Papers

We propose a method for the prediction of stationary max–stable random fields with $\alpha$-Fréchet marginal distribution $H_\alpha$. The method is suitable to cope with heavy tails for $\alpha\in(0,2)$ and is (approximately) exact in marginal distributions. It is based on a recent extrapolation approach via level sets which requires no moment assumptions. An explicit connection between the excursion metric and the Davis-Resnick distance is established. The existence of the predictor is proven. The non-uniqueness of the forecast is demonstrated on several examples. The method is tested on multiple simulated time series and random fields as well as applied to real data of annual maximum precipitation.

In variety testing, multi-environment trials (MET) are essential for evaluating the genotypic performance of crop plants. A persistent challenge in the statistical analysis of MET data is the estimation of variance components, which are often still inaccurately estimated or shrunk to exactly zero when using residual (restricted) maximum likelihood (REML) approaches. At the same time, institutions conducting MET typically possess extensive historical data that can, in principle, be leveraged to improve variance component estimation. However, these data are rarely incorporated sufficiently. The purpose of this paper is to address this gap by proposing a Bayesian framework that systematically integrates historical information to stabilize variance component estimation and better quantify uncertainty. Our Bayesian linear mixed model (BLMM) reformulation uses priors and Markov chain Monte Carlo (MCMC) methods to maintain the variance components as positive, yielding more realistic distributional estimates. Furthermore, our model incorporates historical prior information by managing MET data in successive historical data windows. Variance component prior and posterior distributions are shown to be conjugate and belong to the inverse gamma and inverse Wishart families. While Bayesian methodology is increasingly being used for analyzing MET data, to the best of our knowledge, this study comprises one of the first serious attempts to objectively inform priors in the context of MET data. This refers to the proposed Bayesian updating approach. To demonstrate the framework, we consider an application where posterior variance component samples are plugged into an A-optimality experimental design criterion to determine the average optimal allocations of trials to agro-ecological zones in a sub-divided target population of environments (TPE).

Classical latent-score ranking models often fail to distinguish objects' intrinsic scores from contextual effects, which are typically nonlinear and can dominate the observed outcomes. To address this, we introduce a semiparametric ranking framework in which the log-score of each object is modeled as the sum of a utility parameter and a nonparametric covariate effects. Within this framework, we establish model identifiability under mild regularity and connectivity conditions. For estimation, we approximate the covariate effects using a neural network and estimate the parameters via maximum likelihood. Under random design assumptions, we prove that the resulting estimator exists with high probability and derive non-asymptotic error bounds that achieve minimax optimality for both the parametric and nonparametric components. Numerical experiments on both synthetic data and an ATP tennis dataset are conducted to support our findings.

We study the sample complexity of learning an $\epsilon$-optimal policy in the Stochastic Shortest Path (SSP) problem. We first derive sample complexity bounds when the learner has access to a generative model. We show that there exists a worst-case SSP instance with $S$ states, $A$ actions, minimum cost $c_{\min}$, and maximum expected cost of the optimal policy over all states $B_{\star}$, where any algorithm requires at least $\Omega(SAB_{\star}^3/(c_{\min}\epsilon^2))$ samples to return an $\epsilon$-optimal policy with high probability. Surprisingly, this implies that whenever $c_{\min} = 0$ an SSP problem may not be learnable, thus revealing that learning in SSPs is strictly harder than in the finite-horizon and discounted settings. We complement this lower bound with an algorithm that matches it, up to logarithmic factors, in the general case, and an algorithm that matches it up to logarithmic factors even when $c_{\min} = 0$, but only under the condition that the optimal policy has a bounded hitting time to the goal state.

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of $\mathcal{O}(T^{-1/8})$ on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performance, with the best attainable rate being $\Omega(T^{-1/4})$ in contrast to the usual $\Omega(T^{-1/2})$ rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate up to constant and logarithmic factors. The first algorithm leverages a straightforward trade-off between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.

One of the dominant paradigms in self-supervised learning (SSL), illustrated by MoCo or DINO, aims to produce robust representations by capturing features that are insensitive to certain image transformations such as illumination, or geometric changes. This strategy is appropriate when the objective is to recognize objects independently of their appearance. However, it becomes counterproductive as soon as appearance itself constitutes the discriminative signal. In weather analysis, for example, rain streaks, snow granularity, atmospheric scattering, as well as reflections and halos, are not noise: they carry the essential information. In critical applications such as autonomous driving, ignoring these cues is risky, since grip and visibility depend directly on ground conditions and atmospheric conditions. We introduce ST-STORM, a hybrid SSL framework that treats appearance (style) as a semantic modality to be disentangled from content. Our architecture explicitly separates two latent streams, regulated by gating mechanisms. The Content branch aims at a stable semantic representation through a JEPA scheme coupled with a contrastive objective, promoting invariance to appearance variations. In parallel, the Style branch is constrained to capture appearance signatures (textures, contrasts, scattering) through feature prediction and reconstruction under an adversarial constraint. We evaluate ST-STORM on several tasks, including object classification (ImageNet-1K), fine-grained weather characterization, and melanoma detection (ISIC 2024 Challenge). The results show that the Style branch effectively isolates complex appearance phenomena (F1=97% on Multi-Weather and F1=94% on ISIC 2024 with 10% labeled data), without degrading the semantic performance (F1=80% on ImageNet-1K) of the Content branch, and improves the preservation of critical appearance

To extend cognitive diagnostic models (CDMs) to longitudinal settings, stepwise approaches that integrate a CDM model with a latent transition model and covariates are widely used due to their flexibility. Previous research has shown that stepwise estimation can yield biased results, motivating classification-error correction as a means of improving inference over uncorrected stepwise procedures. In this study, we evaluate a unified Bayesian dynamic cognitive diagnostic model that jointly estimates measurement (item parameters, latent attribute profiles) and transition components (transition parameters) in longitudinal settings with covariates. We compare this joint approach with the bias-corrected stepwise latent transition CDM through a Monte Carlo study. Results demonstrate that joint modeling provides more accurate recovery of transition parameters, particularly under limited test length and sample size, underscoring its advantages for longitudinal diagnostic analysis and offering practical guidance for applied researchers.

This paper examines a stochastic deconvolution problem on compact symmetric spaces which is referred to as decompounding. This involves estimating the step distributions of a random walk, where in addition the number of steps between observations is unknown. The harmonic analysis of symmetric spaces is used to construct an estimator to the problem which converges in mean squared error, extending and improving on the analogous problem on compact Lie groups. The rates of convergence are shown to coincide with asymptotic lower bounds of density estimation in Euclidean space. We provide proofs that while the same rates hold for general density estimation problems in compact symmetric spaces, the decompounding problem lies in a subclass of these with different lower bounds depending on the rank of the space. Consequently, the optimality of the estimator depends on the rank of the symmetric space. Decompounding is a broad problem which appears in applications ranging from mathematical finance to wave optics, and the extension to compact symmetric spaces covers manifolds that commonly appear in the statistics literature.

Fixed Radius Near Neighbor (FRNN) search is an alternative to the widely used k Nearest Neighbors (kNN) search. Unlike kNN, FRNN determines a label or an estimate for a test sample based on all training samples within a predefined distance. While this approach is beneficial in certain scenarios, assuming a fixed maximum distance for all training samples can decrease the accuracy of the FRNN. Therefore, in this paper we propose the Adaptive Radius Near Neighbor (ARNN) and the Weighted ARNN (WARNN), which employ adaptive distances and in latter case weights. All three methods are compared to kNN and twelve of its variants for a regression problem, namely WiFi fingerprinting indoor positioning, using 22 different datasets to provide a comprehensive analysis. While the performances of the tested FRNN and ARNN versions were amongst the worse, three of the four best methods in the test were WARNN versions, indicating that using weights together with adaptive distances achieves performance comparable or even better than kNN variants.

Rooted bifurcating trees are mathematical objects used to model evolutionary relationships and arise naturally in both coalescent theory and phylogenetics. Recent numerical representations of tree topologies, known as F-matrices, allow for summarizing a sample of trees via Fréchet means and provide new measures of tree balance. However, the number of ranked unlabelled trees grows super-exponentially with the number of leaves. This makes computation intensive and current methods rely on mixed integer programming and simulation-based methods. Moreover, F-matrices are difficult to interpret, and their distribution is only described in terms of first- and second-order moments under neutral branching. In this paper, we introduce a Markov chain embedding of ranked and unlabelled trees that drastically decreases the size of the state space. Leveraging this embedding, we develop an algorithm that efficiently computes all Fréchet means and use discrete phase-type theory to obtain the joint distribution of tree balance indices. We also use discrete phase-type theory to generalize previous results regarding moments of F-matrices to arbitrary order for any time homogeneous and bifurcating coalescent model. Using this framework, we construct three tests for neutrality and demonstrate their improved power compared to previous methods on simulated data.

We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the thermodynamic limit. This perspective provides a general, order-parameter-free framework that does not rely on model-specific insights or learning procedures. We show that conventional approaches, such as those based on the Binder parameter, can be reinterpreted as special cases within this framework. As a concrete realization, we employ a distribution-free two-sample run test and demonstrate that the critical point of the two-dimensional Ising model is accurately identified without prior knowledge of the order parameter.

In finite-width deep neural networks, the empirical kernel $G$ evolves stochastically across layers. We develop a collective kernel effective field theory (EFT) for pre-activation ResNets based on a $G$-only closure hierarchy and diagnose its finite validity window. Exploiting the exact conditional Gaussianity of residual increments, we derive an exact stochastic recursion for $G$. Applying Gaussian approximations systematically yields a continuous-depth ODE system for the mean kernel $K_0$, the kernel covariance $V_4$, and the $1/n$ mean correction $K_{1,\mathrm{EFT}}$, which emerges diagrammatically as a one-loop tadpole correction. Numerically, $K_0$ remains accurate at all depths. However, the $V_4$ equation residual accumulates to an $O(1)$ error at finite time, primarily driven by approximation errors in the $G$-only transport term. Furthermore, $K_{1,\mathrm{EFT}}$ fails due to the breakdown of the source closure, which exhibits a systematic mismatch even at initialization. These findings highlight the limitations of $G$-only state-space reduction and suggest extending the state space to incorporate the sigma-kernel.

We propose a testing and estimation methodology for univariate and bivariate symmatric $\alpha$-stable distributions using a modified version of the Greenwood statistic. Originally designed for positive-valued random variables, the Greenwood statistic, and its modified version tailored for symmetric distributions, have been predominantly applied to univariate random samples. In this paper, we extend the modified Greenwood statistic to a bivariate setting and examine its probabilistic properties within the class of $\alpha$-stable distributions, with a focus on the sub-Gaussian case. Additionally, we introduce a novel testing approach that considers two variations of the modified Greenwood statistic as test statistics for the bivariate case. In the univariate setting, we adapt the proposed testing methodology for estimating the stability index. The simulation studies presented demonstrate that our proposed methodology outperforms classical approaches previously used in this context and serves as an effective tool for distinguishing between Gaussian and $\alpha$-stable distributions with a stability index close to 2. The theoretical and simulation results are further illustrated with practical data examples.

We study the polynomial coefficients of lightning self-attention as coordinates of an algebraic variety. In the single-token case, we characterize the coefficient variety as a rank-constrained Chow-type variety and derive algebraic equations from this description. For multiple tokens, linear relations reduce the nonlinear geometry to coefficients involving interactions between distinct tokens. We characterize the resulting variety by a common linear factor together with a low-rank condition on the remaining factors. This structure yields explicit families of determinantal, Veronese-type, and Sylvester resultant-based invariants. In the rank-one case, natural pencil and flattening equations define the variety set-theoretically. We complement these results with computations in small dimensions, where the theoretical constructions recover the generators of the defining ideals. Overall, the paper gives a structural description of the algebraic constraints imposed on polynomial coefficient arrays by lightning self-attention and provides explicit certificates of non-realizability.

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across a range of scales, including count data collected across a series of fixed sampling regions to characterize population-level dispersal, as well as individual trajectory data to examine at the motion of individuals within a diffusive population. In this work we consider a lattice-based random walk model and examine the extent to which model parameters can be determined by collecting count data and/or trajectory data. Our analysis combines agent-based stochastic simulations, mean-field partial differential equation approximations, likelihood-based estimation, identifiability analysis, and model-based prediction. These combined tools reveal that working with count data alone can sometimes lead to challenges involving structural non-identifiability that can be alleviated by collecting trajectory data. Furthermore, these tools allow us to explore how different experimental designs impact inferential precision by comparing how different trajectory data collection protocols affects practical identifiability. Open source implementations of all algorithms used in this work are available on GitHub.

We present "Sequestering CARbon through Forests, AgriCulture, and land usE (SCARFACE)", a harmonized spatio-temporal dataset that integrates climate, air quality, airborne pollutant emissions, land cover, soil properties, agro-industry dynamics and socio-economic indicators, to jointly investigate interconnected processes linking agricultural systems, atmospheric dynamics, emissions, and socioeconomic conditions in the Po Valley, Northern Italy. The spatial reference unit is the Agrarian Sub Region (ASR), that is, groups of contiguous municipalities that are considered homogeneous with respect to physical geography, agronomic characteristics, and prevailing agricultural production systems. The dataset adopts an annual panel structure from 2011 to 2024 defined over the 256 ASRs partitioning the Po Valley and comprises more than 2,700 indicators sourced from national and international public institutions. Heterogeneous data are harmonized within a processing workflow, tailored to the specific characteristics of each dataset, that guarantee spatial and temporal consistency of the output dataset. The resource supports reuse in applied econometrics, spatio-temporal modeling, clustering, and policy analysis focused on agriculture, air quality, and land use in a major European hotspot.

External validation is widely regarded as the gold standard for prognostic model evaluation. In this study, we challenge the assumption that successful external calibration guarantees model generalizability and propose two complementary strategies to improve transportability of prognostic models across cohorts. Using six real-world surgical cohorts from tertiary academic centers, we tested whether successful external calibration depends largely on similarity in covariates and outcomes between training and validation cohorts, quantified using Kullback-Leibler (KL) divergence, with calibration assessed by the Integrated Calibration Index (ICI). From the model-developer's perspective, we trained the "best-on-average" prognostic model by tuning toward a meta-analysis-derived covariate and outcome distribution as an approximation of the broader target population. From the end-user perspective, we proposed a simple measure for cohort outcome similarity to identify, among published models, the one most suitable for a given target cohort in terms of both calibration and clinical utility. External calibration worsened as distributional mismatch increased. Higher KL divergence was associated with higher ICI in both surgery-alone (Spearman $\rho=0.614$, $p=0.004$) and surgery + adjuvant chemotherapy cohorts (Spearman $\rho=0.738$, $p<0.001$). Meta-analysis-informed weighting improved calibration in most settings without materially affecting discrimination, with the clearest benefit when evaluated on the aggregated external population ($p=0.037$). Models developed in more similar cohorts achieved lower ICI in surgery-alone (Spearman $\rho=0.803$, $p<0.001$) and surgery + adjuvant chemotherapy cohorts (Spearman $\rho=0.737$, $p<0.001$), and provided greater clinical utility on DCA.

This paper presents a comprehensive review of univariate process capability indices (PCIs), which are critical metrics for assessing how effectively a manufacturing process satisfies customer specifications based on a single quality characteristic. The primary objective of this review is to develop practical procedural workflows for conducting process capability analysis under various preconditions, including those less frequently addressed scenarios in existing literature. Key analytical components, such as outlier detection, normality test, and best distribution fitting, are integrated into the proposed framework to ensure accurate and robust capability assessments. By systematically evaluating a range of methodologies, this study offers guidance for researchers and practitioners in selecting the most appropriate PCIs for specific process conditions. Ultimately, the work aims to simplify the complexity of PCI analysis while enhancing its precision and utility in quality control and process improvement efforts.

Supervised No Free Lunch Theorems (NFLTs) are well studied, yet unsupervised NFLTs remain underexplored. For elliptical distributions, we prove that there exist two equally optimal, scientifically meaningful bump-hunting strategies that are exact opposites, with no universal winner. Specifically, peeling $k$ orthogonal dimensions from $\mathbb{R}^d$ ($d \ge k$), retaining an inter-quantile region of probability $1-\alpha$ per peeled dimension, maximizes total variance and Frobenius norm when the $k$ smallest principal components (called pettiest components) are selected, and minimizes them when the selected dimensions are the $k$ leading principal components. These optima inspire PRIM-based bump-hunting algorithms either by minimizing variance or by minimizing volume, thereby motivating an NFLT. We test our results on the Fashion-MNIST database, showing that peeling the largest principal components captures multiplicity, while peeling the smallest principal components isolates popular styles.

Adaptive specification search generates statistically significant backtests even under martingale-difference nulls. We introduce a falsification audit testing complete predictive workflows against synthetic reference classes, including zero-predictability environments and microstructure placebos. Workflows generating significant walk-forward evidence in these environments are falsified. For passing workflows, we quantify selection-induced performance inflation using an absolute magnitude gap linking optimized in-sample evidence to disjoint walk-forward realizations, adjusted for effective multiplicity. Simulations validate extreme-value scaling under correlated searches and demonstrate detection power under genuine structure. Empirical case studies confirm that many apparent findings represent methodological artifacts rather than genuine predictability.

Home eviction poses a significant threat to housing stability, a critical determinant of health. This study examines the relationship between eviction and health and substance use within the unhoused population of King County, Washington. Using a sample of 1,106 individuals experiencing homelessness, we employed a quasi-experimental design to compare the health outcomes of those who have experienced eviction with those who have not. Our findings reveal eviction is associated with an 8.3% point increase (SE = 0.039) in the likelihood of reporting poor general health and an 9.5% increase (SE = 0.032) in substance use disorder. No significant effect was found for mental health outcomes. While these results highlight the severe health risks linked to eviction, further research with more precise estimates is necessary to better understand long-term effects. These findings contribute to the growing evidence of how home eviction undermines the well-being of vulnerable populations.

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior distributions to changes in prior assumptions by tracking how a sample representation of the posterior changes as the prior parameters change. This enables sensitivity analysis for small perturbations in the prior, providing insights into the robustness of the posterior estimates under minor changes in assumptions. It also allows solution continuation when dealing with significant alterations in prior beliefs, facilitating a comprehensive understanding of how large shifts in assumptions affect the posterior distribution. We focus on a class of non-conjugate hierarchical models tailored to encourage sparsity in linear inverse problems. The specific hierarchical model of interest is chosen since it is parameterized by a small number of shape parameters, and includes most classical sparsity promoting priors as special cases. As the shape parameters change, the posterior can transition continuously from a tractable unimodal distribution to an intractable multimodal distribution. To track the change in the posterior, we adopt particle based variational inference methods, specifically Stein Variational Gradient Descent (SVGD). SVGD iteratively updates a set of samples to minimize the KL-divergence away from a desired target distribution. We augment SVGD by Birth-Death sampling, which can efficiently exchange mass between separated modes, while simultaneously optimizing the kernel bandwidth used to derive the SVGD update. This method enables the discovery of new modes by tracing the modes as they branch out of a simpler, unimodal posterior, derived within the same family of priors.

This work develops a block aggregation approach to spatial estimation and prediction when the response is observed at a coarse spatial scale, for example as counts of events in administrative areas, or blocks, while covariates are available at a finer spatial resolution, typically as raster images. Our approach specifies a linear predictor at the finer resolution as a combination of covariate effects and a latent, spatially continuous Gaussian process. This linear predictor then determines the distribution of the response through an inverse link function and spatial integration. We use a simulation study to evaluate the performance of the proposed approach in comparison to two industry standard approaches: a traditional geostatistical model that associates each response with the centroid of its block; and a Markov random field (MRF) approach that aggregates covariate data to block-level. As expected, the differences in performance among the three approaches are small with respect to block-level prediction. The rationale for, and advantage of, the block aggregation approach lies in its delivery of reliable inferences at whatever spatial resolution is required in a particular application. We describe two applications: a linear Gaussian sampling model of wastewater virus concentrations in England, using population density as covariate; and log-linear Poisson model of cardiovascular hospitalisations in England using socio-demographic variables at fine-scale administrative units as covariates.

We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure $P_0$ to a target measure $P_1$ by integrating a velocity field of the form $v_t(x) = \mathbb{E}[\dot X_t \mid X_t = x]$, where $X_\bullet = (X_t)_t$ is a stochastic process satisfying $(X_0,X_1)\sim{P_0}\otimes{P_1}$ and $\dot X_t$ is its time derivative. We investigate when $X_\bullet$ induces a straight-line flow: a flow whose pointwise acceleration vanishes and is therefore exactly integrable by any first-order method. First, we develop multiple characterizations of straight-line flows in terms of PDEs involving the conditional statistics of the process. Then, we prove that straight-line flows under endpoint independence exhibit a sharp dichotomy. On the one hand, we construct explicit, computable straight-line processes for arbitrary Gaussian endpoints. On the other hand, we show that straight-line processes do not exist for targets with sufficiently well-separated modes. We demonstrate this obstruction through a sequence of increasingly general impossibility theorems that uncover a fundamental relationship between the sample-path behavior of a process with independent endpoints and the space-time geometry of this process' flow map. Taken together, these results provide a structural theory of when straight-line generative flows can, and cannot, exist.

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss landscapes. We propose a lightweight curvature-aware optimization framework that augments existing first-order optimizers with an adaptive predictive correction based on secant information. Consecutive gradient differences are used as a cheap proxy for local geometric change, together with a step-normalized secant curvature indicator to control the correction strength. The framework is plug-and-play, computationally efficient, and broadly compatible with existing optimizers, without explicitly forming second-order matrices. Experiments on diverse PDE benchmarks show consistent improvements in convergence speed, training stability, and solution accuracy over standard optimizers and strong baselines, including on the high-dimensional heat equation, Gray–Scott system, Belousov–Zhabotinsky system, and 2D Kuramoto–Sivashinsky system.

Pearl's front-door criterion provides a set of sufficient conditions for estimating the total causal effect from observational data in the presence of latent confounding, using the functional P(y | do(x := x*)) = \sum_z P(z | x*) \sum_x P(y | x, z) P(x). An open question is whether these conditions can be generalized to be both necessary and sufficient for the validity of this functional, similar to the generalization achieved for the back-door adjustment criterion by Shpitser. In this paper, we present a new, weakened set of graph-based conditions sufficient for the front-door formula to estimate the total causal effect, expanding the scope of problems amenable to front-door identification.

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product orthonormal basis, the fitted decision function can be expanded exactly in intrinsic RKHS coordinates. This leads to Orthogonal Representation Contribution Analysis (ORCA), a diagnostic framework based on normalized Orthogonal Kernel Contribution (OKC) indices. These indices quantify how the squared RKHS norm of the classifier is distributed across interaction orders, total polynomial degrees, marginal coordinate effects, and pairwise contributions. The methodology is fully post-training and requires neither surrogate models nor retraining. We illustrate its diagnostic value on a synthetic double-spiral problem and on a real five-dimensional echocardiogram dataset. The results show that the proposed indices reveal structural aspects of model complexity that are not captured by predictive accuracy alone.

The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to fully learn the state. Rather than arbitrary unknown states, modern quantum learning theory often considers structured classes of states and exploits such structure to develop learning algorithms that outperform general-state tomography. This raises the question: How do the sample complexities of learning and cloning relate for such structured classes? We answer this question for an important class of states. Namely, for $n$-qubit stabilizer states, we show that the optimal sample complexity of cloning is $\Theta(n)$. Thus, also for this structured class of states, cloning is as hard as learning. To prove these results, we use representation-theoretic tools in the recently proposed Abelian State Hidden Subgroup framework and a new structured version of the recently introduced random purification channel to relate stabilizer state cloning to a variant of the sample amplification problem for probability distributions that was recently introduced in classical learning theory. This allows us to obtain our cloning lower bounds by proving new sample amplification lower bounds for classes of distributions with an underlying linear structure. Our results provide a more fine-grained perspective on No-Cloning theorems, opening up connections from foundations to quantum learning theory and quantum cryptography.

We study the problem of learning minimax policies in zero-sum matrix games. Fiegel et al. (2025) recently showed that achieving last-iterate convergence in this setting is harder when the players are uncoupled, by proving a lower bound on the exploitability gap of Omega(t^{-1/4}). Some online mirror descent algorithms were proposed in the literature for this problem, but none have truly attained this rate yet. We show that the use of a log-barrier regularization, along with a dual-focused analysis, allows this O-tilde(t^{-1/4}) convergence with high-probability. We additionally extend our idea to the setting of extensive-form games, proving a bound with the same rate.

Non-parametric approaches to test for trends in time series make use of the Mann-Kendall statistic. Based on asymptotic arguments, these tests assume that its distribution follows a Gaussian distribution, even for autocorrelated time series. Recent results on the lack of validity of this assumption urge a robustness analysis of these approaches. While the issue is relevant across a wide range of applications, we illustrate it here in the context of detecting early warning signals (EWS) of critical transitions, which are used across a variety of research domains, and where commonly applied methods generate autocorrelation. We present a broad analysis, covering all types of critical transitions commonly investigated in EWS studies. We compare empirical distributions of the Mann-Kendall statistic computed from classical EWS indicators preceding critical transitions to the theoretical distributions hypothesized by Mann-Kendall tests. We detect mismatches leading to inflated type I error rates, which would routinely lead to announcing a critical transition while it is not occurring. In contrast to a recent recommendation, we conclude that the use of Mann-Kendall tests for trend detection in the context of forecasting critical transitions should be avoided. We point out several alternative methods available instead.