Credit risk models are a critical decision-support tool for financial institutions, yet tightening data-protection rules (e.g., GDPR, CCPA) increasingly prohibit cross-border sharing of borrower data, even as these models benefit from cross-institution learning. Traditional default prediction suffers from two limitations: binary classification ignores default timing, treating early defaulters (high loss) equivalently to late defaulters (low loss), and centralized training violates emerging regulatory constraints. We propose a Federated Survival Learning framework with Bayesian Differential Privacy (FSL-BDP) that models time-to-default trajectories without centralizing sensitive data. The framework provides Bayesian (data-dependent) differential privacy (DP) guarantees while enabling institutions to jointly learn risk dynamics. Experiments on three real-world credit datasets (LendingClub, SBA, Bondora) show that federation fundamentally alters the relative effectiveness of privacy mechanisms. While classical DP performs better than Bayesian DP in centralized settings, the latter benefits substantially more from federation (+7.0\% vs +1.4\%), achieving near parity of non-private performance and outperforming classical DP in the majority of participating clients. This ranking reversal yields a key decision-support insight: privacy mechanism selection should be evaluated in the target deployment architecture, rather than centralized benchmarks. These findings provide actionable guidance for practitioners designing privacy-preserving decision support systems in regulated, multi-institutional environments.

In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise) and allocated to node servers, where each node estimates the row (or column) loading matrix via two-dimensional tensor PCA. These local estimates are then transmitted to a central server and aggregated, followed by a final PCA step to obtain the global row (or column) loading matrix estimator. Given the estimated loading matrices, the corresponding factor matrices are subsequently computed. Unlike existing distributed approaches, our framework preserves the latent matrix structure, thereby improving computational efficiency and enhancing information utilization. We also discuss row- and column-wise clustering procedures for settings in which the group memberships are unknown. Furthermore, we extend the analysis to unit-root nonstationary matrix-variate time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. Simulation results assess the computational efficiency and estimation accuracy of the proposed framework, and real data applications further validate its predictive performance.

Classification imbalance arises when one class is much rarer than the other. We frame this setting as transfer learning under label (prior) shift between an imbalanced source distribution induced by the observed data and a balanced target distribution under which performance is evaluated. Within this framework, we study a family of oversampling procedures that augment the training data by generating synthetic samples from an estimated minority-class distribution to roughly balance the classes, among which the celebrated SMOTE algorithm is a canonical example. We show that the excess risk decomposes into the rate achievable under balanced training (as if the data had been drawn from the balanced target distribution) and an additional term, the cost of transfer, which quantifies the discrepancy between the estimated and true minority-class distributions. In particular, we show that the cost of transfer for SMOTE dominates that of bootstrapping (random oversampling) in moderately high dimensions, suggesting that we should expect bootstrapping to have better performance than SMOTE in general. We corroborate these findings with experimental evidence. More broadly, our results provide guidance for choosing among augmentation strategies for imbalanced classification.

Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing methods almost exclusively address the item-level DP setting, where each user contributes a single observation. Many scientific and economic applications instead involve longitudinal or panel data, in which each user contributes multiple dependent observations. In these settings, item-level DP offers inadequate protection, and user-level DP - shielding an individual's entire trajectory - is the appropriate privacy notion. We develop a comprehensive framework for estimation and inference in longitudinal linear regression under user-level DP. We propose a user-level private regression estimator based on aggregating local regressions, and we establish finite-sample guarantees and asymptotic normality under short-range dependence. For inference, we develop a privatized, bias-corrected covariance estimator that is automatically heteroskedasticity- and autocorrelation-consistent. These results provide the first unified framework for practical user-level DP estimation and inference in longitudinal linear regression under dependence, with strong theoretical guarantees and promising empirical performance.

We propose a unified framework for fair regression tasks formulated as risk minimization problems subject to a demographic parity constraint. Unlike many existing approaches that are limited to specific loss functions or rely on challenging non-convex optimization, our framework is applicable to a broad spectrum of regression tasks. Examples include linear regression with squared loss, binary classification with cross-entropy loss, quantile regression with pinball loss, and robust regression with Huber loss. We derive a novel characterization of the fair risk minimizer, which yields a computationally efficient estimation procedure for general loss functions. Theoretically, we establish the asymptotic consistency of the proposed estimator and derive its convergence rates under mild assumptions. We illustrate the method's versatility through detailed discussions of several common loss functions. Numerical results demonstrate that our approach effectively minimizes risk while satisfying fairness constraints across various regression settings.

With grid operators confronting rising uncertainty from renewable integration and a broader push toward electrification, Demand-Side Management (DSM) -- particularly Demand Response (DR) -- has attracted significant attention as a cost-effective mechanism for balancing modern electricity systems. Unprecedented volumes of consumption data from a continuing global deployment of smart meters enable consumer segmentation based on real usage behaviours, promising to inform the design of more effective DSM and DR programs. However, existing clustering-based segmentation methods insufficiently reflect the behavioural diversity of consumers, often relying on rigid temporal alignment, and faltering in the presence of anomalies, missing data, or large-scale deployments. To address these challenges, we propose a novel two-stage clustering framework -- Clustered Representations Optimising Consumer Segmentation (CROCS). In the first stage, each consumer's daily load profiles are clustered independently to form a Representative Load Set (RLS), providing a compact summary of their typical diurnal consumption behaviours. In the second stage, consumers are clustered using the Weighted Sum of Minimum Distances (WSMD), a novel set-to-set measure that compares RLSs by accounting for both the prevalence and similarity of those behaviours. Finally, community detection on the WSMD-induced graph reveals higher-order prototypes that embody the shared diurnal behaviours defining consumer groups, enhancing the interpretability of the resulting clusters. Extensive experiments on both synthetic and real Australian smart meter datasets demonstrate that CROCS captures intra-consumer variability, uncovers both synchronous and asynchronous behavioural similarities, and remains robust to anomalies and missing data, while scaling efficiently through natural parallelisation. These results...

Batch effects represent a major confounder in genomic diagnostics. In copy number variant (CNV) detection from NGS, many algorithms compare read depth between test samples and a reference sample, assuming they are process-matched. When this assumption is violated, with causes ranging from reagent lot changes to multi-site processing, the reference becomes inappropriate, introducing false CNV calls or masking true pathogenic variants. Detecting such heterogeneity before downstream analysis is critical for reliable clinical interpretation. Existing batch effect detection methods either cluster samples based on raw features, risking conflation of biological signal with technical variation, or require known batch labels that are frequently unavailable. We introduce a method that addresses both limitations by clustering samples according to their Bayesian model evidence. The central insight is that evidence quantifies compatibility between data and model assumptions, technical artifacts violate assumptions and reduce evidence, whereas biological variation, including CNV status, is anticipated by the model and yields high evidence. This asymmetry provides a discriminative signal that separates batch effects from biology. We formalize heterogeneity detection as a likelihood ratio test for mixture structure in evidence space, using parametric bootstrap calibration to ensure conservative false positive rates. We validate our approach on synthetic data demonstrating proper Type I error control, three clinical targeted sequencing panels (liquid biopsy, BRCA, and thalassemia) exhibiting distinct batch effect mechanisms, and mouse electrophysiology recordings demonstrating cross-modality generalization. Our method achieves superior clustering accuracy compared to standard correlation-based and dimensionality-reduction approaches while maintaining the conservativeness required for clinical usage.

Finite-time central limit theorem (CLT) rates play a central role in modern machine learning. In this paper, we study CLT rates for multivariate dependent data in Wasserstein-$p$ ($W_p$) distance, for general $p \geq 1$. We focus on two fundamental dependence structures that commonly arise in machine learning: locally dependent sequences and geometrically ergodic Markov chains. In both settings, we establish the first optimal $O(n^{-1/2})$ rate in $W_1$, as well as the first $W_p$ ($p\ge 2$) CLT rates under mild moment assumptions, substantially improving the best previously known bounds in these dependent-data regimes. As an application of our optimal $W_1$ rate for locally dependent sequences, we further obtain the first optimal $W_1$-CLT rate for multivariate $U$-statistics. On the technical side, we derive a tractable auxiliary bound for $W_1$ Gaussian approximation errors that is well suited for studying dependent data. For Markov chains, we further prove that the regeneration time of the split chain associated with a geometrically ergodic chain has a geometric tail without assuming strong aperiodicity or other restrictive conditions. These tools may be of independent interests and enable our optimal $W_1$ rates and underpin our $W_p$ ($p\ge 2$) results.

Estimating the Riesz representer is central to debiased machine learning for causal and structural parameter estimation. We propose generalized Riesz regression, a unified framework that estimates the Riesz representer by fitting a representer model via Bregman divergence minimization. This framework includes the squared loss and the Kullback--Leibler (KL) divergence as special cases: the former recovers Riesz regression, while the latter recovers tailored loss minimization. Under suitable model specifications, the dual problems correspond to covariate balancing, which we call automatic covariate balancing. Moreover, under the same specifications, outcome averages weighted by the estimated Riesz representer satisfy Neyman orthogonality even without estimating the regression function, a property we call automatic Neyman orthogonalization. This property not only reduces the estimation error of Neyman orthogonal scores but also clarifies a key distinction between debiased machine learning and targeted maximum likelihood estimation. Our framework can also be viewed as a generalization of density ratio fitting under Bregman divergences to Riesz representer estimation, and it applies beyond density ratio estimation. We provide convergence analyses for both reproducing kernel Hilbert space (RKHS) and neural network model classes. A Python package for generalized Riesz regression is available at https://github.com/MasaKat0/grr.

Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them inherently vulnerable to malicious behavior. In this work, we investigate an adversarial threat that we term the ``Pac-Man'' attack, in which a malicious node probabilistically terminates any RW that visits it. This stealthy behavior gradually eliminates active RWs from the network, effectively halting the learning process without triggering failure alarms. To counter this threat, we propose the Average Crossing (AC) algorithm--a fully decentralized mechanism for duplicating RWs to prevent RW extinction in the presence of Pac-Man. Our theoretical analysis establishes that (i) the RW population remains almost surely bounded under AC and (ii) RW-based stochastic gradient descent remains convergent under AC, even in the presence of Pac-Man, with a quantifiable deviation from the true optimum. Our extensive empirical results on both synthetic and real-world datasets corroborate our theoretical findings. Furthermore, they uncover a phase transition in the extinction probability as a function of the duplication threshold. We offer theoretical insights by analyzing a simplified variant of the AC, which sheds light on the observed phase transition.