Papers

Timely transition from intravenous (IV) to oral antibiotic therapy shortens hospital stays, reduces catheter-related infections, and lowers healthcare costs, yet one in five patients in England remain on IV antibiotics despite meeting switching criteria. Clinical decision support systems can improve switching rates, but approaches that learn from historical decisions reproduce the delays and inconsistencies of routine practice. We propose using neural processes to model vital sign trajectories probabilistically, predicting switch-readiness by comparing forecasts against clinical guidelines rather than learning from past actions, and ranking patients to prioritise clinical review. The design yields interpretable outputs, adapts to updated guidelines without retraining, and preserves clinical judgement. Validated on MIMIC-IV (US intensive care, 6,333 encounters) and UCLH (a large urban academic UK hospital group, 10,584 encounters), the system selects 2.2-3.2$\times$ more relevant patients than random. Our results demonstrate that forecasting patient physiology offers a principled foundation for decision support in antibiotic stewardship.

Long-term time series forecasting (LTSF) is widely recognized as a central challenge in data mining and machine learning. LTSF has increasingly evolved into a benchmark-driven ”GAME,” where models are ranked, compared, and declared state-of-the-art based primarily on marginal reductions in aggregated pointwise error metrics such as MSE and MAE. Across a small set of canonical datasets and fixed forecasting horizons, progress is communicated through leaderboard-style tables in which lower numerical scores define success. In this GAME, what is measured becomes what is optimized, and incremental error reduction becomes the dominant currency of advancement. We argue that this metric-centric regime is not merely incomplete, but structurally misaligned with the broader objectives of forecasting. In real-world settings, forecasting often prioritizes preserving temporal structure, trend stability, seasonal coherence, robustness to regime shifts, and supporting downstream decision processes. Optimizing aggregate pointwise error does not necessarily imply modeling these structural properties. As a result, leaderboard improvement may increasingly reflect specialization in benchmark configurations rather than a deeper understanding of temporal dynamics. This paper revisits LTSF evaluation as a foundational question in data science: what does it mean to measure forecasting progress? We propose a multi-dimensional evaluation perspective that integrates statistical fidelity, structural coherence, and decision-level relevance. By challenging the current metric monoculture, we aim to redirect attention from winning benchmark tables toward advancing meaningful, context-aware forecasting.

We introduce the $W$-footrule coefficient $\Phi_C$, a copula-based coefficient of negative association defined as the $L^1$-distance to the countermonotonic copula $W$. We prove that Gini's gamma admits the decomposition $\gamma_C = \frac{2}{3}(\varphi_C+\Phi_C)$, linking it to Spearman's footrule $\varphi_C$. A rank-based estimator is introduced, with its strong consistency and asymptotic normality established via the functional delta method. Monte Carlo simulations confirm the estimator's finite-sample validity and its sensitivity to negative dependence structures.

We present a novel Explainable methodology for Condition Monitoring, relying on healthy data only. Since faults are rare events, we propose to focus on learning the probability distribution of healthy observations only, and detect Anomalies at runtime. This objective is achieved via the definition of probabilistic measures of deviation from nominality, which allow to detect and anticipate faults. The Bayesian perspective underpinning our approach allows us to perform Uncertainty Quantification to inform decisions. At the same time, we provide descriptive tools to enhance the interpretability of the results, supporting the deployment of the proposed strategy also in safety-critical applications. The methodology is validated experimentally on two use cases: a publicly available benchmark for Predictive Maintenance, and a real-world Helicopter Transmission dataset collected over multiple years. In both applications, the method achieves competitive detection performance with respect to state-of-the-art anomaly detection methods.

The rapid expansion of the French offshore wind sector requires a critical reassessment of structural durability in the face of evolving marine conditions driven by climate change. Traditional design methodologies, which rely on the assumption of stationary environmental conditions, are no longer adequate. This study introduces a novel statistical framework to assess future changes in significant wave height by employing non-stationary Generalized Extreme Value (GEV) models applied to monthly maxima. This approach aims to reduce uncertainty and provide robust design tools adapted to the non-stationary conditions of the future. Based on CMIP6 climate models and reanalysis data, results reveal a projected trend towards a more pronounced seasonal contrast along the French Atlantic and English Channel coasts under future scenarios (SSP1-2.6 and SSP5-8.5), whereas the French Mediterranean Sea exhibits results that are more difficult to interpret, due to a weaker increase of extremes and large uncertainties (inter-model spread). Projections indicate more intense winters and calmer summers, along with a shift in the seasonal cycle. Overall, the multi-model ensemble suggests an increase in the design levels for extreme sea states. The research concludes by defining a new methodology for calculating an equivalent design level over the structure's operational lifespan. This tool is deemed essential for ensuring the resilience and economic viability of future offshore wind farms in a changing climate.

We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level – the "type-I error" – is selected prior to seeing or analyzing any data. This restriction leads to some drawbacks. For instance, if an analyst generates an inconclusive confidence interval, repeating the process with a larger significance level is not an option – the result is final. Recently, e-values have emerged as the solution to this problem, being both necessary and sufficient tools for performing various forms of post-hoc inference. All such results, however, have thus far been nonasymptotic. As a result, they inherit familiar limitations of nonasymptotic inferential procedures such as requiring strong moment assumptions and being conservative in general. This paper develops a theory of post-hoc inference in the asymptotic setting, yielding asymptotic post-hoc confidence sets and asymptotic post-hoc p-values that make weaker assumptions and are sharper than their nonasymptotic counterparts.

Maximum inner product search (MIPS) is a crucial subroutine in machine learning, requiring the identification of a vector taken within a database (the keys) that best aligns with a given query. We propose amortized MIPS: a regression-based approach that trains neural networks to directly predict MIPS solutions, amortizing the cost of repeatedly solving MIPS for queries drawn from a known distribution over a fixed key database. Our key insight is that the MIPS value function is the support function of the set of keys, a well-studied convex function whose gradient yields the optimal key. This motivates two complementary amortized models: SupportNet, an input-convex neural network trained to regress the support function, and KeyNet, a vector-valued network that directly regresses the optimal key. SupportNet can serve as a cluster router, steering queries toward relevant database partitions, while KeyNet can be used as a drop-in replacement for the original query, fed directly to off-the-shelf indexing pipelines. Our experiments on the BEIR benchmark show that, for document embeddings, learned \SupportNet{}s and \KeyNet{}s significantly improve IVF match rates when accounting for compute effort, whether measured in FLOPs, number of probes, or wall-clock time. Our code is available at: https://github.com/apple/ml-amips.

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order restrictions. This information should be taken into account to obtain improved estimators. In this paper, we study the problems of point-wise and interval estimation of the entropy of two normal populations under a general location-invariant loss function. For the point-wise estimation, we have derived the maximum likelihood estimator (MLE), restricted MLE and the uniformly minimum variance unbiased estimator (UMVUE). Further, we derive a sufficient condition for improvement over affine equivariant estimators. A class of improved estimators is derived that dominates the best affine equivariant estimator (BAEE). Furthermore, we obtain a class of smooth improved estimator that dominates BAEE. We present special loss functions and derive expressions for the proposed improved estimators. A numerical study is conducted to compare the risk performance of the proposed estimators under quadratic and linex loss functions. For interval estimation, we have derived asymptotic confidence interval, bootstrap confidence intervals, HPD credible interval, and intervals based on generalized pivot variables. A comprehensive numerical comparison of these intervals is carried out in terms of coverage probabilities and average lengths. Finally, the proposed results are illustrated with a real example: the failure of the air-conditioning systems on Boeing 720 jet planes.

Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality. We propose Local Constrained Bayesian Optimization (LCBO), a novel framework tailored for such settings. Unlike trust-region methods that are prone to premature shrinking when confronting tight or complex constraints, LCBO leverages the differentiable landscape of constraint-penalized surrogates to alternate between rapid local descent and uncertainty-driven exploration. Theoretically, we prove that LCBO achieves a convergence rate for the Karush-Kuhn-Tucker (KKT) residual that depends polynomially on the dimension $d$ for common kernels under mild assumptions, offering a rigorous alternative to global BO where regret bounds typically scale exponentially. Extensive evaluations on high-dimensional benchmarks (up to 100D) demonstrate that LCBO consistently outperforms state-of-the-art baselines.

We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on “very hard” unknot diagrams and, using diagram inflation, on $4_1\#9_{10}$ where we investigate the recently established and surprising upper bound of three for the unknotting number. In addition, we explain a self-improving workbook-driven extension of the pipeline that systematically improves unknotting number upper bounds on the prime knots.

Robust Markov Decision Processes (MDPs) address environmental shift through distributionally robust optimization (DRO) by finding an optimal worst-case policy within an uncertainty set of transition kernels. However, standard DRO approaches require enlarging the uncertainty set under large shifts, which leads to overly conservative and pessimistic policies. In this paper, we propose a framework for transfer under environment shift that derives a robust target-domain policy via estimate-centered uncertainty sets, constructed through constrained estimation that integrates limited target samples with side information about the source-target dynamics. The side information includes bounds on feature moments, distributional distances, and density ratios, yielding improved kernel estimates and tighter uncertainty sets. The side information includes bounds on feature moments, distributional distances, and density ratios, yielding improved kernel estimates and tighter uncertainty sets. Error bounds and convergence results are established for both robust and non-robust value functions. Moreover, we provide a finite-sample guarantee on the learned robust policy and analyze the robust sub-optimality gap. Under mild low-dimensional structure on the transition model, the side information reduces this gap and improves sample efficiency. We assess the performance of our approach across OpenAI Gym environments and classic control problems, consistently demonstrating superior target-domain performance over state-of-the-art robust and non-robust baselines.

The reliable operation of modern power grids requires probabilistic load forecasts with well-calibrated uncertainty estimates. However, existing deep learning models produce overconfident point predictions that fail catastrophically under extreme weather distributional shifts. This study proposes a Bayesian Transformer (BT) framework that integrates three complementary uncertainty mechanisms into a PatchTST backbone: Monte Carlo Dropout for epistemic parameter uncertainty, variational feed-forward layers with log-uniform weight priors, and stochastic attention with learnable Gaussian noise perturbations on pre-softmax logits, representing, to the best of our knowledge, the first application of Bayesian attention to probabilistic load forecasting. A seven-level multi-quantile pinball-loss prediction head and post-training isotonic regression calibration produce sharp, near-nominally covered prediction intervals. Evaluation of five grid datasets (PJM, ERCOT, ENTSO-E Germany, France, and Great Britain) augmented with NOAA covariates across 24, 48, and 168-hour horizons demonstrates state-of-the-art performance. On the primary benchmark (PJM, H=24h), BT achieves a CRPS of 0.0289, improving 7.4% over Deep Ensembles and 29.9% over the deterministic LSTM, with 90.4% PICP at the 90% nominal level and the narrowest prediction intervals (4,960 MW) among all probabilistic baselines. During heat-wave and cold snap events, BT maintained 89.6% and 90.1% PICP respectively, versus 64.7% and 67.2% for the deterministic LSTM, confirming that Bayesian epistemic uncertainty naturally widens intervals for out-of-distribution inputs. Calibration remained stable across all horizons (89.8-90.4% PICP), while ablation confirmed that each component contributed a distinct value. The calibrated outputs directly support risk-based reserve sizing, stochastic unit commitment, and demand response activation.

Inference-time methods that aggregate and prune multiple samples have emerged as a powerful paradigm for steering large language models, yet we lack any principled understanding of their accuracy-cost tradeoffs. In this paper, we introduce a route to rigorously study such approaches using the lens of *particle filtering* algorithms such as Sequential Monte Carlo (SMC). Given a base language model and a *process reward model* estimating expected terminal rewards, we ask: *how accurately can we sample from a target distribution given some number of process reward evaluations?* Theoretically, we identify (1) simple criteria enabling non-asymptotic guarantees for SMC; (2) algorithmic improvements to SMC; and (3) a fundamental limit faced by all particle filtering methods. Empirically, we demonstrate that our theoretical criteria effectively govern the *sampling error* of SMC, though not necessarily its final *accuracy*, suggesting that theoretical perspectives beyond sampling may be necessary.

For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which we refer to as a depth statistic. In practice, its sampling distribution is approximated by a resampling method such as bootstrap. While achieving accurate sizes, a test based on the proposed depth statistic produces stronger power, as it remains sensitive even to subtle variations arising from complex functional patterns in the alternatives. Moreover, it is broadly applicable to a broad range of inference problems for functional parameters, including two-sample tests, analysis of variance, regression, etc. We provide its theoretical guarantee under mild assumptions along with examples of bootstrap methods and functional depths that satisfy these conditions. Its effectiveness is thoroughly investigated through numerical studies under two popular frameworks: (i) two-sample functional mean tests and (ii) mean response inference for function-on-function regression. The proposed depth statistic is illustrated with two data examples: Canadian weather and German electricity prices datasets.

Detecting structural instability and anomalies in high-dimensional financial time series is challenging due to complex temporal dependence and evolving cross-sectional structure. We propose ReGEN-TAD, an interpretable generative framework that integrates modern machine learning with econometric diagnostics for anomaly detection. The model combines joint forecasting and reconstruction within a refined convolutional–transformer architecture and aggregates complementary signals capturing predictive inconsistency, reconstruction degradation, latent distortion, and volatility shifts. Robust calibration yields a unified anomaly score without labeled data. Experiments on synthetic and financial panels demonstrate improved robustness to structured deviations while enabling economically coherent factor-level attribution.

In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction accuracy. In this work, we develop a variational inference approach for estimation and variable selection in scalar-on-function regression, involving only functional covariates, and in partially functional regression models that also include scalar covariates. Specifically, we develop a variational expectation-maximization (VEM) algorithm, with a variational Bayes procedure implemented in the E-step to obtain approximate marginal posterior distributions for most model parameters, except for the regularization parameters, which are updated in the M-step. Our method accurately identifies relevant covariates while maintaining strong predictive performance, as demonstrated through extensive simulation studies across diverse scenarios. Compared with alternative approaches, including BGLSS (Bayesian Group Lasso with Spike-and-Slab priors), grLASSO (group Least Absolute Shrinkage and Selection Operator), grMCP (group Minimax Concave Penalty), and grSCAD (group Smoothly Clipped Absolute Deviation), our approach achieves a superior balance between goodness-of-fit and sparsity in most scenarios. We further illustrate its practical utility through real-data applications involving spectral analysis of sugar samples and weather measurements from Japan.

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" – learning from live, uncurated enterprise "data swamps" – supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer” to overcome static generalizability limitations.

We argue that formal certification of AI alignment over open-ended or unbounded input domains is impossible under standard assumptions in computational complexity and learning theory, and characterise what remains achievable. Two structurally independent impossibility theorems support this position. The semantic barrier (Theorem 1): deciding whether a system satisfies any non-trivial alignment property over the full input domain is NP-hard for feedforward networks and undecidable for Turing-complete architectures – a direct consequence of neural-network verification complexity and Rice's Theorem. The statistical barrier (Theorem 2): any verification procedure that is both sound and tractable cannot satisfy Completeness over the full input domain – a direct consequence of the impossibility of certifying infinite-domain properties from finite observations. These two theorems jointly entail a trilemma: no procedure can simultaneously satisfy soundness (no misaligned system is certified), completeness (no aligned system is rejected), and tractability (polynomial runtime). Each pair is simultaneously achievable; all three are not. We combine these results as a joint framework of two structurally independent barriers, prove their independence, and characterise the achievable Pareto frontier quantitatively via a constructive coverage-gap lower bound.

Weighted aggregations of i.i.d. risks without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger, rather than less dispersed. Existing results establish stochastic dominance between pairs of linear combinations, or between a convex combination and the underlying variable, under shape restrictions on the distribution and structural assumptions on the weights. Nonetheless, two practical limitations remain: (i) the sufficient conditions vary across results, and (ii) being non-necessary, they exclude many relevant configurations. Moreover, under a statistical perspective, where the true distribution of the data is assumed to be unknown, these conditions cannot be checked. Motivated by this gap, we develop nonparametric procedures to test whether two linear combinations are stochastically ordered. We propose two complementary approaches: a least-favorable calibration and a bootstrap-based method. We establish their asymptotic validity under the null of stochastic dominance and their consistency against the alternative of non-dominance. Monte Carlo experiments illustrate the finite-sample performance of the proposed procedures across a range of models and weight configurations. An application to insurance claim-severity data illustrates how the tests can be used to assess whether pooling leads to a stochastically larger loss.

We propose a simple binarization of predictors, an "at-risk" transformation, as an alternative to the standard practice of using continuous, standardized variables in recession forecasting models. By converting predictors into indicators of unusually weak states based on a thresholding rule estimated from training data, we demonstrate their ability to capture the discrete nature of rare events such as U.S. recessions. Using a large panel of monthly U.S. macroeconomic and financial data, we show that binarized predictors consistently improve out-of-sample forecasting performance, often making linear models competitive with flexible machine learning methods, and that the gains are particularly pronounced around the onset of recessions.

Bayesian hierarchical models fitted to complex survey data often use weighted pseudo-posteriors, followed by a correction to match a design-based sandwich covariance. Correcting every parameter can needlessly widen or spuriously narrow credible intervals for parameters stabilized by shrinkage or identified by between-group variation. We propose the Design Effect Ratio (DER) to guide selective correction. It is the ratio of each parameter's design-based sandwich variance under a declared target to its model-based posterior variance. For hierarchical Gaussian models, we derive exact finite-sample decompositions under balance and common-design-effect assumptions. Fixed-effect DERs scale with the design effect, attenuated by the between-group share of identifying variation. Random-effect DERs factor into design effect, shrinkage, and a group-count term; a conservation identity links the two levels. A general matrix formula covers arbitrary parameter blocks and non-Gaussian likelihoods. We evaluate the diagnostic in a simulation with informative two-stage sampling and a re-analysis of the 2019 National Survey of Early Care and Education, reporting both design-PSU and model-group variance targets. These analyses distinguish survey-sensitive parameters from those protected by shrinkage and show how selective correction avoids the interval distortions caused by blanket rescaling. The R package svyder implements the workflow.

A standard assumption in the Bayesian estimation of linear regression models is that the regressors are exogenous in the sense that they are uncorrelated with the model error term. In practice, however, this assumption can be invalid. In this paper, using the exponentially tilted empirical likelihood framework, we develop a Bayes factor test for endogeneity that compares a base model that is correctly specified under exogeneity but misspecified under endogeneity against an extended model that is correctly specified in either case. We provide a comprehensive study of the log-marginal exponentially tilted empirical likelihood. We demonstrate that our testing procedure is consistent from a frequentist point of view: as the sample grows, it almost surely selects the base model if and only if the regressors are exogenous, and the extended model if and only if the regressors are endogenous. The methods are illustrated with simulated data, and problems concerning the causal effect of automobile prices on automobile demand and the causal effect of potentially endogenous airplane ticket prices on passenger volume.

The Galton board is a well known device for showing how repeated Bernoulli trials on a triangular lattice produce an approximately normal distribution. Marking the 150th anniversary of Galton's 1875 construction, this paper revisits the original apparatus and extends it to a cylindrical setting in which the peg lattice is wrapped around a cylinder. This creates angular periodicity and leads to height dependent behaviour that does not arise in the classical planar design. The cylindrical form links Galton's demonstration of variation and the emergence of the normal distribution with modern ideas in circular statistics, giving a physical realisation of binomial random walks on a circular linear product space. We distinguish cases where the wrapped lattice covers only an arc from those that span the full circumference, and show how these geometries lead to wrapped binomial and wrapped normal behaviour. We describe the construction of our physical model, discuss practical issues for replication, and analyse its statistical and pedagogical properties as a modern reinterpretation of Galton's work.

We report the first realization of a fractional topological phase in a fully unitary, noninteracting discrete-time quantum walk implemented on finite cyclic graphs. Using a single-coin split-step cyclic quantum walk (SCSS-CQW), we uncover topological phenomena that are inaccessible within conventional cyclic quantum-walk dynamics. The protocol enables controlled engineering of quasienergy spectra, flat bands, and topological phase transitions through the step-dependency parameter and coin-rotation angle. We show that cyclic graphs with even and odd numbers of sites exhibit qualitatively different band structures, while rotational flat bands arise exclusively in $4n$-site cycles; a general analytic condition for their emergence is derived. The SCSS-CQW produces fractional winding numbers $\pm \frac{1}{2}$ (Zak phases $\pm \frac{\pi}{2}$), in sharp contrast with the integer invariants in standard cyclic quantum walks. These fractional invariants lead to an unconventional bulk-boundary correspondence and support protected {zero energy} edge states beyond the usual integer topological classification. In the step-dependent protocol, transitions between distinct fractional winding sectors generate robust edge modes pinned at zero quasienergy. Numerical simulations show that these states remain stable in the presence of both dynamic and static coin disorder as well as phase-preserving perturbations, while survival-probability analysis demonstrates their long-time persistence. Requiring only a constant number of detectors independent of the evolution time and fewer operators, the proposed scheme offers a minimal-resource and experimentally accessible platform for realizing fractional topology, flat bands, and protected zero energy edge states in small-scale synthetic quantum systems.

Longitudinal associations may vary over time, yet allowing every regression effect to be dynamic can inflate estimation variance and obscure interpretable structure. We develop time-varying-effect selection (TV-Select), a group-sparse smoothing framework that classifies covariate effects as zero, constant, or time varying. Each coefficient is decomposed into a constant mean and a centered temporal deviation represented by a full-rank, L2-normalized effective spline basis. A group penalty identifies varying components, while a roughness penalty controls their curvature. The resulting convex criterion is solved by cyclic block proximal-gradient updates and followed by smooth refitting. Under a full-column-rank unpenalized design and an effective model dimension that is small relative to the total number of observations, we establish prediction and parameter rates, blockwise function-estimation bounds, and exact recovery of the varying set under irrepresentability and beta-min conditions. A stable classification refit further separates zero from constant effects. For fixed-dimensional contrasts, we construct an oracle-equivalent one-step estimator with cluster-robust asymptotic normality and consistent sandwich variance estimation. Simulations demonstrate that TV-Select combines low false-positive rates with accurate function estimation and competitive prediction across a range of longitudinal settings. An application to Sleep-EDF data produces smooth and parsimonious temporal effect estimates with essentially unchanged held-out predictive performance.

Granger causality (GC), a popular statistical method for the inference of directional influences between time series measured from a complex network, is sensitive to high-order (non-pairwise) interactions which fundamentally shape the collective network dynamics. This work introduces Partial Decomposition of Granger Causality (PDGC), a tool eliciting redundant and synergistic causal interactions in the pattern of information flow between the subsystems of physiological networks. The tool exploits the framework of partial information decomposition to dissect the multivariate GC from a set of driver random processes to a target process into unique effects carried exclusively by each driver, redundant effects carried identically by more drivers, and synergistic effects carried jointly by some drivers but not by any of them individually. Computation is based on multivariate state-space models expanded in the frequency domain to assess PDGC both in specific bands of physiological interest and in the time domain after whole-band integration. The validation on benchmark simulations demonstrates that the measures of unique, redundant, and synergistic GC reflect the underlying causal mechanisms and are computationally reliable. The application to arterial pressure, respiration, cerebral blood velocity and heart period variability reveals striking differences in the response to postural stress of patients prone to neurally-mediated syncope compared to healthy controls. The extraction of high-order causality patterns from the spectral GC favors dissecting the mechanisms of causal influence underlying multivariate interactions among oscillatory processes in many data-driven applications of network science.

In this paper, we address a fundamental limitation of the classical Wasserstein barycenter – its sensitivity to outliers. To overcome these issues, we propose the robust Wasserstein barycenter (RWB) based on a recent concept of the robust optimal transport. Theoretical guarantees, including existence and consistency, are established for the proposed RWB. Through extensive numerical experiments on both simulated and real-world data – including image processing and financial data analysis – we demonstrate that the RWB exhibits superior robustness compared to the classical Wasserstein barycenter.

We develop an efficient posterior sampling scheme for the Poisson INGARCH models. The proposed method is based on the approximation of the posterior density that exploits the Poisson limit of the negative binomial distribution. It allows us to rewrite the model in a form amenable to Pólya-Gamma data augmentation scheme, which yields simple conditionally Gaussian updates for the autoregressive coefficients. Sampling from the approximate posterior is straightforward via Gibbs-type iterations and remains numerically stable even under strong temporal dependence. Using this sampler as a proposal distribution will enhance the efficiency in Metropolis-Hastings algorithm and adaptive importance sampling. Numerical simulations indicate accurate posterior estimates, high effective sample sizes, and rapidly mixing chains.

Privacy protection and uncertainty quantification are increasingly important in data-driven decision making. Conformal prediction provides finite-sample marginal coverage, but existing private approaches often rely on data splitting, reducing the effective sample size. We propose a full-data privacy-preserving conformal prediction framework that avoids splitting. Our framework leverages stability induced by differential privacy to control the gap between in-sample and out-of-sample conformal scores, and pairs this with a conservative private quantile routine designed to prevent under-coverage. We show that a generic differential privacy guarantee yields a universal coverage floor, yet cannot generally recover the nominal $1-\alpha$ level. We then provide a refined, mechanism-specific stability analysis and yields asymptotic recovery of the nominal level. Experiments demonstrate sharper prediction sets than the split-based private baseline.

While the traditional goal of statistics is to infer population parameters, modern practice increasingly demands protection of individual privacy. One way to address this need is to adapt classical statistical procedures into privacy-preserving algorithms. In this paper, we develop differentially private tail-robust methods for linear regression. The trade-off among bias, privacy, and robustness is controlled by a tunable robustification parameter in the Huber loss. We implement noisy clipped gradient descent for low-dimensional settings and noisy iterative hard thresholding for high-dimensional sparse models. Under sub-Gaussian errors, our method achieves near-optimal convergence rates while relaxing several assumptions required in earlier work. For heavy-tailed errors, we explicitly characterize how the non-asymptotic convergence rate depends on the moment index, privacy parameters, sample size, and intrinsic dimension. Our analysis shows how the moment index influences the choice of robustification parameters and, in turn, the resulting statistical error and privacy cost. By quantifying the interplay among bias, privacy, and robustness, we extend classical perspectives on privacy-preserving robust regression. The proposed methods are evaluated through simulations and two real datasets.