Papers

Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such hardness, but existing frameworks rely on additive Gaussian perturbations, making them unsuitable for discrete domains. We introduce a new smoothed agnostic learning framework for Boolean inputs, where perturbations are modeled via random bit flips. This defines a natural discrete analogue of smoothed optimality generalizing the Gaussian case. Under strictly subexponential assumptions on the input distribution, we give an efficient algorithm for learning halfspaces in this model, with runtime and sample complexity approximately n raised to a poly(1/(sigma * epsilon)) factor. Previously, such algorithms were known only with strong structural assumptions for the discrete hypercube, for example, independent coordinates or symmetric distributions. Our result provides the first computationally efficient guarantee for smoothed agnostic learning of halfspaces over the Boolean hypercube, bridging the gap between worst-case intractability and practical learnability in discrete settings.

We prove that a denoising diffusion sampler equipped with a sequential bias across the batch dimension is exactly an Euler-Maruyama integrator for overdamped Langevin dynamics. Each reverse denoising step, with its associated spring stiffness, can be interpreted as one step of a stochastic differential equation with an effective time step set jointly by the noise schedule and that stiffness. The learned score then plays the role of the drift, equivalently the gradient of a learned energy, yielding a precise correspondence between diffusion sampling and Langevin time evolution. This equivalence recasts molecular dynamics (MD) in terms of diffusion models. Accuracy is no longer tied to a fixed, extremely small MD time step; instead, it is controlled by two scalable knobs: model capacity, which governs how well the drift is approximated, and the number of denoising steps, which sets the integrator resolution. In practice, this leads to a fully data-driven MD framework that learns forces from uncorrelated equilibrium snapshots, requires no hand-engineered force fields, uses no trajectory data for training, and still preserves the Boltzmann distribution associated with the learned energy. We derive trajectory-level, information-theoretic error bounds that cleanly separate discretization error from score-model error, clarify how temperature enters through the effective spring, and show that the resulting sampler generates molecular trajectories with MD-like temporal correlations, even though the model is trained only on static configurations.

We propose a new Bayesian approach for spatiotemporal areal data with censored and missing observations, where the response is represented as a tensor indexed by spatial units and time points. The method introduces a flexible random effect that combines the spatial dependence structures of the Simultaneous Autoregressive (SAR) and Directed Acyclic Graph Autoregressive (DAGAR) models with a temporal autoregressive component. This formulation brings both spatial models into a unified spatiotemporal framework by expressing them as Gaussian Markov random fields in innovation form, providing an interpretable representation of spatial, temporal, and joint spatiotemporal dependence while preserving the multiway structure of the data. The innovation-based structure enables scalable Bayesian implementation in Stan for datasets of moderate size. Simulation studies show that the proposed model outperforms common ad hoc imputation strategies for censored and missing data. We further illustrate its practical value through an application to carbon monoxide (CO) concentrations, where the proposed framework captures complex spatiotemporal dependence in the presence of censoring and missingness.

Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown excellent performance in these areas, but assimilating data into such models is challenging due to their intractable likelihood functions. This limitation restricts the use of standard Bayesian data assimilation methodologies for DGFMs. To overcome this, we introduce prequential posteriors, based upon a predictive-sequential (prequential) loss function; an approach naturally suited for temporally dependent data which is the focus of forecasting tasks. Since the true data-generating process often lies outside the assumed model class, we adopt an alternative notion of consistency and prove that, under mild conditions, both the prequential loss minimizer and the prequential posterior concentrate around parameters with optimal predictive performance. For scalable inference, we employ easily parallelizable wastefree sequential Monte Carlo (SMC) samplers with preconditioned gradient-based kernels, enabling efficient exploration of high-dimensional parameter spaces such as those in DGFMs. We validate our method on both a synthetic multi-dimensional time series and a real-world meteorological dataset; highlighting its practical utility for data assimilation for complex dynamical systems.

This study proposes a Quantum Fourier Transform (QFT)-enhanced quantum kernel for short-term time-series forecasting. Each signal is windowed, amplitude-encoded, transformed by a QFT, then passed through a protective rotation layer to avoid the QFT/QFT adjoint cancellation; the resulting kernel is used in kernel ridge regression (KRR). Exogenous predictors are incorporated by convexly fusing feature-specific kernels. On multi-station solar irradiance data across Koppen climate classes, the proposed kernel consistently improves median R2 and nRMSE over reference classical RBF and polynomials kernels, while also reducing bias (nMBE); complementary MAE/ERMAX analyses indicate tighter average errors with remaining headroom under sharp transients. For both quantum and classical models, the only tuned quantities are the feature-mixing weights and the KRR ridge alpha; classical hyperparameters (gamma, r, d) are fixed, with the same validation set size for all models. Experiments are conducted on a noiseless simulator (5 qubits; window length L=32). Limitations and ablations are discussed, and paths toward NISQ execution are outlined.

Arnold and Arvanitis (2020) introduced a novel class of bivariate conditionally specified distributions, in which dependence between two random variables is established by defining the distribution of one variable conditional on the other. This conditioning regime was formulated through survival functions and termed the accelerated failure conditionals model. Subsequently, Lakhani (2025) extended this conditioning framework to encompass distributional families whose marginal densities may exhibit unimodality and skewness, thereby moving beyond families with non-increasing densities. The present study builds on this line of work by proposing a conditional survival specification derived from a location-scale distributional family, where the dependence between $X$ and $Y$ arises not only through the acceleration function but also via a location function. An illustrative example of this new specification is developed using a Weibull marginal for $X$. The resulting models are fully characterized by closed-form expressions for their moments, and simulations are implemented using the Metropolis-Hastings algorithm. Finally, the model is applied to a dataset in which the empirical distribution of $Y$ lies on the real line, demonstrating the models' capacity to accommodate $Y$ marginals defined over $\mathbb{R}$.

Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become computationally unfeasible as the system dimension grows. The increasing prevalence of panel data, characterized by multiple related time series, therefore necessitates the development of inference algorithms that are effective for this class of high-dimensional mechanistic models. Nonlinear, non-Gaussian mechanistic models are routinely fitted to time series data but seldom to panel data, despite its widespread availability, suggesting that the practical difficulties for existing procedures are prohibitive. We investigate the use of iterated filtering algorithms for this purpose. We introduce a novel algorithm that contains a marginalization step that mitigates issues arising from particle filtering in high dimensions. Our approach enables likelihood-based inference for models that were previously considered intractable, thus broadening the scope of dynamic models available for panel data analysis.

Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. While such objectives shape first- and second-order statistics of the representation, they largely ignore the local geometry of the underlying data manifold. In this paper, we introduce CurvSSL, a curvature-regularized self-supervised learning framework, and its RKHS extension, kernel CurvSSL. Our approach retains a standard two-view encoder-projector architecture with a Barlow Twins-style redundancy-reduction loss on projected features, but augments it with a curvature-based regularizer. Each embedding is treated as a vertex whose $k$ nearest neighbors define a discrete curvature score via cosine interactions on the unit hypersphere; in the kernel variant, curvature is computed from a normalized local Gram matrix in an RKHS. These scores are aligned and decorrelated across augmentations by a Barlow-style loss on a curvature-derived matrix, encouraging both view invariance and consistency of local manifold bending. Experiments on MNIST and CIFAR-10 datasets with a ResNet-18 backbone show that curvature-regularized SSL yields competitive or improved linear evaluation performance compared to Barlow Twins and VICReg. Our results indicate that explicitly shaping local geometry is a simple and effective complement to purely statistical SSL regularizers.

The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for building efficient and accurate GP models. Inspired by Bayesian bridge regression, we propose the Bayesian Bridge Gaussian Process Regression (B\textsuperscript{2}GPR) model. This framework places $\ell_q$-norm constraints on key GP parameters to automatically induce sparsity and identify active variables. We formulate two distinct versions: one for $q=2$ using conjugate Gaussian priors, and another for $0<q<2$ that employs constrained flat priors, leading to non-standard, norm-constrained posterior distributions. To enable posterior inference, we design a Gibbs sampling algorithm that integrates Spherical Hamiltonian Monte Carlo (SphHMC) to efficiently sample from the constrained posteriors when $0<q<2$. Simulations and a real-data application confirm that B\textsuperscript{2}GPR offers superior variable selection and prediction compared to alternative approaches.

This chapter presents a short overview of real elliptically symmetric (RES) distributions, complemented by circular complex elliptically symmetric (C-CES) and noncircular CES (NC-CES) distributions as complex representations of RES distributions. These distributions are both an extension of the multivariate Gaussian distribution and a multivariate extension of univariate symmetric distributions. They are equivalently defined through their characteristic functions and their stochastic representations, which naturally follow from the spherically symmetric distributions after affine transformations. Particular attention is paid to the absolutely continuous case and to the subclass of compound Gaussian distributions. Results related to moments, affine transformations, marginal and conditional distributions, and summation stability are also presented. Some well-known instances of RES distributions are provided with their main properties. Finally, the estimation of the symmetry center and scatter matrix is briefly discussed through the sample mean (SM), sample covariance matrix (SCM) estimate, maximum estimate (ML), $M$-estimators, and Tyler's $M$-estimators. Particular attention will be paid to the asymptotic Gaussianity of the $M$-estimators of the scatter matrix. To conclude, some hints about the Slepian-Bangs formula are provided.

In causal inference literature, potential outcomes are often indexed by the "elimination of all right-censoring events," leading to the perception that such a restriction is necessary for defining well-posed causal estimands. In this paper, we clarify that this restriction is not required: a well-defined estimand can be formulated without indexing on the elimination of such events. Achieving this requires a more precise classification of right-censoring events than has historically been considered, as the nature of these events has direct implications for identification of the target estimand. We provide a framework that distinguishes different types of right-censoring events from a causal perspective, and demonstrate how this framework relates to censoring definitions and assumptions in classical survival analysis literature. By bridging these perspectives, we provide a clearer understanding of how to handle right-censoring events and provide guidance for identifying causal estimands when right-censored events are present.

With the development of novel therapies such as molecularly targeted agents and immunotherapy, the maximum tolerated dose paradigm that "more is better" does not necessarily hold anymore. In this context, doses and schedules of novel therapies may be inadequately characterized and oncology drug dose-finding approaches should be revised. This is increasingly recognized by health authorities, notably through the Optimus project. We developed a Bayesian dose-finding design, called U-DESPE, which allows to either determine the optimal dosing regimen at the end of the dose-escalation phase, or use of dedicated cohorts for randomizing patients to candidate optimal dosing regimens after that safe dosing regimens have been found. U-DESPE design relies on a dose-exposure model built from pharmacokinetic data using non-linear mixed-effect modeling approaches. Then three models are built to assess the relationships between exposure and the probability of selected relevant endpoints on safety, efficacy, and pharmacodynamics. These models are then combined to predict the different endpoints for every candidate dosing regimens. Finally, a utility function is proposed to quantify the trade-off between these endpoints and to determine the optimal dosing regimen. We applied the proposed method on a clinical trial case study and performed an extensive simulation study to evaluate the operating characteristics of the method.

Community detection is a central task in network analysis, with applications in social, biological, and technological systems. Traditional algorithms rely primarily on network topology, which can fail when community signals are partly encoded in node-specific attributes. Existing covariate-assisted methods often assume the number of clusters is known, involve computationally intensive inference, or are not designed for weighted networks. We propose $\text{C}^4$: Covariate Connectivity Combined Clustering, an adaptive spectral clustering algorithm that integrates network connectivity and node-level covariates into a unified similarity representation. $\text{C}^4$ balances the two sources of information through a data-driven tuning parameter, estimates the number of communities via an eigengap heuristic, and avoids reliance on costly sampling-based procedures. Simulation studies show that $\text{C}^4$ achieves higher accuracy and robustness than competing approaches across diverse scenarios. Application to an airport reachability network demonstrates the method's scalability, interpretability, and practical utility for real-world weighted networks.

Our work introduces SAVeD (Semantically Aware Version Detection), a contrastive learning-based framework for identifying versions of structured datasets without relying on metadata, labels, or integration-based assumptions. SAVeD addresses a common challenge in data science of repeated labor due to a difficulty of similar work or transformations on datasets. SAVeD employs a modified SimCLR pipeline, generating augmented table views through random transformations (e.g., row deletion, encoding perturbations). These views are embedded via a custom transformer encoder and contrasted in latent space to optimize semantic similarity. Our model learns to minimize distances between augmented views of the same dataset and maximize those between unrelated tables. We evaluate performance using validation accuracy and separation, defined respectively as the proportion of correctly classified version/non-version pairs on a hold-out set, and the difference between average similarities of versioned and non-versioned tables (defined by a benchmark, and not provided to the model). Our experiments span five canonical datasets from the Semantic Versioning in Databases Benchmark, and demonstrate substantial gains post-training. SAVeD achieves significantly higher accuracy on completely unseen tables in, and a significant boost in separation scores, confirming its capability to distinguish semantically altered versions. Compared to untrained baselines and prior state-of-the-art dataset-discovery methods like Starmie, our custom encoder achieves competitive or superior results.

Reducing the number of experimental units is one of the three pillars of the 3R principles (Replace, Reduce, Refine) in animal research. At the same time, statistical error rates need to be controlled to enable reliable inferences and decisions. This paper proposes to adopt diagnostic likelihood ratios and the diagnostic odds ratio to statistical hypothesis tests and to adjust it for sample size to obtain a novel measure to quantify for the evidentiary value of one experimental unit. The experimental unit information index (EUII) is based on power, Type-I error and sample size, and has attractive interpretations both in terms of frequentist error rates and Bayesian posterior odds. We introduce the EUII in simple statistical test settings and show that its asymptotic value depends only on the assumed relative effect size under the alternative. We then extend the definition to adaptive designs where early stopping for efficacy or futility may cause reductions in sample size. Application to group-sequential designs show the usefulness of the approach when the goal is to maximize the evidentiary value of one experimental unit. A reanalysis of 2738 animal experiments with simulated results from (post-hoc) interim analyses illustrates the possible savings in sample size.

The increasing use of vine copulas in high-dimensional settings, where the number of parameters is often of the same order as the sample size, calls for asymptotic theory beyond the traditional fixed-$p$, large-$n$ framework. We establish consistency and asymptotic normality of the stepwise maximum likelihood estimator for vine copulas when the number of parameters diverges as $n \to \infty$. Our theoretical results cover both parametric and nonparametric estimation of the marginal distributions, as well as truncated vines, and are also applicable to general estimation problems, particularly other sequential procedures. Numerical experiments suggest that the derived assumptions are satisfied if the pair copulas in higher trees converge to independence copulas sufficiently fast. A simulation study substantiates these findings and identifies settings in which estimation becomes challenging. In particular, the vine structure strongly affects estimation accuracy, with D-vines being more difficult to estimate than C-vines, and estimates in Gumbel vines exhibit substantially larger biases than those in Gaussian vines.

Premium automotive manufacturers face increasingly complex forecasting challenges due to high product variety, sparse variant-level data, and volatile market dynamics. This study addresses monthly automobile demand forecasting across a multi-product, multi-market, and multi-level hierarchy using data from a German premium manufacturer. The methodology combines point and probabilistic forecasts across strategic and operational planning levels, leveraging ensembles of LightGBM models with pooled training sets, quantile regression, and a mixed-integer linear programming reconciliation approach. Results highlight that spatiotemporal dependencies, as well as rounding bias, significantly affect forecast accuracy, underscoring the importance of integer forecasts for operational feasibility. Shapley analysis shows that short-term demand is reactive, shaped by life cycle maturity, autoregressive momentum, and operational signals, whereas medium-term demand reflects anticipatory drivers such as online engagement, planning targets, and competitive indicators, with online behavioral data considerably improving accuracy at disaggregated levels.

Systemic risk measures quantify the potential risk to an individual financial constituent arising from the distress of entire financial system. As a generalization of two widely applied risk measures, Value-at-Risk and Expected Shortfall, the Conditional Value-at-Risk (CoVaR) and Conditional Expected Shortfall (CoES) have recently been receiving growing attention on applications in economics and finance, since they serve as crucial metrics for systemic risk measurement. However, existing approaches confront some challenges in statistical inference and asymptotic theories when estimating CoES, particularly at high risk levels. In this paper, within a framework of upper tail dependence, we propose several extrapolative methods to estimate both extreme CoVaR and CoES nonparametrically via an adjustment factor, which are intimately related to the nonparametric modelling of the tail dependence function. In addition, we study the asymptotic theories of all proposed extrapolative methods based on multivariate extreme value theory. Finally, some simulations and real data analyses are conducted to demonstrate the empirical performances of our methods.

We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints. Second, instead of testing whether the coordinates are pairwise independent, we are interested in determining whether certain pairwise associations between the components (such as all pairwise Kendall's $\tau$ coefficients) do not exceed a given threshold in absolute value. Considering hypotheses of this form is motivated by the observation that in the high-dimensional regime, it is rare and perhaps impossible to have a null hypothesis that can be modeled exactly by assuming that all pairwise associations are precisely equal to zero. The formulation of the null hypothesis as a composite hypothesis makes the problem of constructing tests already non-standard in the non-private setting. Additionally, under privacy constraints, state of the art procedures rely on permutation approaches that are rendered invalid under a composite null. We propose a novel bootstrap based methodology that is especially powerful in sparse settings, develop theoretical guarantees under mild assumptions and show that the proposed method enjoys good finite sample properties even in the high privacy regime. Additionally, we present applications in medical data that showcase the applicability of our methodology.

Extreme heat represents a growing threat to public health as climate change intensifies. While its mortality impacts are well recognised, the interplay between heat, air pollution, and socioeconomic vulnerability remains insufficiently understood. We quantified the associations of extreme maximum temperatures and heatwaves with daily mortality in Catalonia (2012-2022) and evaluated how air pollutants-particularly ozone, nitrogen dioxide and particulate matter-and socioeconomic factors confound or modify this relationship. We conducted a time-series ecological analysis across 379 Basic Health Areas during summer months, linking mortality with meteorological, air pollution and socioeconomic indicators. Hierarchical Bayesian zero-inflated negative binomial models were fitted with nested spatiotemporal random effects (Matérn SPDE field evolving over years; month nested within year; unstructured ABS frailty). Among 210.860 summer deaths in the complete environmental sample, extreme heat and heatwaves were associated with higher mortality after multi-pollutant and socioeconomic adjustment (e.g., extreme heat at lag 2: RR $1.105$, 95% CrI $1.086$-$1.125$; heatwave at lag 3: RR $1.142$, 95% CrI $1.116$-$1.167$; posterior Prob $\approx 1$). Ozone concentrations $\geq 100\,\mu$g/m$^3$ were positively associated with mortality, and extreme heat$\times$high ozone interactions further elevated risk. Areas with higher income inequality and older population structures also showed elevated mortality. These findings indicate that heat indicators raise summer mortality in Catalonia even after environmental and socioeconomic adjustment, while compound ozone exposure and contextual vulnerability further shape risk. Adaptation strategies should therefore combine heat-health warnings with air quality management and equity-oriented interventions.

We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and a proposal distribution derived from an approximate conditional posterior, thereby exploiting the structure of the quasi-likelihood. Two implementations are introduced. DA-MCMC-Exact fully incorporates prior information into the proposal distribution and maximizes per-iteration efficiency, whereas DA-MCMC-Approx omits the prior in the proposal to reduce matrix inversions, improving numerical stability and computational speed in higher dimensions. Simulation studies on heteroskedastic linear regressions show substantial gains over standard MCMC and conventional DA-MCMC baselines, measured by multivariate effective sample size per iteration and per second. The Approx variant yields the best overall throughput, while the Exact variant attains the highest per-iteration efficiency. Applications to two empirical instrumental variable regressions corroborate these findings: the Approx implementation scales to larger designs where other methods become impractical, while still delivering precise inference. Although developed for moment-based quasi-posteriors, the proposed approach also extends to risk-based quasi-Bayesian formulations when first-order conditions are linear and can be transformed analogously. Overall, the proposed algorithms provide a practical and robust tool for quasi-Bayesian analysis in statistical applications.

Traditional boxplots are widely used for summarizing and visualizing the distribution of numerical data, yet they exhibit significant limitations when applied to skewed or heavy-tailed distributions, often leading to misclassification of outliers through swamping – flagging typical observations as outliers – or masking – failing to detect true outliers. This paper addresses these limitations by systematically evaluating several alternative boxplots specifically designed to accommodate distributional asymmetry. We introduce ggskewboxplots, an R package that integrates multiple robust and skewness-aware boxplot variants, providing a unified and user-friendly framework for exploratory data analysis. Using extensive Monte Carlo simulations under controlled skewness and kurtosis conditions, implemented via the mosaic approach based on the Skewed Exponential Power distribution, we assess the sensitivity and specificity of each method. Simulation results indicate that classical Tukey-style boxplots are highly prone to swamping and masking, whereas robust skewness-adjusted variants – particularly those leveraging quartile-based skewness measures or medcouple-based adjustments – achieve substantially better performance. These findings offer practical guidance for selecting reliable boxplot methods in applied settings and demonstrate how the ggskewboxplots package facilitates accessible, distribution-aware visualizations within the familiar ggplot2 workflow.

1. Hidden Markov models (HMMs) are powerful tools for modelling time-series data with underlying state structure. However, selecting appropriate parametric forms for the state-dependent distributions is often challenging and can lead to model misspecification. To address this, P-spline-based nonparametric estimation of state-dependent densities has been proposed. While offering great flexibility, these approaches can result in overly complex densities (e.g. bimodal) that hinder interpretability. 2. We propose a straightforward method that builds on shape-constrained spline theory to enforce unimodality in the estimated state-dependent densities through enforcing unimodality of the spline coefficients. This constraint strikes a practical balance between model flexibility, interpretability, and parsimony. 3. Through two simulation studies and a real-world case study using narwhal (Monodon monoceros) dive data, we demonstrate the proposed approach yields more stable estimates compared to fully flexible, unconstrained models improving model performance and interpretability. 4. Our method bridges a key methodological gap, by providing a parsimonious HMM framework that balances the interpretability of parametric models with the flexibility of nonparametric estimation. This provides ecologists with a powerful tool to derive ecologically meaningful inference from telemetry data while avoiding the pitfalls of overly complex models.

Geometric frameworks for analyzing curves are common in applications as they focus on invariant features and provide visually satisfying solutions to standard problems such as computing invariant distances, averaging curves, or registering curves. We show that for any smooth curve in R^d, d>1, the generalized curvatures associated with the Frenet-Serret equation can be used to define a Riemannian geometry that takes into account all the geometric features of the shape. This geometry is based on a Square Root Curvature Transform that extends the square root-velocity transform for Euclidean curves (in any dimensions) and provides likely geodesics that avoid artefacts encountered by representations using only first-order geometric information. Our analysis is supported by simulated data and is especially relevant for analyzing human motions. We consider trajectories acquired from sign language, and show the interest of considering curvature and also torsion in their analysis, both being physically meaningful.

Empirical claims often rely on one population, design, and analysis. Many-analysts, multiverse, and robustness studies expose how results can vary across plausible analytic choices. Synthesizing these results, however, is nontrivial as all results are computed from the same dataset. We introduce single-dataset meta-analysis, a weighted-likelihood approach that incorporates the information in the dataset at most once. It prevents overconfident inferences that would arise if a standard meta-analysis was applied to the data. Single-dataset meta-analysis yields meta-analytic point and interval estimates of the average effect across analytic approaches and of between-analyst heterogeneity, and can be supplied by classical and Bayesian hypothesis tests. Both the common-effect and random-effects versions of the model can be estimated by standard meta-analytic software with small input adjustments. We demonstrate the method via application to the many-analysts study on racial bias in soccer, the many-analysts study of marital status and cardiovascular disease, and the multiverse study on technology use and well-being. The results show how single-dataset meta-analysis complements the qualitative evaluation of many-analysts and multiverse studies.

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior: the prior offers limited guidance, while reconstruction is largely driven by the measurement-consistency term, leading to an inference process that is effectively decoupled from the diffusion dynamics. We show that the diffusion prior in these solvers functions primarily as a warm initializer that places estimates near the data manifold, while reconstruction is driven almost entirely by measurement consistency. Based on this observation, we introduce DAPS++, which fully decouples diffusion-based initialization from likelihood-driven refinement, allowing the likelihood term to guide inference more directly while maintaining numerical stability and providing insight into why unified diffusion trajectories remain effective in practice. By requiring fewer function evaluations (NFEs) and measurement-optimization steps, DAPS++ achieves high computational efficiency and robust reconstruction performance across diverse image restoration tasks.

Consider nonparametric domain adaptation for regression, which assumes the same conditional distribution of the response given the covariates but different marginal distributions of the covariates. An important goal is to understand how the source data may improve the minimax convergence rate of learning the regression function when the likelihood ratio of the covariate marginal distributions of the target data and the source data are unbounded. A previous work of Pathak et al. (2022) show that the minimax transfer learning rate is simply determined by the faster rate of using either the source or the target data alone. In this paper, we present a new synergistic learning phenomenon (SLP) that the minimax convergence rate based on both data may sometimes be faster (even much faster) than the better rate of convergence based on the source or target data only. The SLP occurs when and only when the target sample size is smaller (in order) than but not too much smaller than the source sample size in relation to the smoothness of the regression function and the nature of the covariate densities of the source and target distributions. Interestingly, the SLP happens in two different ways according to the relationship between the two sample sizes. One is that the target data help alleviate the difficulty in estimating the regression function at points where the density of the source data is close to zero and the other is that the source data (with its larger sample size than that of the target data) help the estimation at points where the density of the source data is not small. Extensions to handle unknown source and target parameters and smoothness of the regression function are also obtained.

Deep equilibrium models (DEQs) have recently emerged as a powerful paradigm for training infinitely deep weight-tied neural networks that achieve state of the art performance across many modern machine learning tasks. Despite their practical success, theoretically understanding the gradient descent dynamics for training DEQs remains an area of active research. In this work, we rigorously study the gradient descent dynamics for DEQs in the simple setting of linear models and single-index models, filling several gaps in the literature. We prove a matrix conservation law for linear DEQs which implies that the parameters remain trapped on spheres along gradient flow and use this property to show that gradient flow remains well-conditioned for all time. We then prove linear convergence of gradient descent to a global minimizer for linear DEQs and deep equilibrium single-index models under appropriate initialization and with a sufficiently small step size. In these simple settings, we also study the effect of common Neumann approximations used to reduce the cost of backpropagation; for linear DEQs, we show that increasing the number of terms in the Neumann approximation can prevent convergence to zero risk, even with exact forward solves. For nonlinear single-index DEQs, we prove linear convergence for fixed Neumann approximations, including Jacobian-free backpropagation under suitable assumptions. Finally, we validate our theoretical findings through experiments.

The Perturbation Discrimination Score (PDS) is increasingly used to evaluate whether predicted perturbation effects remain distinguishable, including in Systema and the Virtual Cell Challenge. However, its behavior in high-dimensional gene-expression settings has not been examined in detail. We show that PDS is highly sensitive to the choice of similarity or distance measure and to the scale of predicted effects. Analysis of observed perturbation responses reveals that $\ell_1$ and $\ell_2$-based PDS behave very differently from cosine-based measures, even after norm matching. We provide geometric insight and discuss implications for future discrimination-based evaluation metrics.

Epidemic risk assessment poses inherent challenges, with traditional approaches often failing to balance health outcomes and economic constraints. This paper presents a data-driven decision support tool that models epidemiological dynamics and optimises vaccination strategies to control disease spread whilst minimising economic losses. The proposed economic-epidemiological framework comprises three phases: modelling, optimising, and analysing. First, a stochastic compartmental model captures epidemic dynamics. Second, an optimal control problem is formulated to derive vaccination strategies that minimise pandemic-related expenditure. Given the analytical intractability of epidemiological models, neural networks are employed to calibrate parameters and solve the high-dimensional control problem. The framework is demonstrated using COVID-19 data from Victoria, Australia, empirically deriving optimal vaccination strategies that simultaneously minimise disease incidence and governmental expenditure. By employing this three-phase framework, policymakers can adjust input values to reflect evolving transmission dynamics and continuously update strategies, thereby minimising aggregate costs, aiding future pandemic preparedness.