Papers

We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test the resulting residuals for marginal independence. This approach yields tests that are sensitive to a broad range of conditional dependencies. Existing methods, however, rely heavily on kernel ridge regression, which is computationally expensive when properly tuned and yields poorly calibrated tests when left untuned, which limits their practical usefulness. We propose the Generalised Kernel Covariance Measure (GKCM), a regression-model-agnostic kernel-based CI test that accommodates a broad class of regression estimators. Building on the Generalised Hilbertian Covariance Measure framework (Lundborg et al., 2022), we characterise conditions under which GKCM satisfies uniform asymptotic level guarantees. In simulations, GKCM paired with tree-based regression models frequently outperforms state-of-the-art CI tests across a diverse range of data-generating processes, achieving better type I error control and competitive or superior power.

Using a modification of Stein's method, we generalize the results of Bentkus, Götze, and Tikhomirov \cite{bentkus1997berry} to obtain Berry-Esseen bounds for a broad class of statistics of sequences of $\phi$-mixing, non-stationary random variables with polynomial mixing rates. %and linear variance. We then consider applications of this theorem to ensure Berry-Esseen rates for various classes of non-stationary $\phi$-mixing random variables, including rates for a general class of processes of $\phi$-mixing random variables satisfying an aggregate third moment bound.

We develop likelihood-based bias reduction for nonlinear panel models with additive individual and time effects. In two-way panels, integrated-likelihood corrections are attractive but challenging because the required integration is high dimensional and standard Laplace approximations may fail when the parameter dimension grows with the sample size. We propose a target-centered full-exponential Laplace–cumulant expansion that exploits the sparse higher-order derivative structure implied by additive effects, delivering a tractable approximation with a negligible remainder under large-$N,T$ asymptotics. The expansion motivates robust priors that yield bias reduction for both common parameters and fixed effects. We provide implementations for binary, ordered, and multinomial response models with two-way effects. For average partial effects, we show that the remaining first-order bias has a simple variance form and can be removed by a closed-form adjustment. Monte Carlo experiments and an empirical illustration show substantial bias reduction with accurate inference.

Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity driven by latent trend and periodic components. Traditional Euclidean time series methods fail to account for the intrinsic non-Euclidean geometry of the sphere, leaving a critical gap in rigorous methodologies for modelling and forecasting nonstationary spherically embedded time series. To address this methodological gap, we propose a unified geometric framework to analyse nonstationary spherically embedded time series. Central to our approach is a novel nonparametric spherical trend-periodicity decomposition model that uses an optimal-transport-based removal operation to sequentially extract the smooth trend and periodic components while preserving spherical topology. The resulting de-trended and de-seasonalised stationary residuals can be further modelled using a spherical autoregressive model, formalising a novel trend-periodic spherical autoregressive model. Theoretical foundations for the modelling procedure are established on the consistency under temporal dependence. Extensive simulations corroborate these theoretical guarantees and demonstrate the superior finite-sample predictive performance of the trend-periodic spherical autoregressive model. Finally, we validate the practical utility of our methodology through applications to electricity generation compositions and bike trip volume profiles, yielding significantly enhanced forecasting accuracy while providing interpretable insights into the underlying structural dynamics.

Fréchet regression, or conditional Barycenters, is a flexible framework for modeling relationships between covariates (usually Euclidean) and response variables on general metric spaces, e.g., probability distributions or positive definite matrices. However, in contrast to classical barycenter problems, computing conditional counterparts in many non-Euclidean spaces remains an open challenge, as they yield non-convex optimization problems with an affine structure. In this work, we study the existence and computation of conditional barycenters, specifically in the space of positive-definite matrices with the Bures-Wasserstein metric. We provide a sufficient condition for the existence of a minimizer of the conditional barycenter problem that characterizes the regression range of extrapolation. Moreover, we further characterize the optimization landscape, proving that under this condition, the objective is free of local maxima. Additionally, we develop a projection-free and provably correct algorithm for the approximate computation of first-order stationary points. Finally, we provide a stochastic reformulation that enables the use of off-the-shelf stochastic Riemannian optimization methods for large-scale setups. Numerical experiments validate the performance of the proposed methods on regression problems of real-world biological networks and on large-scale synthetic Diffusion Tensor Imaging problems.

We develop a framework for quantifying omitted variable bias (OVB) in nonlinear instrumental variable (IV) estimators, including the local average treatment effect (LATE), the LATE for the treated (LATT), and the partially linear IV model (PLIVM). Extending sensitivity analysis beyond linear settings, we derive bias decompositions, establish partial identification bounds, and construct OVB-adjusted confidence intervals. We estimate OVB bounds and conduct inference using double machine learning (DML), allowing flexible control for high-dimensional covariates. An application to the U.S. Job Training Partnership Act (JTPA) experiment shows that, at conventional significance levels, first-stage compliance estimates are robust to omitted variables, whereas intention-to-treat and treatment effects are more sensitive. Program impacts are robust and significant for females but fragile for males.

This study surveys the historical development of regularization, tracing its evolution from stepwise regression in the 1960s to recent advancements in formal error control, structured penalties for non-independent features, Bayesian methods, and l0-based regularization (among other techniques). We empirically evaluate the performance of four canonical frameworks – Ridge, Lasso, ElasticNet, and Post-Lasso OLS – across 134,400 simulations spanning a 7-dimensional manifold grounded in eight production-grade machine learning models. Our findings demonstrate that for prediction accuracy when the sample-to-feature ratio is sufficient (n/p >= 78), Ridge, Lasso, and ElasticNet are nearly interchangeable. However, we find that Lasso recall is highly fragile under multicollinearity; at high condition numbers (kappa) and low SNR, Lasso recall collapses to 0.18 while ElasticNet maintains 0.93. Consequently, we advise practitioners against using Lasso or Post-Lasso OLS at high kappa with small sample sizes. The analysis concludes with an objective-driven decision guide to assist machine learning engineers in selecting the optimal scikit-learn-supported framework based on observable feature space attributes.

Regression discontinuity (RD) analysis with latent variables as introduced by Morell et al. (2025), offers a useful augmentation of the conventional RD by incorporating measurement model. This approach is particularly relevant in education research, where noisy proxy (e.g., observed test score) of underlying latent construct is adopted for the running variable. This extension enables extrapolation of average treatment effect (ATE) away from the cutoff score and assessment of heterogeneous treatment effects. However, a key limitation of the original framework is its single-level structure, which does not account for the multilevel structure commonly found in education data, such as students nested within classrooms or schools. In this study, we extend the framework to multilevel contexts. We discuss models for both hierarchical RD design, where treatment is assigned at the cluster level, and multisite RD design, where treatment is assigned at the individual level within clusters. In both cases, multilevel measurement model is incorporated to describe the relationship between the latent running variable and observed indicators. Monte Carlo simulations demonstrate recovery of ATEs including extrapolated estimates beyond the cutoff given adequate cluster-level sample sizes. The study highlights the applicability of RD analysis with latent variables for broader use in educational research, without being restricted by the limitations of multilevel data.

Ultra-high-dimensional genomic studies require simultaneous identification of sparse signals, control of spurious discoveries, and computationally feasible inference when the number of predictors can reach hundreds of thousands or more. We propose Bayesian Univariate-Guided Sparse Regression (BUGS), a global–local shrinkage framework that incorporates marginal association information directly into the prior through continuous modulation of shrinkage. By embedding univariate guidance within the nonlinear variance structure of a regularized horseshoe prior, BUGS adaptively differentiates predictors with strong and weak marginal evidence without relying on hard screening. We establish theoretical results on prior concentration, posterior contraction, and guidance-induced shrinkage separation, and characterize the behavior of the prior under uninformative guidance. For ultra-high-dimensional problems, we develop BUGS-Active, an active-set MCMC approximation that reduces the cost of local-scale updates from $O(p)$ to $O(|A_n|)$ while retaining global coefficient updates. Simulations under independent and correlated designs show strong signal recovery and substantially lower empirical false discovery rates relative to competing methods. We apply BUGS-Active to a DNA methylation study of developmental age with $n=1051$ samples and approximately $850{,}000$ CpG sites, jointly analyzing all probes without pre-screening. The analysis yields strong out-of-sample prediction and a sparse set of age-associated CpG sites with stable posterior support. These results illustrate the practical value of marginally guided Bayesian shrinkage for large-scale genomic regression.

We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility when transitions depend on nonlinear and context-dependent effects. We replace this assumption with learned functions $f_0, f_1 \in \calH$, where $\calH$ is either a reproducing kernel Hilbert space or a spline approximation space, and define transition probabilities as $p_{jk,t} = \sigmoid(f(\bx_{t-1}))$. The transition functions are estimated jointly with emission parameters using a generalized Expectation-Maximization algorithm. The E-step uses the standard forward-backward recursion, while the M-step reduces to a penalized regression problem with weights from smoothed occupation measures. We establish identifiability conditions and provide a consistency argument for the resulting estimators. Experiments on synthetic data show improved recovery of nonlinear transition dynamics compared to parametric baselines. An empirical study on financial time series demonstrates improved regime classification and earlier detection of transition events.

We study identification and inference in nonlinear dynamic systems defined on unknown interaction networks. The system evolves through an unobserved dependence matrix governing cross-sectional shock propagation via a nonlinear operator. We show that the network structure is not generically identified, and that identification requires sufficient spectral heterogeneity. In particular, identification arises when the network induces non-exchangeable covariance patterns through heterogeneous amplification of eigenmodes. When the spectrum is concentrated, dependence becomes observationally equivalent to common shocks or scalar heterogeneity, leading to non-identification. We provide necessary and sufficient conditions for identification, characterize observational equivalence classes, and propose a semiparametric estimator with asymptotic theory. We also develop tests for network dependence whose power depends on spectral properties of the interaction matrix. The results apply to a broad class of economic models, including production networks, contagion models, and dynamic interaction systems.

Quasi-experimental evaluations are central for generating real-world causal evidence and complementing insights from randomized trials. The regression discontinuity design (RDD) is a quasi-experimental design that can be used to estimate the causal effect of treatments that are assigned based on a running variable crossing a threshold. Such threshold-based rules are ubiquitous in healthcare, where predictive and prognostic biomarkers frequently guide treatment decisions. However, standard RD estimators rely on complete outcome data, an assumption often violated in time-to-event analyses where censoring arises from loss to follow-up. To address this issue, we propose a nonparametric approach that leverages doubly robust censoring corrections and can be paired with existing RD estimators. Our approach can handle multiple survival endpoints, long follow-up times, and covariate-dependent variation in survival and censoring. We discuss the relevance of our approach across multiple areas of applications and demonstrate its usefulness through simulations and the prostate component of the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial where our new approach offers several advantages, including higher efficiency and robustness to misspecification. We have also developed an open-source software package, $\texttt{rdsurvival}$, for the $\texttt{R}$ language.

While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence sets for cluster labels. The key challenge is that labels are unobserved and estimated from data, so naively using deterministic cluster labels can violate exchangeability and induce severe under-coverage. To address this, we propose split conformal clustering with stochastic labels, which samples labels from soft cluster labels, fits a soft classifier to predict these stochastic labels, and calibrates conformal scores to construct confidence sets for cluster labels at any query point. We establish a finite-sample lower bound on marginal coverage that reveals how under-coverage is controlled by two properties of the clustering algorithm: consistency of estimated soft labels and replace-one stability. Under mild conditions, we prove asymptotic coverage and verify these conditions for correctly specified parametric mixture models. Simulations for mixture models show that our method attains target coverage with informative set sizes, validating our theoretical results. Applications to clustering cell types in single-cell RNA-seq data demonstrate the practical utility and interpretability of our approach to quantifying cluster label uncertainty.

This systematic review synthesized empirical evidence on human ability to distinguish generative artificial intelligence content from human produced content across text, image, and voice modalities. A structured search of Scopus identified 22,541 records from 2025 to 2026, of which 1200 were screened and 30 studies were included. Across these studies, human detection accuracy varied widely but generally clustered around chance performance. Overall, the literature shows that humans are generally unreliable detectors of gen AI content, raising broader questions about whether the ability to tell should matter for how we evaluate or trust content.

Quantitative research in the social and behavioral sciences relies heavily on nonlinear posterior functionals such as indirect effects, standardized coefficients, effect sizes, intraclass correlations, and multilevel variance-explained measures. The posterior standard deviation (PostSD) is the default uncertainty summary for these quantities, yet it presupposes a correctly specified model. When the working model is wrong, as is common with behavioral data that exhibit heavy tails and heteroskedasticity, PostSD can severely underestimate the frequentist standard error. The nonparametric bootstrap offers robustness but requires repeated MCMC refits, while the delta method demands a separate analytic gradient derivation for every new functional. The infinitesimal jackknife standard error (Giordano & Broderick, 2023) sidesteps both limitations: it approximates the bootstrap variance through influence functions computed from a single MCMC run, applies to any posterior functional without modification, and requires no analytic derivatives. We discuss the use the IJSE methodology at both the observation level and the cluster level and evaluate it through four simulation studies covering six functionals from mediation analysis, ANOVA, and multilevel modeling, which are commonly used in the social and behavioral sciences. Under misspecification, PostSD substantially underestimated the true standard error across all settings, whereas IJSE closely tracked the bootstrap at a fraction of the computational cost. Under correct specification all three methods agreed, confirming that IJSE introduces no distortion when the model is right. These results show IJSE as a practical, general-purpose tool for robust uncertainty quantification in Bayesian workflows throughout the social and behavioral sciences

When deploying large language models (LLMs) to safety-critical applications, uncertainty quantification (UQ) is of utmost importance to self-assess the reliability of the LLM-based decisions. However, such decisions typically suffer from overconfidence, particularly after parameter-efficient fine-tuning (PEFT) for downstream domain-specific tasks with limited data. Existing methods to alleviate this issue either rely on Laplace approximation based post-hoc framework, which may yield suboptimal calibration depending on the training trajectory, or variational Bayesian training that requires multiple complete forward passes through the entire LLM backbone at inference time for Monte Carlo estimation, posing scalability challenges for deployment. To address these limitations, we build on the Bayesian last layer (BLL) model, where the LLM-based deterministic feature extractor is followed by random last layer parameters for uncertainty reasoning. Since existing low-rank adapters (LoRA) for PEFT have limited expressiveness due to rank collapse, we address this with Polar-decomposed Low-rank Adapter Representation (PoLAR), an orthogonalized parameterization paired with Riemannian optimization to enable more stable and expressive adaptation. Building on this PoLAR-BLL model, we leverage the variational (V) inference framework to put forth a scalable Bayesian fine-tuning approach which jointly seeks the PoLAR parameters and approximate posterior of the last layer parameters via alternating optimization. The resulting PoLAR-VBLL is a flexible framework that nicely integrates architecture-enhanced optimization with scalable Bayesian inference to endow LLMs with well-calibrated UQ. Our empirical results verify the effectiveness of PoLAR-VBLL in terms of generalization and uncertainty estimation on both in-distribution and out-of-distribution data for various common-sense reasoning tasks.

This study investigates the climatic index time series over the most recent 80 years, using monthly mean values from the Pacific Decadal Oscillation Index (PDO), Southern Oscillation Index (SOI), and monthly solar activity represented by sunspot numbers (MS), obtained from the National Weather Service Climate Prediction Center and the World Data Center SILSO, Royal Observatory of Belgium, Brussels. The statistical software R was used with the WaveletComp package to generate Morlet wavelet power spectra, and bivariate cross-wavelet analysis using the biwavelet package. The results show predominant cycles with variability scales of 32, 64, 128, and 256 months, corresponding approximately to 2.66, 5.33, 10.66, and 21.33 years. These frequencies are observed in the period from January 1933 to September 2016, totaling 993 months (82.75 years), characterizing decadal and multidecadal variability. These multidecadal cycles (of the order of 10.66 and 21.33 years) suggest a possible association with solar activity variability and climate variability in the ocean-atmosphere system. Rainfall data from January 1951 to September 2017 were analyzed for Belém, São Luiz, Fortaleza, Natal, and Fernando de Noronha, forming a north to northeast Brazilian transect. These series show similarity with the decadal and multidecadal cycles observed in the SOI, PDO, and sunspot series.

Using the 1951–2017 historical series of the Atlantic Meridional Mode (AMM) index and the monthly number of sunspots, it was possible to observe a significant association between them. The use of wavelet and cross-wavelet analysis showed the presence of multidecadal cycles pronounced in eleven years, as well as cycles of 2.66 and 5.33 years. The AMM index showed, in the Sea Surface Temperature (SST) component, the presence of a weak signal of 21.33 years. The influence and association of sunspot variability on surface temperature in Northern and Northeastern regions of Brazil were investigated. Using a non-parametric statistical correlation test, the historical series of surface temperature anomalies in five locations (Belém, São Luiz, Fortaleza, Fernando de Noronha, and Natal) were compared with the monthly solar-series anomalies. The temperature series used were the minimum monthly average, the monthly average, and maximum monthly average temperatures, with their respective anomalies in relation to the mean. However, among all the series (except for São Luiz), the analyzed minimum temperature anomalies showed a negative correlation with sunspots. As a preliminary result, the analyzed climatic indices present an apparent degree of memory associated with the variability of sunspot activity.

This study aimed to analyze the time series behavior of the Southern Oscillation Index through techniques using Fast Fourier Transform, computing the autocorrelation function, and the calculation of the Hurst coefficient. The methodology of Hurst exponent calculation uses different lags, which are computed in the time series of Southern Oscillation Index. The persistent behavior in the time series can be characterized by calculating the Hurst exponent, seeking for more behavioral information, such as the existence of persistence and/or terms of long-range memory in the series. The results show a persistence of the climate in terms of long-memory Southern Oscillation Index time series, which can help to understand complex dynamic behavior in climate effects at global-scale level and specifically its influence in northeastern Brazil, in the region of the Alcântara Launch Center. The R package tseriesChaos was used in the analysis of the Southern Oscillation Index time series, estimating the largest Lyapunov exponent, which indicates the existence of chaotic behavior in time series. The resampling technique was used in a permutation test between the surface wind data in the São Luís airport, Maranhão State, and the Southern Oscillation Index. The permutation test results showed that the time series of monthly average wind speed in the São Luís airport is correlated with the variability of Southern Oscillation Index, statistically significant at the 5% confidence level. The results also indicate the possibility of using autoregressive models to represent average meteorological variables in behavioral analysis, as well as trends in the climate, more specifically a possible climatic influence of El Niño–Southern Oscillation on wind strength in the Alcântara Launch Center.

Digital twins require high-quality data to achieve predictive capability, but time and resource limitations make efficient experiment design essential. Model-based design of experiments can address this challenge, especially when coupled with equation-oriented optimization and first-principles models. Pyomo.DoE is a software package for optimal experimental design of high-fidelity, equation-oriented models; however, embedding linear algebra operations such as matrix inversion and eigenvalue computation within these optimization problems remains difficult. This work extends Pyomo.DoE with callback-based capabilities that enable rigorous computation of eigenvalue-based design metrics, including minimum eigenvalue optimality (E-optimality) and condition number optimality (ME-optimality), within equation-oriented optimization frameworks. These additions allow experimental design to focus directly on poorly informed or numerically problematic parameter directions. We also present a new experiment-creation modeling abstraction for intrusive uncertainty quantification in Pyomo that reduces user modeling effort by aligning model and software abstractions across the digital twin workflow. In addition, a brief tutorial on experimental design metrics is provided in the methodology and supplementary information. Overall, this work expands the range of practical optimal design criteria available in Pyomo.DoE and improves the workflow for building and refining high-value digital twins.

We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of distributions, and then specialise our results to tempering sequences. We use our results to derive the complexity of SMC samplers with respect to the parameters of the problem, such as $T$, the number of target distributions, in the general case, or $d$, the dimension of the ambient space, in the tempering case. We use these bounds to derive practical recommendations for the implementation of SMC samplers for end users.

General Circulation Models (GCMs) are widely used for future climate projections, but their coarse spatial resolution and systematic biases limit their direct use for impact studies. This limitation is particularly critical for wind-related applications, such as wind energy, which require spatially coherent, multivariate, and physically plausible near-surface wind fields. Classical statistical downscaling and bias correction methods partly address this issue. Still, they struggle to preserve spatial structure, inter-variable consistency, and robustness under climate change, especially in high-dimensional settings. Recent advances in generative machine learning offer new opportunities for downscaling and bias correction, eliminating the need for explicitly paired low- and high-resolution datasets. However, many existing approaches remain difficult to interpret and challenging to deploy in operational climate impact studies. In this work, we apply SerpentFlow, an interpretable, generative, domain alignment framework, to the multivariate downscaling and bias correction of wind variables from GCM outputs. This is a method that generates low-resolution/high-resolution training data pairs by separating large-scale spatial patterns from small-scale variability. Large-scale components are aligned across climate model and observational domains. Conditional fine-scale variability is then learned using a flow-matching generative model. We apply the approach to multiple wind variables downscaling, including average and maximal wind speed, zonal and meridional components, and compare it with widely used multivariate bias correction methods. Results show improved spatial coherence, inter-variable consistency, and robustness under future climate conditions, highlighting the potential of interpretable generative models for wind and energy applications.

Genotype-environment (GxE) interactions can influence the performance of genotypes across diverse environments, limiting the reliability of genotype evaluation and selection in breeding programs. In-depth analysis of GxE interactions is therefore essential for understanding how genetic advantages or defects are expressed under varying environmental conditions and for identifying superior and stable genotypes. This study presents an integrated computational framework for GxE analysis that combines significance and stability evaluation within a unified analytical workflow. The framework incorporates the mixed effect modeling to quantify the significance of environment, genotype, and GxE effects, together with multiple stability analysis approaches for characterizing genotype adaptability, environmental representativeness, and performance consistency across environments. To support reproducible statistical analysis, we develop GxEStat, an interactive R platform that automates model construction, parameter estimation, statistical inference, and graphical visualization. GxEStat substantially improves analytical efficiency, reproducibility, and accessibility for multi-environment trial analysis. Applications to real breeding datasets demonstrate the effectiveness of the proposed framework for practical breeding research. Codes are available at https://github.com/mason-ching/GxEStat.

We study power-one sequential testing for an i.i.d. law on a Polish sample space. Given a nonempty composite null class $\Pcal\subseteq\mathcal M_1(\X)$, we ask when there exists a level-$\alpha$ stopping rule that rejects almost surely under every alternative in a prescribed class $\Qcal\subseteq\Pcal^c$. Our main sufficient condition is local weak lower semicontinuity and positivity of the information projection functional \( \Phi_\Pcal(Q):=\inf_{P\in\Pcal}\KL(Q\|P). \) In particular, if $\Pcal$ is weakly compact, then for every $\alpha\in(0,1)$ there is a single level-$\alpha$ sequential test with power one against the entire complement $\Pcal^c$. The proof combines Csiszár's nonasymptotic Sanov bound for weakly closed convex empirical-measure sets with a Lindelöf countable-subcover argument. We also show that weak lower semicontinuity is sufficient but not necessary by giving examples where discontinuous finite-sample events separate alternatives that weak neighborhoods cannot detect. Finally, we construct an $e$-process that is asymptotically relatively growth-rate optimal under weak compactness. We verify the weak-lower-semicontinuity condition for weakly compact nulls, $f$-divergence balls, several integral probability metric balls, Wasserstein balls on proper spaces, and a number of non-weakly-compact semiparametric examples.

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of rank-transformed variables, thereby quantifying the behavior of one variable when the other takes extreme values. We investigate the theoretical asymptotic behavior of the associated estimator. The effectiveness of the approach is demonstrated through an extensive simulation study. In addition, we discuss the use of the proposed coefficient for the detection of causal effects in extreme events. Finally, we apply the method to an oceanographic dataset, where the results highlight the strong asymmetric nature of extreme events and identify the dominant directions of extremal influence among key oceanographic variables. As a directional measure of tail dependence, our approach provides a natural tool for exploring causal-effect relationships in extreme-value settings.

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max characterization of key statistics, enabling approximation of the mean $\mu_{\hat{\theta}}$ and covariance $C_{\hat{\theta}}$ of the ERM estimator $\hat{\theta}$. Specifically, under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that for a test covariate $x$ independent of the training data, the projection $\hat{\theta}^\top x$ approximately follows the convolution of the generally non-Gaussian distribution of $\mu_{\hat{\theta}}^\top x$ with an independent centered Gaussian variable of variance $\mathrm{tr}(C_{\hat{\theta}} \mathbb{E}[xx^\top])$. This result clarifies the scope and limits of Gaussian universality for ERMs. Numerical simulations across diverse losses and models are provided to validate our theoretical predictions and qualitative insights.

This paper investigates the impact of carbon pricing under the EU Emissions Trading System (EU ETS) on the Italian electricity market, focusing on the carbon cost pass-through rate (CPTR) across market zones during Phases 3 and 4 (2016-2024). Using daily data, the study applies an econometric framework based on a linear regression model with autoregressive dynamics to estimate the extent to which carbon costs are reflected in wholesale electricity prices. It further incorporates robustness checks and quantile regression to assess how the CPTR varies across different fuel spread levels. The results show that carbon costs are positively and significantly transmitted to electricity prices, confirming the relevance of carbon pricing as a key market driver. However, pass-through is incomplete, with CPTR values consistently below 100%. At the national level, the pass-through estimate is around 32%, with no statistically significant change between Phase 3 and Phase 4. Substantial heterogeneity emerges across market zones: pass-through increases in the North, Centre-North, and Sardinia during Phase 4, while it declines in the Centre-South and Sicily, reflecting differences in generation mix, carbon intensity, and market conditions. Overall, the findings highlight the importance of market zones factors in shaping the effectiveness of carbon pricing in electricity markets.

In this paper, we consider the academic department ranking system of Italy, which is based on a performance index named Indice Standardizzato di Performance Dipartimentale (ISPD). While critiques to the ISPD have been moved for its marked tendency to polarization, we here formalize a yet unexplored determinant of this phenomenon, that is, the presence of within-department homogeneity among the standardized scores used to build the index. We account for this intra-departmental correlation by modeling it as a function of departments' size. The proposed model, estimated via Maximum Likelihood, allows to build a fairer ranking procedure via the definition of a properly adjusted version of the ISPD. The estimation framework is also adapted to fit publicly available data, which are coarsened by rounding and/or left-truncated. To this end, a novel probability distribution termed Betoidal is introduced. Empirical evidence in favor of the proposed model is found in the 2017 and 2022 data. Moreover, a simulation study shows that the adjusted index significantly overcomes not only the original ISPD, but also other more data-demanding competing proposals.

We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher–student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples $M$ diverge at fixed ratio $\alpha = M/N$, and for finite hidden widths $(p,p^*)$ of the student and teacher, respectively, we study the low-dimensional ordinary differential equations that govern the evolution of the student–teacher and student–student overlap matrices. We show that overparameterization ($p>p^*$) only modestly accelerates escape from a plateau of poor generalization by modifying the prefactor of the exponential decay of the loss. We then examine how unconstrained weight norms introduce a continuous rotational symmetry that results in a nontrivial manifold of zero-loss solutions for $p>1$. From this manifold the dynamics consistently selects the closest solution to the random initialization, as enforced by a conserved quantity in the ODEs governing the evolution of the overlaps. Finally, a Hessian analysis of the population-loss landscape confirms that the plateau and the solution manifold correspond to saddles with at least one negative eigenvalue and to marginal minima in the population-loss geometry, respectively.

Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $\theta \in \mathbb{R}^d$. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of $n$ and $\theta$, illustrating regimes where the output and the desired true distribution are close. Further, under some assumptions, we prove the TV-accuracy of running Diffusion on these tilted samples. Our theoretical results are supported by extensive simulations. Applications of our work include finance, weather and climate modelling, and many other domains, where the aim may be to generate samples from a tilted distribution that satisfies practically motivated moment constraints.