance on how to transfer information inferred from arbitrary combinations of datasets collected under different conditions – observational or experimental – and from heterogeneous environments. In this paper, we investigate the structural causal bandit with transportability, where priors from the source environments are fused to enhance learning in the deployment setting. We demonstrate that it is possible to exploit invariances across environments to consistently improve learning. The resulting bandit algorithm achieves a sub-linear regret bound with an explicit dependence on informativeness of prior data, and it may outperform standard bandit approaches that rely solely on online learning.

We investigate the asymptotic properties of the minimum $L_1$-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process driven by a Hermite process.

A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact asymptotic distribution of the changepoint existence test statistic gauging whether or not a second segment is necessary. The identified asymptotic distribution, a supremum of a Gaussian process over the unit interval, is rather unwieldy. The work presented here provides the result and its derivation; quantiles of the asymptotic distribution are presented for the user. This addresses a subtle gap in the changepoint literature.

Many deployed learning systems must update models on streaming data under memory constraints. The default strategy, sequential fine-tuning on each new phase, is architecture-agnostic but often suffers catastrophic forgetting when later phases correspond to different sub-populations or tasks. Replay with a finite buffer is a simple alternative, yet its behaviour across generative and predictive objectives is not well understood. We present a unified study of stateful replay for streaming autoencoding, time series forecasting, and classification. We view both sequential fine-tuning and replay as stochastic gradient methods for an ideal joint objective, and use a gradient alignment analysis to show when mixing current and historical samples should reduce forgetting. We then evaluate a single replay mechanism on six streaming scenarios built from Rotated MNIST, ElectricityLoadDiagrams 2011-2014, and Airlines delay data, using matched training budgets and three seeds. On heterogeneous multi task streams, replay reduces average forgetting by a factor of two to three, while on benign time based streams both methods perform similarly. These results position stateful replay as a strong and simple baseline for continual learning in streaming environments.

This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit theorems in network statistics and econometrics, which are based on weak dependence concepts such as strong mixing, near-epoch dependence, or $\psi$-dependence. All these weak dependence concepts presuppose an underlying metric. By relaxing the assumption of an underlying metric space, our theorems can be applied to a broader range of network data, including financial and social networks. To derive the limit theorems, we generalize the concept of functional dependence (also known as physical dependence) from time series to random variables with network dependence. Using this framework, we establish several inequalities, a law of large numbers, and central limit theorems. Furthermore, we demonstrate the verifiability of our high-level conditions by deriving primitive sufficient conditions for spatial autoregressive models, which are widely used in network data analysis.

Doubly robust estimators (DRE) are widely used in causal inference because they yield consistent estimators of average causal effect when at least one of the nuisance models, the propensity for treatment (exposure) or the outcome regression, is correct. However, double robustness does not extend to variance estimation; the influence-function (IF)-based variance estimator is consistent only when both nuisance parameters are correct. This raises concerns about applying DRE in practice, where model misspecification is inevitable. The recent paper by Shook-Sa et al. (2025, Biometrics, 81(2), ujaf054) demonstrated through Monte Carlo simulations that the IF-based variance estimator is biased. However, the paper's findings are empirical. The key question remains: why does the variance estimator fail in double robustness, and under what conditions do alternatives succeed, such as the ones demonstrated in Shook-Sa et al. 2025. In this paper, we develop a formal theory to clarify the efficiency properties of DRE that underlie these empirical findings. We also introduce alternative strategies, including a mixture-based framework underlying the sample-splitting and crossfitting approaches, to achieve valid inference with misspecified nuisance parameters. Our considerations are illustrated with simulation and real study data.

Distributed Fiber Optic Sensing (DFOS) has emerged as a promising technology for long-range and real-time perimeter security in critical infrastructure monitoring. However, DFOS signals collected from different field deployments often exhibit substantial distribution shifts caused by variations in fiber installation, structural coupling, and environmental noise. These deployment-dependent changes make reliable event recognition difficult in practical perimeter security systems, especially when labeled samples from new target sites are scarce or unavailable. To address these challenges, this paper proposes DUPLE, an intelligent cross-deployment recognition framework for fiber-optic perimeter security under label-scarce target deployments. DUPLE employs statistically guided meta-learning to enhance recognition robustness across unseen deployments. Specifically, a dual-domain multi-prototype learner jointly models temporal and frequency-domain evidence to capture intra-class variability under deployment shifts. A statistical guidance network estimates sample-specific domain reliability from raw signal statistics, while a query-aware aggregation mechanism adaptively selects relevant prototypes for each test sample. Extensive experiments on two real-world cross-deployment DFOS benchmarks demonstrate that DUPLE consistently outperforms representative traditional machine learning, deep learning, domain generalization, and meta-learning baselines. Ablation, few-shot, per-deployment, and efficiency analyses further verify the effectiveness and practicality of DUPLE for reliable DFOS-based perimeter security monitoring.

We develop an arbitrage-free deep learning framework for yield curve and bond price forecasting based on the Heath-Jarrow-Morton (HJM) term-structure model and a dynamic Nelson-Siegel parameterization of forward rates. Our approach embeds a no-arbitrage drift restriction into a neural state-space architecture by combining Kalman, extended Kalman, and particle filters with recurrent neural networks (LSTM/CLSTM), and introduces an explicit arbitrage error regularization (AER) term during training. The model is applied to U.S. Treasury and corporate bond data, and its performance is evaluated for both yield-space and price-space predictions at 1-day and 5-day horizons. Empirically, arbitrage regularization leads to its strongest improvements at short maturities, particularly in 5-day-ahead forecasts, increasing market-consistency as measured by bid-ask hit rates and reducing dollar-denominated prediction errors.

Single changepoint tests have become a staple check for homogeneity of a climate time series, suggesting how climate has changed should non-homogeneity be declared. This paper summarizes the most prominent single changepoint tests used in today's climate literature, relating them to one and other and unifying their presentations. Asymptotic quantiles for the individual tests are presented. Derivations of the quantiles are given, enabling the reader to tackle cases not considered within. Our work here studies both mean and trend shifts, covering the most common settings arising in climatology. SOI and global temperature series are analyzed within to illustrate the techniques.

Conformal prediction (CP) is a general framework to quantify the predictive uncertainty of machine learning models that uses a set prediction to include the true label with a valid probability. To align the uncertainty measured by CP, conformal training methods minimize the size of the prediction sets. A typical way is to use a surrogate indicator function, usually Sigmoid or Gaussian error function. However, these surrogate functions do not have a uniform error bound to the indicator function, leading to uncontrollable learning bounds. In this paper, we propose a simple cost-sensitive conformal training algorithm that does not rely on the indicator approximation mechanism. Specifically, we theoretically show that minimizing the expected size of prediction sets is upper bounded by the expected rank of true labels. To this end, we develop a rank weighting strategy that assigns the weight using the rank of true label on each data sample. Our analysis provably demonstrates the tightness between the proposed weighted objective and the expected size of conformal prediction sets. Extensive experiments verify the validity of our theoretical insights, and superior empirical performance over other conformal training in terms of predictive efficiency with 21.38% reduction for average prediction set size.

Transformers can acquire Chain-of-Thought (CoT) capabilities to solve reasoning tasks via fine-tuning. Reinforcement learning (RL) and supervised fine-tuning (SFT) are two primary approaches to this end. In this work, we examine RL with verifiable process rewards and SFT for learning $k$-sparse Boolean functions with a one-layer transformer through intermediate reasoning steps akin to CoT. In particular, we consider Boolean functions that can be recursively decomposed into fixed 2-sparse Boolean functions. We first analyze the learning dynamics of RL fine-tuning with verifiable process rewards and SFT in a unified way, allowing us to identify sufficient conditions under which the transformer provably learns these functions. We then verify that the conditions hold for three examples, including $k$-PARITY, $k$-AND, and $k$-OR, thus demonstrating their learnability via both RL and SFT. Notably, we reveal that RL and SFT exhibit distinct learning behaviors depending on supervision: RL learns the whole CoT chain simultaneously, whereas SFT without teacher forcing learns the CoT step-by-step. Overall, our findings provide insights on the mechanisms underlying RL and SFT and how they differ in triggering the CoT capabilities of transformers, and suggest that the comparison between RL and SFT should consider the intermediate supervision.

Interpretable topic modeling is essential for tracking how research interests evolve within co-author communities. In scientific corpora, where novelty is prized, identifying underrepresented niche topics is particularly important. However, contemporary models built from dense transformer embeddings tend to miss rare topics and therefore also fail to capture smooth temporal alignment. We propose a geometric method that integrates multimodal text and co-author network data, using Hellinger distances and Ward's linkage to construct a hierarchical topic dendrogram. This approach captures both local and global structure, supporting multiscale learning across semantic and temporal dimensions. Our method effectively identifies rare-topic structure and visualizes smooth topic drift over time. Experiments highlight the strength of interpretable bag-of-words models when paired with principled geometric alignment.

Deterministic inference is increasingly critical for large language model (LLM) applications such as LLM-as-a-judge evaluation, multi-agent systems, and Reinforcement Learning (RL). However, existing LLM serving frameworks exhibit non-deterministic behavior: identical inputs can yield different outputs when system configurations (e.g., tensor parallel (TP) size, batch size) vary, even under greedy decoding. This arises from the non-associativity of floating-point arithmetic and inconsistent reduction orders across GPUs. While prior work has addressed batch-size-related nondeterminism through batch-invariant kernels, determinism across different TP sizes remains an open problem, particularly in RL settings, where the training engine typically uses Fully Sharded Data Parallel (i.e., TP = 1) while the rollout engine relies on multi-GPU TP to maximize the inference throughput, creating a natural mismatch between the two. This precision mismatch problem may lead to suboptimal performance or even collapse for RL training. We identify and analyze the root causes of TP-induced inconsistency and propose Tree-Based Invariant Kernels (TBIK), a set of TP-invariant matrix multiplication and reduction primitives that guarantee bit-wise identical results regardless of TP size. Our key insight is to align intra- and inter-GPU reduction orders through a unified hierarchical binary tree structure. We implement these kernels in Triton and integrate them into vLLM and FSDP. Experiments confirm zero probability divergence and bit-wise reproducibility for deterministic inference across different TP sizes. Also, we achieve bit-wise identical results between vLLM and FSDP in RL training pipelines with different parallel strategy. Code is available at https://github.com/nanomaoli/llm_reproducibility.

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper explores a novel approach to k-means clustering. Here we present a k-means clustering algorithm that takes both the within cluster distance (WCD) and the inter cluster distance (ICD) as the distance metric to cluster the data into k clusters pre-determined by the Calinski-Harabasz criterion in order to provide a more robust output for the clustering analysis. The idea with this approach is that by including both the measurement metrics, the convergence of the data into their clusters becomes solidified and more robust. We run the algorithm with some synthetically produced data and also some benchmark data sets obtained from the UCI repository. The results show that the convergence of the data into their respective clusters is more accurate by using both WCD and ICD measurement metrics. The algorithm is also better at clustering the outliers into their true clusters as opposed to the traditional k means method. We also address some interesting possible research topics that reveal themselves as we answer the questions we initially set out to address.

In list-decodable learning, we are given a set of data points such that an $\alpha$-fraction of these points come from a nice distribution $D$, for some small $\alpha \ll 1$, and the goal is to output a short list of candidate solutions, such that at least one element of this list recovers some non-trivial information about $D$. By now, there is a large body of work on this topic; however, while many algorithms can achieve optimal list size in terms of $\alpha$, all known algorithms must incur error which decays, in some cases quite poorly, with $1 / \alpha$. In this paper, we ask if this is inherent: is it possible to trade off list size with accuracy in list-decodable learning? More formally, given $\epsilon > 0$, can we can output a slightly larger list in terms of $\alpha$ and $\epsilon$, but so that one element of this list has error at most $\epsilon$ with the ground truth? We call this problem high-accuracy list-decodable learning. Our main result is that non-trivial high-accuracy guarantees, both information-theoretically and algorithmically, are possible for the canonical setting of list-decodable mean estimation of identity-covariance Gaussians. Specifically, we demonstrate that there exists a list of candidate means of size at most $L = \exp \left( O\left( \tfrac{\log^2 1 / \alpha}{\epsilon^2} \right)\right)$ so that one of the elements of this list has $\ell_2$ distance at most $\epsilon$ to the true mean. We also design an algorithm that outputs such a list with runtime and sample complexity $n = d^{O(\log L)} + \exp \exp (\widetilde{O}(\log L))$. We do so by demonstrating a completely novel proof of identifiability, as well as a new algorithmic way of leveraging this proof without the sum-of-squares hierarchy, which may be of independent technical interest.

Wastewater-based epidemiology (WBE) is an effective tool for tracking community circulation of respiratory viruses. We address estimating the effective reproduction number ($R_t$) and the relative number of infections from wastewater viral load. Using weekly Houston data on respiratory syncytial virus (RSV), we implement a parsimonious Bayesian renewal model that links latent infections to measured viral load through biologically motivated generation and shedding kernels. The framework yields estimates of $R_t$ and relative infections, enabling a coherent interpretation of transmission timing and phase. We compare two input strategies-(i) raw viral-load measurements with a log-scale standard deviation, and (ii) state-space-filtered load estimates with time-varying variances-and find no practically meaningful differences in inferred trajectories or peak timing. Given this equivalence, we report the filtered input as a pragmatic default because it embeds week-specific variances while leaving epidemiological conclusions unchanged.

Multi-label feature selection (FS) reduces the dimensionality of multi-label data by removing irrelevant, noisy, and redundant features, thereby boosting the performance of multi-label learning models. However, existing methods typically require centralized data, which makes them unsuitable for distributed and federated environments where each device/client holds its own local dataset. Additionally, federated methods often assume that clients have labeled data, which is unrealistic in cases where clients lack the expertise or resources to label task-specific data. To address these challenges, we propose a Semi-Supervised Federated Multi-Label Feature Selection method, called SSFMLFS, where clients hold only unlabeled data, while the server has limited labeled data. SSFMLFS adapts fuzzy information theory to a federated setting, where clients compute fuzzy similarity matrices and transmit them to the server, which then calculates feature redundancy and feature-label relevancy degrees. A feature graph is constructed by modeling features as vertices, assigning relevancy and redundancy degrees as vertex weights and edge weights, respectively. PageRank is then applied to rank the features by importance. Extensive experiments on five real-world datasets from various domains, including biology, images, music, and text, demonstrate that SSFMLFS outperforms other federated and centralized supervised and semi-supervised approaches in terms of three different evaluation metrics in non-IID data distribution setting.

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities. We study uniform random sampling on the $d$-dimensional unit hypercube and analyze the number of uncovered subcubes after discretization. By applying a concentration inequality to the uncovered-count statistic, we derive a sample complexity bound with a logarithmic dependence on the failure probability ($\delta$), i.e., $M =O( \tilde{C}\ln(\frac{2\tilde{C}}{\delta}))$, which contrasts sharply with the classical linear $1/\delta$ dependence. Under standard Lipschitz and uniformity assumptions, we present a self-contained derivation and compare our result with classical coupon-collector rates. Numerical studies across dimensions, precision levels, and confidence targets indicate that our bound tracks practical coverage requirements more tightly and scales favorably as $\delta \to 0$. Our findings offer a sharper theoretical tool for algorithms that rely on grid-based coverage guarantees, enabling more efficient sampling, especially in high-confidence regimes.

Node popularity is recognized as a key factor in modeling real-world networks, capturing heterogeneity in connectivity across communities. This concept is equally important in bipartite networks, where nodes in different partitions may exhibit varying popularity patterns, motivating models such as the Two-Way Node Popularity Model (TNPM). Existing methods, such as the Two-Stage Divided Cosine (TSDC) algorithm, provide a scalable estimation approach but may have limitations in terms of accuracy or applicability across different types of networks. In this paper, we develop a computationally efficient and theoretically justified variational expectation-maximization (VEM) framework for the TNPM. We establish label consistency for the estimated community assignments produced by the proposed variational estimator in bipartite networks. Through extensive simulation studies, we show that our method achieves superior estimation accuracy across a range of bipartite as well as undirected networks compared to existing algorithms. Finally, we evaluate our method on real-world bipartite and undirected networks, further demonstrating its practical effectiveness and robustness.