Papers

Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models, current reward modeling heavily relies on experimental feedback data collected from human annotators under controlled and costly conditions. In this work, we introduce observational reward modeling – learning reward models with observational user feedback (e.g., clicks, copies, and upvotes) – as a scalable and cost-effective alternative. We identify two fundamental challenges in this setting: (1) observational feedback is noisy due to annotation errors, which deviates it from true user preference; (2) observational feedback is biased by user preference, where users preferentially provide feedback on responses they feel strongly about, which creats a distribution shift between training and inference data. To address these challenges, we propose CausalRM, a causal-theoretic reward modeling framework that aims to learn unbiased reward models from observational feedback. To tackle challenge (1), CausalRM introduces a noise-aware surrogate loss term that is provably equivalent to the primal loss under noise-free conditions by explicitly modeling the annotation error generation process. To tackle challenge (2), CausalRM uses propensity scores – the probability of a user providing feedback for a given response – to reweight training samples, yielding a loss function that eliminates user preference bias. Extensive experiments across diverse LLM backbones and benchmark datasets validate that CausalRM effectively learns accurate reward signals from noisy and biased observational feedback and delivers substantial performance improvements on downstream RLHF tasks – including a 49.2% gain on WildGuardMix and a 32.7% improvement on HarmBench. Code is available on our project website.

Reservoir computing is a well-established approach for processing data with a much lower complexity compared to traditional neural networks. Despite two decades of experimental progress, the core properties of reservoir computing (namely separation, robustness, and fading memory) still lack rigorous mathematical foundations. This paper addresses this gap by providing a control-theoretic framework for the analysis of time-delay-based reservoir computers. We introduce formal definitions of the separation property and fading memory in terms of functional norms, and establish their connection to well-known stability notions for time-delay systems as incremental input-to-state stability. For a class of linear reservoirs, we derive an explicit lower bound for the separation distance via Fourier analysis, offering a computable criterion for reservoir design. Numerical results on the NARMA10 benchmark and continuous-time system prediction validate the approach with a minimal digital implementation.

The No-U-Turn Sampler (NUTS) is the computational workhorse of modern Bayesian software libraries, yet its qualitative and quantitative convergence guarantees were established only recently. A significant gap remains in the theoretical comparison of its two main variants: NUTS-mul and NUTS-BPS, which use multinomial sampling and biased progressive sampling, respectively, for index selection. In this paper, we address this gap in three contributions. First, we derive the first necessary conditions for geometric ergodicity for both variants. Second, we establish the first sufficient conditions for geometric ergodicity and ergodicity for NUTS-mul. Third, we obtain the first mixing time result for NUTS-BPS on a standard Gaussian distribution. Our results show that NUTS-mul and NUTS-BPS exhibit nearly identical qualitative behavior, with geometric ergodicity depending on the tail properties of the target distribution. However, they differ quantitatively in their convergence rates. More precisely, when initialized in the typical set of the canonical Gaussian measure, the mixing times of both NUTS-mul and NUTS-BPS scale as $O(d^{1/4})$ up to logarithmic factors, where $d$ denotes the dimension. Nevertheless, the associated constants are strictly smaller for NUTS-BPS.

A basic issue in both teaching of and practice of statistics is the interplay between modelling assumptions and inference performance. The general message conveyed is that stronger assumptions lead to better statistical performance of the relevant estimators, tests and confidence intervals, provided that these assumptions hold. On the other hand, fewer assumptions often lead to safer and more robust methods that are good also outside narrow conditions, but not quite as good as specialist methods that exploit such narrower conditions, if these are fulfilled. This interplay is nicely illustrated in the context of density estimation, where parametric and nonparametric methods can be contrasted. The parametric ones have mean squared errors of size $O(n^{-1})$ in terms of sample size $n$ if the parametric model is right, but are not even consistent outside the model. The nonparametric methods are everywhere consistent and have mean squared errors of size $O(n^{-4/5})$ for broad classes of estimands. The point we are making here is that this picture is not universally true! We show that a simple kernel density estimator can perform better than a directly estimated parametric density on the latter's home turf, for small sample sizes, in the sense of mean integrated squared error. Our main example is that of estimating an unknown normal density. In the process of developing and discussing this somewhat counter-intuitive and half-paradoxical example we touch on several tangential issues of interest, pertaining to exact small-sample analysis of density estimators.

Decentralized Federated Learning (DFL) remains highly vulnerable to adaptive backdoor attacks designed to bypass traditional passive defense metrics. To address this limitation, we shift the defensive paradigm toward a novel active, interventional auditing framework. First, we establish a dynamical model to characterize the spatiotemporal diffusion of adversarial updates across complex graph topologies. Second, we introduce a suite of proactive auditing metrics, stochastic entropy anomaly, randomized smoothing Kullback-Leibler divergence, and activation kurtosis. These metrics utilize private probes to stress-test local models, effectively exposing latent backdoors that remain invisible to conventional static detection. Furthermore, we implement a topology-aware defense placement strategy to maximize global aggregation resilience. We provide theoretical property for the system's convergence under co-evolving attack and defense dynamics. Numeric empirical evaluations across diverse architectures demonstrate that our active framework is highly competitive with state-of-the-art defenses in mitigating stealthy, adaptive backdoors while preserving primary task utility.

Motivated by the principle of satisficing in decision-making, we study satisficing regret guarantees for nonstationary $K$-armed bandits. We show that in the general realizable, piecewise-stationary setting with $L$ stationary segments, the optimal regret is $\Theta(L\log T)$ as long as $L\geq 2$. This stands in sharp contrast to the case of $L=1$ (i.e., the stationary setting), where a $T$-independent $\Theta(1)$ satisficing regret is achievable under realizability. In other words, the optimal regret has to scale with $T$ even if just a little nonstationarity presents. A key ingredient in our analysis is a novel Fano-based framework tailored to nonstationary bandits via a post-interaction reference construction. This framework strictly extends the classical Fano method for passive estimation as well as recent interactive Fano techniques for stationary bandits. As a complement, we also discuss a special regime in which constant satisficing regret is again possible.

We prove that finite multivariate Erlang mixture densities with a common rate parameter are dense in the class of probability densities on $\mathbb{R}_{+}^{d}$ that belong to $L^{p}$, for every dimension $d\in\mathbb{N}$ and every $1\le p<\infty$. The argument is constructive: the one-dimensional Szász–Mirakjan–Kantorovich operator yields Erlang mixture approximations, and its tensor product yields multivariate approximants with a common scale. We then obtain several quantitative consequences. These include compact-set uniform approximation bounds and, under local Hölder conditions of order $\alpha\in(0,1]$, rates of order $n^{-\alpha/2}$ as the common scale $1/n$ tends to zero, whole-domain convergence in weighted sup norms, weighted and unweighted $L^{p}$ rates, and explicit rates for finite mixtures indexed by the number of mixture components. In particular, if the approximating density is required to have at most $K$ mixture components, then on fixed compact cubes we obtain an algebraic rate of order $K^{-\alpha/(2d)}$; in global weighted sup norms we obtain the explicit algebraic component-count rate $K^{-\alpha/[2d(2d+\alpha)]}$; and for $1<p<\infty$ we obtain corresponding weighted $L^{p}$ component-count rates. The results strengthen the weak-approximation theory for multivariate Erlang mixture distributions and yield immediate corollaries for broader classes such as product-gamma mixtures. \noindentKeywords: multivariate Erlang mixtures; Erlang distributions; Szász–Mirakjan–Kantorovich operator; density approximation; weighted $L^{p}$ approximation; approximation rates.

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded domains without a strictly positive lower bound. For densities bounded away from zero, we give sufficient conditions under which the framework of \cite{shen2001} applies directly. For densities lacking a positive lower bound, the equivalence between Hellinger and weighted $L_2$-norm distance fails, invalidating the original theory. We propose a novel shifting method that lifts the true density $g_0$ to a sequence of proxy densities $g_{0,n}$. We prove a modified convergence theorem applicable to these shifted densities, preserving the optimal rate. We also construct a Gaussian sieve prior that achieves the minimax rate $\varepsilon_n=n^{-p/(2p+1)}$ for any integer $p\geq1$. Numerical results confirm that our estimator approximates the true density well and validates the theoretical convergence rate.

In the present paper we study the performance of linear denoisers for noisy data of the form $\mathbf{x} + \mathbf{z}$, where $\mathbf{x} \in \mathbb{R}^d$ is the desired data with zero mean and unknown covariance $\mathbf{\Sigma}$, and $\mathbf{z} \sim \mathcal{N}(0, \mathbf{\Sigma}_{\mathbf{z}})$ is additive noise. Since the covariance $\mathbf{\Sigma}$ is not known, the standard Wiener filter cannot be employed for denoising. Instead we assume we are given samples $\mathbf{x}_1,\dots,\mathbf{x}_n \in \mathbb{R}^d$ from the true distribution. A standard approach would then be to estimate $\mathbf{\Sigma}$ from the samples and use it to construct an “empirical" Wiener filter. However, in this paper, motivated by the denoising step in diffusion models, we take a different approach whereby we train a linear denoiser $\mathbf{W}$ from the data itself. In particular, we synthetically construct noisy samples $\hat{\mathbf{x}}_i$ of the data by injecting the samples with Gaussian noise with covariance $\mathbf{\Sigma}_1 \neq \mathbf{\Sigma}_{\mathbf{z}}$ and find the best $\mathbf{W}$ that approximates $\mathbf{W}\hat{\mathbf{x}}_i \approx \mathbf{x}_i$ in a least-squares sense. In the proportional regime $\frac{n}{d} \rightarrow \kappa > 1$ we use the Convex Gaussian Min-Max Theorem (CGMT) to analytically find the closed form expression for the generalization error of the denoiser obtained from this process. Using this expression one can optimize over $\mathbf{\Sigma}_1$ to find the best possible denoiser. Our numerical simulations show that our denoiser outperforms the “empirical" Wiener filter in many scenarios and approaches the optimal Wiener filter as $\kappa\rightarrow\infty$.

Why does machine-generated text remain detectable? We investigate a mechanistic explanation at the decoding stage: standard strategies such as top-$k$ and nucleus sampling restrict generation to high-probability tokens, while human writers routinely choose contextually appropriate words from deeper in the model's probability distribution. Truncation makes a measurable share of these choices unreachable; we call this the truncation blind spot. Across five open models and three domains, 8–18% of human-selected tokens fall outside common truncation boundaries. Linguistic analysis further reveals disproportionate exclusion of content-word tokens. In a benchmark comprising 1.8 million machine generations, classifiers using only predictability and lexical diversity achieve mean AUC-ROC near 0.97, with substantial variation across decoding settings and strong transfer across generators. Probability-floor samplers substantially narrow the blind spot, demonstrating that the choice of truncation criterion matters for retaining human-used tokens. Together, these findings characterize a source of human–machine distributional mismatch and motivate decoding methods that preserve contextually appropriate low-probability choices while maintaining generation quality. Code and data are available at https://github.com/EstebanGarces/human_vs_machine.

A data analysis pipeline is a structured sequence of steps that transforms raw data into meaningful insights by integrating multiple analysis algorithms. In many practical applications, analytical findings are obtained only after data pass through several data-dependent procedures within such pipelines. In this study, we address the problem of quantifying the statistical reliability of results produced by data analysis pipelines. As a proof of concept, we focus on clustering pipelines that identify cluster structures from complex and heterogeneous data through procedures such as outlier detection, feature selection, and clustering. We propose a novel statistical testing framework to assess the significance of clustering results obtained through these pipelines. Our framework, based on selective inference, enables the systematic construction of valid statistical tests for clustering pipelines composed of predefined components. We prove that the proposed test controls the type I error rate at any nominal level and demonstrate its validity and effectiveness through experiments on synthetic and real datasets.

Causal representation learning (CRL) aims to learn low-dimensional causal latent variables from high-dimensional observations. While identifiability has been extensively studied for CRL, estimation has been less explored. We use empirical Bayes (EB) to estimate causal representations from multiple domains whose differences reflect interventions in a shared causal model. Multi-domain CRL poses a simultaneous inference problem suited to EB. Here, we propose an EB $f$-modeling algorithm that improves the quality of learned causal variables by exploiting invariant structure within and across domains. Specifically, we consider linear measurement models with interventional priors induced by an acyclic latent causal model with known graph and intervention targets. We develop an EM-style algorithm based on causally structured score matching. In experiments on synthetic and semi-synthetic single-cell data, our proposed method achieves more accurate estimation than alternative methods and baselines.

The distance from calibration, introduced by Błasiok, Gopalan, Hu, and Nakkiran (STOC 2023), has recently emerged as a central measure of miscalibration for probabilistic predictors. We study the fundamental problems of computing and estimating this quantity, given either an exact description of the data distribution or only sample access to it. We give an efficient algorithm that exactly computes the calibration distance when the distribution has a uniform marginal and noiseless labels, which improves the $O(1/\sqrt{|\mathcal{X}|})$ additive approximation of Qiao and Zheng (COLT 2024) for this special case. Perhaps surprisingly, the problem becomes $\mathsf{NP}$-hard when either of the two assumptions is removed. We extend our algorithm to a polynomial-time approximation scheme for the general case. For the estimation problem, we show that $\Theta(1/\epsilon^3)$ samples are sufficient and necessary for the empirical calibration distance to be upper bounded by the true distance plus $\epsilon$. In contrast, a polynomial dependence on the domain size – incurred by the learning-based baseline – is unavoidable for two-sided estimation. Our positive results are based on simple sparsifications of both the distribution and the target predictor, which significantly reduce the search space for computation and lead to stronger concentration for the estimation problem. To prove the hardness results, we introduce new techniques for certifying lower bounds on the calibration distance – a problem that is hard in general due to its $\textsf{co-NP}$-completeness.

Biclustering is a powerful unsupervised learning technique for simultaneously identifying coherent subsets of rows and columns in a data matrix, thus revealing local patterns that may not be apparent in global analyses. However, most biclustering methods are developed for continuous data and are not applicable for binary datasets such as single-nucleotide polymorphism (SNP) or protein-protein interaction (PPI) data. Existing biclustering algorithms for binary data often struggle to recover biclustering patterns under noise, face scalability issues, and/or bias the final results towards biclusters of a particular size or characteristic. We propose a Bayesian method for biclustering binary datasets called Binary Spike-and-Slab Lasso Biclustering (BiSSLB). Our method is robust to noise and allows for overlapping biclusters of various sizes without prior knowledge of the noise level or bicluster characteristics. BiSSLB is based on a logistic matrix factorization model with spike-and-slab priors on the latent spaces. We further incorporate an Indian Buffet Process (IBP) prior to automatically determine the number of biclusters from the data. We develop a novel coordinate ascent algorithm with proximal steps which allows for scalable computation. The performance of our proposed approach is assessed through simulations and two real applications on HapMap SNP and Homo Sapiens PPI data, where BiSSLB is shown to outperform other state-of-the-art binary biclustering methods when the data is very noisy.

Electroencephalography (EEG)-based emotion recognition suffers from severe performance degradation when models are transferred across heterogeneous datasets due to physiological variability, experimental paradigm differences, and device inconsistencies. Existing domain adversarial methods primarily enforce global marginal alignment and often overlook class-conditional mismatch and decision boundary distortion, limiting cross-corpus generalization. In this work, we propose a unified Prototype-driven Adversarial Alignment (PAA) framework for cross-corpus EEG emotion recognition. The framework is progressively instantiated in three configurations: PAA-L, which performs prototype-guided local class-conditional alignment; PAA-C, which further incorporates contrastive semantic regularization to enhance intra-class compactness and inter-class separability; and PAA-M, the full boundary-aware configuration that integrates dual relation-aware classifiers within a three-stage adversarial optimization scheme to explicitly refine controversial samples near decision boundaries. By combining prototype-guided subdomain alignment, contrastive discriminative enhancement, and boundary-aware aggregation within a coherent adversarial architecture, the proposed framework reformulates emotion recognition as a relation-driven representation learning problem, reducing sensitivity to label noise and improving cross-domain stability. Extensive experiments on SEED, SEED-IV, and SEED-V demonstrate state-of-the-art performance under four cross-corpus evaluation protocols, with average improvements of 6.72%, 5.59%, 6.69%, and 4.83%, respectively. Furthermore, the proposed framework generalizes effectively to clinical depression identification scenarios, validating its robustness in real-world heterogeneous settings. The source code is available at https://github.com/WuCB-BCI/PAA

Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of training efforts over clinical targets. However, even the most modern approaches fall short in two important scenarios: open-loop models with known mean flow and assumed waveform shapes, and anatomies affected by vascular lesions where segmentation influences the reachability of pressure or flow split targets. In both cases, boundary conditions cannot be tuned in isolation. We introduce a general amortized inference framework based on probabilistic flow that treats clinical targets, inflow features, and point cloud embeddings of patient-specific anatomies as either conditioning variables or quantities to be jointly estimated. We demonstrate the approach on two patient-specific models: an aorto-iliac bifurcation with varying stenosis locations and severity, and a coronary arterial tree.

The use of synthetic data to deidentify data and to improve predictive models is well-attested to. The augmentation of datasets using synthetically generated data is an alluring proposition: in the best case, it generates realistic data in silico at a fraction of the cost of authentic data which may be found in vivo or in vitro. This poses novel epistemic challenges. We contend that synthetic data augmentation is best understood as a novel way of accounting for prior knowledge. In this manuscript, we propose a definition of synthetic distributions and analyze how synthetic data augmentation interplays with standard accounts of maximum likelihood and Bayesian estimation. We observe that the marginal Fisher information contributed by synthetic data processes is subject to fundamental bounds, and enumerate obstacles to the use of synthetic data augmentation to aid in inferential tasks. We then articulate a Bayesian formulation of the way that synthetic data augmentation can be coherently understood, but argue that naive approaches to the specification of the prior are epistemically unjustifiable. This suggests that enhanced scrutiny must be placed on identifying justifiable priors to warrant the use and inclusion of data drawn from specific synthetic distributions. While our analysis shows the challenges and limitations of using synthetic data augmentation to improve upon traditional statistical model reasoning, it does suggest that augmentation is the principal approach analysts using outcome reasoning (i.e. using train/test splits to justify the analysis) can constrain an otherwise high-dimensional model space, providing an alternative to trying to encode the constraints into the potentially complex architecture of the algorithm.

Chain-of-thought reasoning, where language models expend additional computation by producing thinking tokens prior to final responses, has driven significant advances in model capabilities. However, training these reasoning models is extremely costly in terms of both data and compute, as it involves collecting long traces of reasoning behavior from humans or synthetic generators and further post-training the model via reinforcement learning. Are these costs fundamental, or can they be reduced through better algorithmic design? We show that autocurriculum, where the model uses its own performance to decide which problems to focus training on, provably improves upon standard training recipes for both supervised fine-tuning (SFT) and reinforcement learning (RL). For SFT, we show that autocurriculum requires exponentially fewer reasoning demonstrations than non-adaptive fine-tuning, by focusing teacher supervision on prompts where the current model struggles. For RL fine-tuning, autocurriculum decouples the computational cost from the quality of the reference model, reducing the latter to a burn-in cost that is nearly independent of the target accuracy. These improvements arise purely from adaptive data selection, drawing on classical techniques from boosting and learning from counterexamples, and requiring no assumption on the distribution or difficulty of prompts.

Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating or computing likelihoods with GPs limits their scalability to large datasets. This paper introduces the piecewise continuous Gaussian process (PCGP), a new process that retains the rich probabilistic structure of traditional GPs while offering substantial computational efficiency. As will be shown and discussed, existing scalable approaches that define stochastic processes on continuous domains – such as the nearest-neighbour GP (NNGP) and the radial-neighbour GP (RNGP) – rely on conditional independence structures that effectively constrain the measurable space on which the processes are defined, which may induce undesirable probabilistic behaviour and compromise their practical applicability, particularly in complex latent GP models. The PCGP mitigates these limitations and provides a theoretically grounded and computationally efficient alternative, as demonstrated through numerical illustrations.

Estimation of the mean and covariance functions is a fundamental problem in functional data analysis, particularly for discretely observed functional data. In this work, we study a regularization-based framework for estimating the mean and the covariance functions within a reproducing kernel Hilbert space (RKHS) setting. Our approach utilizes a spectral regularization technique under Hölder-type source conditions, allowing for a broad class of regularization schemes and accommodating a wide range of smoothness assumptions on the target functions. In contrast to RKHS formulations that assume the target belongs to the underlying RKHS, our source-condition framework also accommodates misspecified targets. Convergence rates for the proposed estimators are derived, and we derive corresponding minimax lower bounds and identify regimes in which the upper bounds are optimal, or optimal up to logarithmic factors.

In Structural Health Monitoring (SHM), sensor measurements and derived features such as eigenfrequencies often exhibit systematic daily patterns and can therefore be naturally represented as functional data. Furthermore, these patterns are typically influenced by environmental factors, particularly temperature, which can substantially affect the observed system response. While most existing methods for removing environmental effects assume that confounding influences affect only the mean response, it has been shown that environmental and operational factors may also alter the covariance structure of the residual process. To address this limitation in a functional data monitoring framework, we incorporate so-called covariate-dependent functional principal component analysis (CD-FPCA), which allows eigenfunctions and eigenvalues of the residual process to vary smoothly with covariates such as temperature. The proposed methodology is illustrated using an extended version of the KW51 railway bridge eigenfrequency dataset. This case study suggests that accounting for covariate effects beyond the functional mean can improve the robustness of the monitoring procedure, in particular by reducing environmentally induced (false) alarms under challenging low-temperature conditions.

Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where these methods are deployed, there is a natural need to preserve the privacy of the individuals whose data is being scrutinized. While a number of works have attempted to approach the problem of differentially private Bayesian estimation through either reasoning about the inherent privacy of the posterior distribution or privatizing off-the-shelf Bayesian methods, these works generally do not come with rigorous utility guarantees beyond low-dimensional settings. In fact, even for the prototypical tasks of Gaussian mean estimation and linear regression, it was unknown how close one could get to the Bayes-optimal error with a private algorithm, even in the simplest case where the unknown parameter comes from a Gaussian prior. In this work, we give the first efficient algorithms for both of these problems that achieve mean-squared error $(1+o(1))\mathrm{OPT}$ and additionally show that both tasks exhibit an intriguing computational-statistical gap. For Bayesian mean estimation, we prove that the excess risk achieved by our method is optimal among all efficient algorithms within the low-degree framework, yet is provably worse than what is achievable by an exponential-time algorithm. For linear regression, we prove a qualitatively similar lower bound. Our algorithms draw upon the privacy-to-robustness framework of arXiv:2212.05015, but with the curious twist that to achieve private Bayes-optimal estimation, we need to design sum-of-squares-based robust estimators for inherently non-robust objects like the empirical mean and OLS estimator. Along the way we also add to the sum-of-squares toolkit a new kind of constraint based on short-flat decompositions.

Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to oversmooth high-frequency gradients, while neural operators like DeepONet exhibit spectral bias and underpredict localized extremes. Diffusion models can recover fine-scale structure but often introduce low-frequency amplitude drift, degrading physical scaling. To address these limitations, we propose a hybrid surrogate framework, cDDPM-DeepONet, that decouples stress morphology from magnitude. A conditional denoising diffusion probabilistic model (cDDPM), built on a UNet backbone, generates normalized von Mises stress fields conditioned on geometry and loading. In parallel, a modified DeepONet predicts global scaling parameters (minimum and maximum stress), enabling reconstruction of full-resolution physical stress maps. This separation allows the diffusion model to focus on spatial structure while the operator network corrects global amplitude, mitigating spectral and scaling biases. We evaluate the framework on nonlinear hyperelastic datasets with single and multiple polygonal voids. The proposed model consistently outperforms UNet, DeepONet, and standalone cDDPM baselines by one to two orders of magnitude. Spectral analysis shows strong agreement with finite element solutions across all wavenumbers, preserving both global behavior and localized stress concentrations.

The Highly Adaptive Lasso (HAL) delivers unprecedented guarantees in nonparametric minimum loss estimation under minimal smoothness assumptions, such as dimension-free minimax optimal rates. However, the practical use of HAL has been severely limited by its exponentially growing computationally prohibitive indicator basis expansion in moderate to high dimensions. Existing screening strategies drastically reduce this dimension but lack any theoretical justification. We introduce the Principal Component Highly Adaptive (PC-HA) family of estimators, which for the first time provide a principled and theoretically valid dimension reduction. We establish formal results on the score equations solved by these PC-HA estimators, allowing to transfer plug-in efficiency and pointwise asymptotic normality results from HAL to these PC-HA estimators, under comparable complexity control.

Artificial Intelligence (AI) systems are increasingly prominent in emerging smart cities, yet their reliability remains a critical concern. These systems typically operate through a sequence of interconnected functional stages, where upstream errors may propagate to downstream stages, ultimately affecting overall system reliability. Quantifying such error propagation is essential for accurate modeling of AI system reliability. However, this task is challenging due to: i) data availability: real-world AI system reliability data are often scarce and constrained by privacy concerns; ii) model validity: recurring error events across sequential stages are interdependent, violating the independence assumptions of statistical inference; and iii) computational complexity: AI systems process large volumes of high-speed data, resulting in frequent and complex recurrent error events that are difficult to track and analyze. To address these challenges, this paper leverages a physics-based autonomous vehicle simulation platform with a justifiable error injector to generate high-quality data for AI system reliability analysis. Building on this data, a new reliability modeling framework is developed to explicitly characterize error propagation across stages. Model parameters are estimated using a computationally efficient, theoretically guaranteed composite likelihood expectation - maximization algorithm. Its application to the reliability modeling for autonomous vehicle perception systems demonstrates its predictive accuracy and computational efficiency.

This paper pays tribute to Professor Giovanni Andrea Cornia's lifelong contributions to the measurement of global inequality. We review twelve world and regional databases of the Gini coefficient, illustrate their coverage, overlapping, and data gaps, and analyse the major sources of discrepancy among published Ginis. Merging all databases into a unified collection of over 122,000 observations spanning 222 countries from 1867 to 2024, we document how differences in welfare metrics, reference units, sub-metric definitions, post-survey adjustments, and survey design produce Gini estimates that diverge considerably – sometimes by as much as 50 percentage points – for the same country and year. We quantify pairwise cross-database discordance, document the income-consumption Gini gap by region and income group, and discuss the contributions of welfare metric and equivalence scale choices to cross-database dispersion. We extend the analysis with a dedicated discussion of comparability across time and across measurement dimensions, showing how multiple layers of methodological choice interact to make any single Gini figure a product of a complex chain of decisions that are rarely fully disclosed. Our analysis confirms that the choice of welfare metric remains the single most important source of cross-country non-comparability, while sub-metric definitions and equivalence scales introduce further systematic differences that are routinely overlooked in comparative work.

When working with real-world insurance data, practitioners often encounter challenges during the data preparation stage that can undermine the statistical validity and reliability of downstream modeling. This study illustrates that conventional data preparation procedures such as random train-test partitioning, often yield unreliable and unstable results when confronted with highly imbalanced insurance loss data. To mitigate these limitations, we propose a novel data preparation framework leveraging two recent statistical advancements: support points for representative data splitting to ensure distributional consistency across partitions, and the Chatterjee correlation coefficient for initial, non-parametric feature screening to capture feature relevance and dependence structure. We further integrate these theoretical advances into a unified, efficient framework that also incorporates missing-data handling, and embed this framework within our custom InsurAutoML pipeline. The performance of the proposed approach is evaluated using both simulated datasets and datasets often cited in the academic literature. Our findings definitively demonstrate that incorporating statistically rigorous data preparation methods not only significantly enhances model robustness and interpretability but also substantially reduces computational resource requirements across diverse insurance loss modeling tasks. This work provides a crucial methodological upgrade for achieving reliable results in high stakes insurance applications.

We establish convergence of the training dynamics of residual neural networks (ResNets) to their joint infinite depth L, hidden width M, and embedding dimension D limit. Specifically, we consider ResNets with two-layer perceptron blocks in the maximal local feature update (MLU) regime and prove that, after a bounded number of training steps, the error between the ResNet and its large-scale limit is O(1/L + sqrt(D/(L M)) + 1/sqrt(D)). This error rate is empirically tight when measured in embedding space. For a budget of P = Theta(L M D) parameters, this yields a convergence rate O(P^(-1/6)) for the scalings of (L, M, D) that minimize the bound. Our analysis exploits in an essential way the depth-two structure of residual blocks and applies formally to a broad class of state-of-the-art architectures, including Transformers with bounded key-query dimension. From a technical viewpoint, this work completes the program initiated in the companion paper [Chi25] where it is proved that for a fixed embedding dimension D, the training dynamics converges to a Mean ODE dynamics at rate O(1/L + sqrt(D)/sqrt(L M)). Here, we study the large-D limit of this Mean ODE model and establish convergence at rate O(1/sqrt(D)), yielding the above bound by a triangle inequality. To handle the rich probabilistic structure of the limit dynamics and obtain one of the first rigorous quantitative convergence for a DMFT-type limit, we combine the cavity method with propagation of chaos arguments at a functional level on so-called skeleton maps, which express the weight updates as functions of CLT-type sums from the past.

Motivated by the EVA 2025 Data Challenge, we address the problem of predicting extreme rainfall in the eastern United States using data from a large ensemble of climate model runs. The challenge focuses on three quantities of interest related to the spatial extent and/or temporal duration of extreme rainfall, each requiring extrapolation. To tackle these questions, we adopt the recently developed geometric framework for extreme-value analysis, offering substantial flexibility for capturing complex extremal dependence structures and enabling extrapolation across the entire multivariate tail. In this work, we focus on the spatial geometric framework for analysing the spatial extent and consider a sampling procedure that retains the temporal information in the data, thereby enabling estimation of the duration of extreme rainfall events. We also account for the non-stationary behaviour, arising from topographical and seasonal effects, that commonly characterises extreme weather events in both space and time. Using diagnostic metrics, we demonstrate that the proposed model is appropriate for inferring extreme events on this dataset and apply it to estimate target quantities of interest.

We study transfer learning for contextual joint assortment-pricing under a multinomial logit choice model with bandit feedback. A seller operates across multiple related markets and observes only posted prices and realized purchases. While data from source markets can accelerate learning in a target market, cross-market differences in customer preferences may introduce systematic bias if pooled indiscriminately. We model heterogeneity through a structured utility shift, where markets share a common contextual utility structure but differ along a sparse set of latent preference coordinates. Building on this, we develop Transfer Joint Assortment-Pricing (TJAP), a bias-aware framework that combines aggregate-then-debias estimation with a UCB-style policy. TJAP constructs two-radius confidence bounds that separately capture statistical uncertainty and transfer-induced bias, uniformly over continuous prices. We establish matching minimax regret bounds of order $\tilde{O}\!\left(d\sqrt{\frac{T}{1+H}} + s_0\sqrt{T}\right),$revealing a transparent variance-bias tradeoff: transfer accelerates learning along shared preference directions, while heterogeneous components impose an irreducible adaptation cost. Numerical experiments corroborate the theory, showing that TJAP outperforms both target-only learning and naive pooling while remaining robust to cross-market differences.