Papers

The exponential growth of Internet-connected devices has presented challenges to traditional centralized computing systems due to latency and bandwidth limitations. Edge computing has evolved to address these difficulties by bringing computations closer to the data source. Additionally, traditional machine learning algorithms are not suitable for edge-computing systems, where data usually arrives in a dynamic and continual way. However, incremental learning offers a good solution for these settings. We introduce a new approach that applies the incremental learning philosophy within an edge-computing scenario for the industrial sector with a specific purpose: real time quality control in a manufacturing system. Applying continual learning we reduce the impact of catastrophic forgetting and provide an efficient and effective solution.

Amortized Bayesian inference (ABI) offers fast, scalable approximations to posterior densities by training neural surrogates on data simulated from the statistical model. However, ABI methods are highly sensitive to model misspecification: when observed data fall outside the training distribution (generative scope of the statistical models), neural surrogates can behave unpredictably. This makes it a challenge in a model comparison setting, where multiple statistical models are considered, of which at least some are misspecified. Recent work on self-consistency (SC) provides a promising remedy to this issue, accessible even for empirical data (without ground-truth labels). In this work, we investigate how SC can improve amortized model comparison conceptualized in four different ways. Across two synthetic and two real-world case studies, we find that approaches for model comparison that estimate marginal likelihoods through approximate parameter posteriors consistently outperform methods that directly approximate model evidence or posterior model probabilities. SC training improves robustness when the likelihood is available, even under severe model misspecification. The benefits of SC for methods without access of analytic likelihoods are more limited and inconsistent. Our results suggest practical guidance for reliable amortized Bayesian model comparison: prefer parameter posterior-based methods and augment them with SC training on empirical datasets to mitigate extrapolation bias under model misspecification.

This study investigates how different spatiotemporal temperature models affect the estimation of heat-related mortality in Lazio, Italy (2008–2022). First, we compare three methods to reconstruct daily maximum temperature at the municipality level: 1. a Bayesian quantile regression model with spatial interpolation, 2. a Bayesian Gaussian regression model, 3. the gridded reanalysis data from ERA5-Land. Both Bayesian models are station-based and exhibit higher and more spatially variable temperatures compared to ERA5-Land. Then, using individual mortality data for cardiovascular and respiratory causes, we estimate temperature-mortality associations through Bayesian conditional Poisson models in a case-crossover design. Exposure is defined as the mean maximum temperature over the previous three days. Additional models include heatwave definitions combining different thresholds and durations. All models exhibit a marked increase in relative risk at high temperatures; however, the temperature of minimum risk varies significantly across methods. Stratified analyses reveal higher relative risk increases in females and the elderly (80+). Heatwave effects depend on the definitions used, but all methods capture an increased mortality risk associated with prolonged heat exposure. Results confirm the importance of temperature model choice in epidemiology and provide insights for early warning systems and climate-health adaptation strategies.

The VBphenoR package for R provides a closed-form variational Bayes approach to patient phenotyping using Electronic Health Records (EHR) data. We implement a variational Bayes Gaussian Mixture Model (GMM) algorithm using closed-form coordinate ascent variational inference (CAVI) to determine the patient phenotype latent class. We then implement a variational Bayes logistic regression, where we determine the probability of the phenotype in the supplied EHR cohort, the shift in biomarkers for patients with the phenotype of interest versus a healthy population and evaluate predictive performance of binary indicator clinical codes and medication codes. The logistic model likelihood applies the latent class from the GMM step to inform the conditional.

We study the problem of multi-class classification under system-level constraints expressible as linear functionals over randomized classifiers. We propose a post-processing approach that adjusts a given base classifier to satisfy general constraints without retraining. Our method formulates the problem as a linearly constrained stochastic program over randomized classifiers, and leverages entropic regularization and dual optimization techniques to construct a feasible solution. We provide finite-sample guarantees for the risk and constraint satisfaction for the final output of our algorithm under minimal assumptions. The framework accommodates a broad class of constraints, including fairness, abstention, and churn requirements.

The success of modern multimodal representation learning relies on internet-scale datasets. Due to the low quality of a large fraction of raw web data, data curation has become a critical step in the training pipeline. Filtering using a trained model (i.e., teacher-based filtering) has emerged as a successful solution, leveraging a pre-trained model to compute quality scores. To explain the empirical success of teacher-based filtering, we characterize the performance of filtered contrastive learning under the standard bimodal data generation model. Denoting $\eta\in(0,1]$ as the fraction of data with correctly matched modalities among $n$ paired samples, we utilize a linear contrastive learning setup to show a provable benefit of data filtering: $(i)$ the error without filtering is upper and lower bounded by $\frac{1}{\eta \sqrt{n}}$, and $(ii)$ the error with teacher-based filtering is upper bounded by $\frac{1}{\sqrt{\eta n}}$ in the large $\eta$ regime, and by $\frac{1}{\sqrt{n}}$ in the small $\eta$ regime.

Conformal prediction (CP) offers a principled framework for uncertainty quantification, but it fails to guarantee mask-conditional coverage when faced with missing covariates. In addressing the heterogeneity induced by various missing patterns, Mask-Conditional Valid (MCV) Coverage has emerged as a more desirable property than Marginal Coverage. In this work, we adapt split CP to handle missing values by proposing a preimpute-mask-then-correct framework that can offer valid coverage. We show that our method provides guaranteed Marginal Coverage and Mask-Conditional Validity for general missing data mechanisms. A key component of our approach is a reweighted conformal prediction procedure that corrects the prediction sets after distributional imputation (multiple imputation) of the calibration dataset, making our method compatible with standard imputation pipelines. We derive two algorithms and prove that they achieve both marginal validity and MCV. We evaluate them on synthetic and real-world datasets. It reduces significantly the width of prediction intervals w.r.t standard MCV methods, while maintaining the target guarantees.

Identifying the most powerful test in multiple hypothesis testing under strong family-wise error rate (FWER) control is a fundamental problem in statistical methodology. State-of-the-art approaches formulate this as a constrained optimisation problem, for which a dual problem with strong duality has been established in a general sense. However, a constructive method for solving the dual problem is lacking, leaving a significant computational gap. This paper fills this gap by deriving novel, necessary optimality conditions for the dual optimisation. We show that these conditions motivate an efficient coordinate-wise algorithm for computing the optimal dual solution, which, in turn, provides the most powerful test for the primal problem. We prove the linear convergence of our algorithm, i.e., the computational complexity of our proposed algorithm is proportional to the logarithm of the reciprocal of the target error. To the best of our knowledge, this is the first time such a fast and computationally efficient algorithm has been proposed for finding the most powerful test with family-wise error rate control. The method's superior power is demonstrated through simulation studies, and its practical utility is shown by identifying new, significant findings in both clinical and financial data applications.

Copulas are the primary tool for dependence modeling in statistics, and quasi-copulas are their essential companions. The latter appear, say, as infima or suprema of sets of copulas; they form a huge class and have some unpleasant properties. Their statistical interpretation is challenged by the fact that they may lead to negative volumes of some boxes. So, numerous applications call for an intermediate class, and supermodular quasi-copulas are one of them, having many useful properties. An excellent measure, Average Rectangular Volume (ARV in short), to clarify and position this class was proposed in the seminal paper by Anzilli and Durante, The average rectangular volume induced by supermodular aggregation functions, J. Math. Anal. Appl. 555 (2026) 21 pp. While supermodularity is a bivariate notion, its extension to the $d$-variate case for $d>2$ was recently emphasized in a key paper by Arias-Garcia, Mesiar, and De Baets, The unwalked path between quasi-copulas and copulas: Stepping stones in higher dimensions, Int. J. of Appr. Reasoning, 80 (2017) pp. 89-99. Here, an alternative method to ARV is presented, extendable to the multivariate case based on Maximal (in absolute value) Negative Volumes (MNV in short) on boxes, thus helping practitioners when seeking the right (quasi-)copula for their problem. Observe that these volumes on copulas are zero, while their values on quasi-copulas, depending on $d$, have been a long-standing open problem solved only recently. We present a nontrivial extension of this solution, which serves as the main goal of this paper: a measure that clarifies and positions the classes considered based on MNV.

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on "hiding" dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test - of which we show the Generalized Covariance Measure underlying many recent tests is nearly a special case - and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type-I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type-I error.

Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require discarding valuable data, unnecessarily reducing test power. We address this long-standing limitation by extending the theory of generalized U-statistics and applying it to the usual MMD estimator, resulting in new characterization of the asymptotic distributions of the MMD estimator with unequal sample sizes (particularly outside the proportional regimes required by previous partial results). This generalization also provides a new criterion for optimizing the power of an MMD test with unequal sample sizes. Our approach preserves all available data, enhancing test accuracy and applicability in realistic settings. Along the way, we give much cleaner characterizations of the variance of MMD estimators, revealing something that might be surprising to those in the area: while zero MMD implies a degenerate estimator, it is sometimes possible to have a degenerate estimator with nonzero MMD as well; we give a construction and a proof that it does not happen in common situations.

We propose a unified framework for global-local regularization that bridges the gap between classical techniques – such as ridge regression and the nonnegative garotte – and modern Bayesian hierarchical modeling. By estimating local regularization strengths via marginal likelihood under order constraints, our approach generalizes Stein's positive-part estimator and provides a principled mechanism for adaptive shrinkage in high-dimensional settings. We establish that this isotonic empirical Bayes estimator achieves near-minimax risk (up to logarithmic factors) over sparse ordered model classes, constituting a significant advance in high-dimensional statistical inference. Applications to orthogonal polynomial regression demonstrate the methodology's flexibility, while our theoretical results clarify the connections between empirical Bayes, shape-constrained estimation, and degrees-of-freedom adjustments.

We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from non-convex spaces defined as convex sets with convex holes. This defines a novel and challenging problem in constrained sampling. To do so, the sampler incorporates a combination of a spatially adaptive temperature and a repulsive drift to ensure that samples remain within the feasible region. Experiments on a 2D Gaussian mixture and multiple-input multiple-output (MIMO) symbol detection showcase the advantages of the proposed shielded LMC in contrast to unconstrained cases.

Unsupervised representation learning seeks to recover latent generative factors, yet standard methods relying on statistical independence often fail to capture causal dependencies. A central challenge is identifiability: as established in disentangled representation learning and nonlinear ICA literature, disentangling causal variables from observational data is impossible without supervision, auxiliary signals, or strong inductive biases. In this work, we propose the Latent Additive Noise Model Causal Autoencoder (LANCA) to operationalize the Additive Noise Model (ANM) as a strong inductive bias for unsupervised discovery. Theoretically, we prove that while the ANM constraint does not guarantee unique identifiability in the general mixing case, it resolves component-wise indeterminacy by restricting the admissible transformations from arbitrary diffeomorphisms to the affine class. Methodologically, arguing that the stochastic encoding inherent to VAEs obscures the structural residuals required for latent causal discovery, LANCA employs a deterministic Wasserstein Auto-Encoder (WAE) coupled with a differentiable ANM Layer. This architecture transforms residual independence from a passive assumption into an explicit optimization objective. Empirically, LANCA outperforms state-of-the-art baselines on synthetic physics benchmarks (Pendulum, Flow), and on photorealistic environments (CANDLE), where it demonstrates superior robustness to spurious correlations arising from complex background scenes.

Joint models are well suited to modelling linked data from laboratories and health registers. However, there are few examples of joint models that allow for (a) multiple markers, (b) multiple survival outcomes (including terminal events, competing events, and recurrent events), (c) delayed entry and (d) scalability. We propose a full likelihood approach for joint models based on a Gaussian variational approximation to satisfy criteria (a)-(d). We provide an open-source implementation for this approach, allowing for flexible sets of models for the longitudinal markers and survival outcomes. Through simulations, we find that the lower bound for the variational approximation is close to the full likelihood. We also find that our approach and implementation are fast and scalable. We provide an application with a joint model for longitudinal measurements of dense and fatty breast tissue and time to first breast cancer diagnosis. The use of variational approximations provides a promising approach for extending current joint models.

A key methodological challenge in observational studies with interference between units is twofold: (1) each unit's outcome may depend on many others' treatments, and (2) treatment assignments may exhibit complex dependencies across units. We develop a general statistical framework for constructing robust causal effect estimators to address these challenges. We first show that, without restricting the patterns of interference, the standard inverse probability weighting (IPW) estimator is the only uniformly unbiased estimator when the propensity score is known. In contrast, no estimator has such a property if the propensity score is unknown. We then introduce a low-rank structure of potential outcomes as a broad class of structural assumptions about interference. This framework encompasses common assumptions such as anonymous, nearest-neighbor, and additive interference, while flexibly allowing for more complex study-specific interference assumptions. Under this low-rank assumption, we show how to construct an unbiased weighting estimator for a large class of causal estimands. The proposed weighting estimator does not require knowledge of true propensity scores and is therefore robust to unknown treatment assignment dependencies that often exist in observational studies. If the true propensity score is known, we can obtain an unbiased estimator that is more efficient than the IPW estimator by leveraging a low-rank structure. We establish the finite sample and asymptotic properties of the proposed weighting estimator, develop a data-driven procedure to select among candidate low-rank structures, and validate our approach through simulation and empirical studies.

Recently, growing consumer awareness of food quality and sustainability has led to a rising demand for effective food authentication methods. Vibrational spectroscopy techniques have emerged as a promising tool for collecting large volumes of data to detect food adulteration. However, spectroscopic data pose significant challenges from a statistical viewpoint, highlighting the need for more sophisticated modeling strategies. To address these challenges, in this work we propose a latent variable model specifically tailored for food adulterant detection, while accommodating the features of spectral data. Our proposal offers greater granularity with respect to existing approaches, since it does not only identify adulterated samples but also estimates the level of adulteration, and detects the spectral regions most affected by the adulterant. Consequently, the methodology offers deeper insights, and could facilitate the development of portable and faster instruments for efficient data collection in food authenticity studies. The method is applied to both synthetic and real honey mid-infrared spectroscopy data, delivering precise estimates of the adulteration level and accurately identifying which portions of the spectra are most impacted by the adulterant.

Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for other non-Gaussian distributions as well, no matter the tails. Motivated by this, we analyse codifference using as little assumptions as possible about the studied model. It leads us to propose its natural domain and three natural variants of it. Using the wide class of variable scale mixture distributions we argue that the codifference can be interpreted as the measure of bulk properties which ignores the tails much more than the covariance. It can also detect forms of non-linear memory which covariance cannot. Finally, we show the asymptotic distribution of its estimator.

Reliable estimation of feature contributions in machine learning models is essential for transparency, algorithmic fairness, and regulatory compliance. While permutation feature importance is widely used, classical implementations rely on repeated Monte Carlo shuffling, introducing significant computational overhead and stochastic instability. In this paper, we show that replacing $B$ random permutations with a single, max-min rank-optimal deterministic permutation maintains or improves correlation with ground-truth importance while eliminating estimation variance and reducing complexity from $O(B \cdot n \cdot p)$ to $O(n \cdot p)$. Under location-scale feature distributions, we formally prove exact recovery of scale-adjusted linear regression coefficients, alongside improved importance estimation under concave model sensitivity. We extend this deterministic framework along two complementary dimensions. First, Systemic Feature Importance (SFI) integrates empirical feature correlations to quantify indirect feature reliance through proxy variables. Second, Importance Direction extends scalar importance to a signed, directional representation by measuring concordance between covariate displacements and output shifts. Extensive empirical validation across nearly 200 simulation scenarios demonstrates superior bias-variance trade-offs in high-dimensional and low signal-to-noise regimes. Finally, two real-world credit risk case studies show how coupling SFI with Importance Direction enables practitioners and regulators to audit models for both the magnitude and net sign of hidden reliance on protected attributes, delivering a principled, transparent, and scalable framework for model governance.

As bonded composite materials are used more frequently for aerospace applications, it is necessary to certify that parts achieve desired levels of certain physical characteristics (e.g., strength) for safety and performance. Nondestructive evaluation (NDE) of adhesively bonded structures enables verification of bond physical characteristics, but uncertainty quantification (UQ) of NDE estimates is crucial for understanding risks, especially for NDE estimates like bond strength. To address the critical need for NDE UQ for adhesive bond strength estimates, we propose an optimization–based approach to computing finite–sample confidence intervals showing the range of bond strengths that could feasibly be produced by the observed data. A statistical inverse model approach is used to compute a confidence interval of specimen interfacial stiffness from swept–frequency ultrasonic phase observations and a method for propagating the interval to bond strength via a known interfacial stiffness regression is proposed. This approach requires innovating the optimization–based confidence interval to handle both a nonlinear forward model and unknown variance and developing a calibration approach to ensure that the final bond strength interval achieves at least the desired coverage level. Using model assumptions in line with current literature, we demonstrate our approach on simulated measurement data using a variety of low to high noise settings under two prototypical parameter settings. Relative to a baseline approach, we show that our method achieves better coverage and smaller intervals in high–noise settings and when a nuisance parameter is near the constraint boundary.

This thesis presents a fundamental rethink of electricity market design at the wholesale and balancing layers. Rather than treating markets as static spot clearing mechanisms, it reframes them as a continuously online, event driven dynamical control system: a two sided marketplace operating directly on grid physics. Existing energy only, capacity augmented, and zonal market designs are shown to admit no shock robust Nash equilibrium under realistic uncertainty, instead relying on price caps, uplift, and regulatory intervention to preserve solvency and security. In response, the thesis develops a holarchic Automatic Market Maker (AMM) in which prices are bounded, exogenous control signals derived from physical tightness rather than emergent equilibrium outcomes. The AMM generalises nodal and zonal pricing through nested scarcity layers, from node to cluster to zone to region to system, such that participant facing prices inherit from the tightest binding constraint. Nodal and zonal pricing therefore emerge as special cases of a unified scarcity propagation rule. Beyond pricing, the AMM functions as a scarcity aware control system and a digitally enforceable rulebook for fair access and proportional allocation under shortage. Fuel costs are recovered through pay as bid energy dispatch consistent with merit order, while non fuel operating and capital costs are allocated according to adequacy, flexibility, and locational contribution. Large scale simulations demonstrate bounded input bounded output stability, controllable procurement costs, zero structural waste, and improved distributional outcomes. The architecture is climate aligned and policy configurable, but requires a managed transition and new operational tools for system operators and market participants.

In this work, we investigate the existence and effect of percolation in training deep Neural Networks (NNs) with dropout. Dropout methods are regularisation techniques for training NNs, first introduced by G. Hinton et al. (2012). These methods temporarily remove connections in the NN, randomly at each stage of training, and update the remaining subnetwork with Stochastic Gradient Descent (SGD). The process of removing connections from a network at random is similar to percolation, a paradigm model of statistical physics. If dropout were to remove enough connections such that there is no path between the input and output of the NN, then the NN could not make predictions informed by the data. We study new percolation models that mimic dropout in NNs and characterise the relationship between network topology and this path problem. The theory shows the existence of a percolative effect in dropout. We also show that this percolative effect can cause a breakdown when training NNs without biases with dropout; and we argue heuristically that this breakdown extends to NNs with biases.

In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem by shifting the stochastic dynamics to the associated subordinator, enabling a parametric estimation procedure without requiring additional assumptions. This reformulation allows for efficient numerical recovery of the likelihood function via Laplace transform inversion, even in models where closed-form transition densities are unavailable. In addition to offering a flexible approach to parameter estimation, we propose a dynamic simulation framework that generates discrete-time trajectories of CSBPs using the same subordinator-based structure.

Clinicians and scientists have traditionally focussed on whether their findings will be replicated and are very familiar with the concept. The probability that a replication study yields an effect with the same sign, or the same statistical significance as an original study depends on the sum of the variances of the effect estimates. On this basis, when P equals 0.025 one-sided and the replication study has the same sample size and variance as the original study, the probability of achieving a one-sided P is less than or equal to 0.025 a second time is only about 0.283, consistent with currently observed modest replication rates. A higher replication probability would require a larger sample size than that derived from current single variance power calculations. However, if the replication study is based on an infinitely large sample size and thus has negligible variance then the probability that its estimated mean is same sign is 1 - P = 0.975. The reasoning is made clearer by changing continuous distributions to discretised scales and probability masses, thus avoiding ambiguity and improper flat priors. This perspective is consistent with Frequentist and Bayesian interpretations and also requires further reasoning when testing scientific hypotheses and making decisions.

Satellite data of atmospheric pollutants are often available only at coarse spatial resolution, limiting their applicability in local-scale environmental analysis and decision-making. Spatial downscaling methods aim to transform the coarse satellite data into high-resolution fields. In this work, two widely used deep learning architectures, the super-resolution deep residual network (SRDRN) and the encoder-decoder-based UNet, are considered for spatial downscaling of tropospheric ozone. Both methods are extended with a lightweight temporal module, which encodes observation time using either sinusoidal or radial basis function (RBF) encoding, and fuses the temporal features with the spatial representations in the networks. The proposed time-aware extensions are evaluated against their baseline counterparts in a case study on ozone downscaling over Italy. The results suggest that, while only slightly increasing computational complexity, the temporal modules significantly improve downscaling performance and convergence speed.

We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional dependences. In structural causal models with discrete classical variables, observational data and even ideal interventions generally fail to answer all counterfactual questions, since different causal parameters can reproduce the same observational and interventional data while disagreeing on counterfactuals. Using a simple binary example, we demonstrate that if the classical variables of interest are encoded in quantum systems and the causal dependence among them is encoded in a quantum oracle, coherently querying the oracle enables the identification of all causal parameters – hence all classical counterfactuals. We generalize this to arbitrary finite cardinalities and prove that coherent probing 1) allows the identification of all two-way joint counterfactuals p(Y_x=y, Y_{x'}=y'), which is not possible with any number of queries to a classical oracle, and 2) provides tighter bounds on higher-order multi-way counterfactuals than with a classical oracle. This work can also be viewed as an extension to traditional quantum oracle problems such as Deutsch–Jozsa to identifying more causal parameters beyond just, e.g., whether a function is constant or balanced. Finally, we raise the question of whether this quantum advantage relies on uniquely non-classical features like contextuality. We provide some evidence against this by showing that in the binary case, oracles in some classically-explainable theories like Spekkens' toy theory also give rise to a counterfactual identifiability advantage over strictly classical oracles.

Chiral photonic metasurfaces provide unique capabilities for tailoring light-matter interactions, which are essential for next-generation photonic devices. Here, we report an advanced optimization framework that combines deep learning and evolutionary algorithms to significantly improve both the design and performance of chiral photonic nanostructures. Building on previous work utilizing a three-layer perceptron reinforced learning and stochastic evolutionary algorithm with decaying changes and mass extinction for chiral photonic optimization, our study introduces a refined pipeline featuring a two-output neural network architecture to reduce the trade-off between high chiral dichroism (CD) and reflectivity. Additionally, we use an improved fitness function, and efficient data augmentation techniques. A comparative analysis between a neural network (NN)-based approach and a genetic algorithm (GA) is presented for structures of different interface pattern depth, material combinations, and geometric complexity. We demonstrate a twice higher CD and the impact of both the corner number and the refractive index contrast at the example of a GaP/air and PMMA/air metasurface as a result of superior optimization performance. Additionally, a substantial increase in the number of structures explored within limited computational resources is highlighted, with tailored spectral reflectivity suggested by our electromagnetic simulations, paving the way for chiral mirrors applicable to polarization-selective light-matter interaction studies.

Model combination offers an alternative to selecting a single forecasting model, particularly when individual models are sensitive to random initialization and hyperparameter choices. We study online aggregation through Follow-the-Leader (FTL) and Hedge-type algorithms, with an application to ensembles of Multi-Frequency Echo State Networks (MFESNs) for macroeconomic forecasting. On the theoretical side, we derive Hoeffding- and Bernstein-type expected-regret bounds for FTL and decreasing Hedge under independent and $\varphi$-mixing expert losses. Under a positive gap between the best expert's expected loss and those of its competitors, the bounds are uniform in the number of forecasting rounds and exhibit logarithmic dependence on the number of experts. Monte Carlo experiments investigate the effects of temporal dependence and the separation between experts' expected losses. Empirically, we construct MFESN ensembles for forecasting U.S. quarterly GDP growth using mixed-frequency macroeconomic and financial indicators. The results show that adaptive aggregation, particularly FTL and AdaHedge, achieves substantial reductions in out-of-sample mean squared forecasting error relative to individual MFESN models and conventional forecast combinations.

We consider statistical tasks in high dimensions whose loss depends on the data only through its projection into a fixed-dimensional subspace spanned by the parameter vectors and certain ground truth vectors. This includes classifying mixture distributions with cross-entropy loss with one and two-layer networks, and learning single and multi-index models with one and two-layer networks. When the data is drawn from an isotropic Gaussian mixture distribution, it is known that the evolution of a finite family of summary statistics under stochastic gradient descent converges to an autonomous ordinary differential equation (ODE), as the dimension and sample size go to $\infty$ and the step size goes to $0$ commensurately. Our main result is that these ODE limits are universal in that this limit is the same whenever the data is drawn from mixtures of arbitrary product distributions whose first two moments match the corresponding Gaussian distribution, provided the initialization and ground truth vectors are coordinate-delocalized. We complement this by proving two corresponding non-universality results. We provide a simple example where the ODE limits are non-universal if the initialization is coordinate aligned. We also show that the stochastic differential equation limits arising as fluctuations of the summary statistics around their ODE's fixed points are not universal.

Composite endpoints that combine recurrent non-fatal events with a terminal event are increasingly used in randomized clinical trials, yet conventional time-to-first event analyses may obscure clinically relevant information. We compared two statistical frameworks tailored to such endpoints: the joint frailty model (JFM) and the last-event assisted recurrent-event win ratio (LWR). The JFM specifies proportional hazards for the recurrent and terminal events linked through a shared frailty, yielding covariate-adjusted, component-specific hazard ratios that account for informative recurrences and dependence with death. The LWR is a nonparametric, prioritized pairwise comparison that incorporates all observed events over follow-up and summarizes a population-level benefit of treatment while respecting a pre-specified hierarchy between death and recurrences. We first assessed the performance of the methods using simulations that varied both the gamma-frailty variance and the event rates. We next illustrated both approaches using two clinical application examples in oncology and cardiology, highlighting how conclusions depend on whether treatment primarily affects recurrent events, mortality, or both. The JFM provided component-specific estimates, while the LWR led to a summary measure of treatment effect with direction. Power was systematically improved with JFM, which thus appeared as the most reliable approach for inference and sample size estimation. Methodological extensions of the LWR to appropriately handle censoring and to formalize causal estimands remain a promising direction for future research.