Papers

The performance of Metropolis-Hastings algorithms is highly sensitive to the choice of step size, and miss-specification can lead to severe loss of efficiency. We study algorithms with randomized step sizes, considering both auxiliary-variable and marginalized constructions. We show that algorithms with a randomized step size inherit weak Poincaré inequalities/spectral gaps from their fixed-step-size counterparts under minimal conditions, and that the marginalized kernel should always be preferred in terms of asymptotic variance to the auxiliary-variable choice if it is implementable. In addition we show that both types of randomization make an algorithm robust to tuning, meaning that spectral gaps decay polynomially as the step size is increasingly poorly chosen. We further show that step-size randomization often preserves high-dimensional scaling limits and algorithmic complexity, while increasing the optimal acceptance rate for Langevin and Hamiltonian samplers when an Exponential or Uniform distribution is chosen to randomize the step size. Theoretical results are complemented with a numerical study on challenging benchmarks such as Poisson regression, Neal's funnel and the Rosenbrock (banana) distribution.

Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual independence based on $L$-statistics. We establish the asymptotic distribution of the proposed test when the order parameter $k$ is fixed, and prove asymptotic normality when $k$ diverges with the dimension. Moreover, we show the asymptotic independence of the fixed-$k$ and diverging-$k$ statistics, enabling their combination through the Cauchy method. The resulting adaptive test is both theoretically justified and practically powerful across a wide range of alternatives. Simulation studies demonstrate the advantages of our method.

Ambitious decarbonisation targets are rapidly increasing the commission of new offshore wind farms. For these newly commissioned plants to run, accurate power forecasts are needed from the onset. These allow grid stability, good reserve management and efficient energy trading. Despite machine learning models having strong performances, they tend to require large volumes of site-specific data that new farms do not yet have. To overcome this data scarcity, we propose a novel transfer learning framework that clusters power output according to covariate meteorological features. Rather than training a single, general-purpose model, we thus forecast with an ensemble of expert models, each trained on a cluster. As these pre-trained models each specialise in a distinct weather pattern, they adapt efficiently to new sites and capture transferable, climate-dependent dynamics. Our contributions are two-fold - we propose this novel framework and comprehensively evaluate it on eight offshore wind farms, achieving accurate cross-domain forecasting with under five months of site-specific data. Our experiments achieve a MAE of 3.52%, providing empirical verification that reliable forecasts do not require a full annual cycle. Beyond power forecasting, this climate-aware transfer learning method opens new opportunities for offshore wind applications such as early-stage wind resource assessment, where reducing data requirements can significantly accelerate project development whilst effectively mitigating its inherent risks.

Within heterogeneous treatment effect (HTE) analysis, various estimands have been proposed to capture the effect of a treatment conditional on covariates. Recently, the conditional quantile comparator (CQC) has emerged as a promising estimand, offering quantile-level summaries akin to the conditional quantile treatment effect (CQTE) while preserving some interpretability of the conditional average treatment effect (CATE). It achieves this by summarising the treated response conditional on both the covariates and the untreated response. Despite these desirable properties, the CQC's current estimation is limited by the need to first estimate the difference in conditional cumulative distribution functions and then invert it. This inversion obscures the CQC estimate, hampering our ability to both model and interpret it. To address this, we propose the first direct estimator of the CQC, allowing for explicit modelling and parameterisation. This explicit parameterisation enables better interpretation of our estimate while also providing a means to constrain and inform the model. We show, both theoretically and empirically, that our estimation error depends directly on the complexity of the CQC itself, improving upon the existing estimation procedure. Furthermore, it retains the desirable double robustness property with respect to nuisance parameter estimation. We further show our method to outperform existing procedures in estimation accuracy across multiple data scenarios while varying sample size and nuisance error. Finally, we apply it to real-world data from an employment scheme, uncovering a reduced range of potential earnings improvement as participant age increases.

Knowing the link between observed predictive variables and outcomes is crucial for making inference in any regression model. When this link is missing, partially or completely, classical estimation methods fail in recovering the true regression function. Deconvolution approaches have been proposed and studied in detail in the unmatched setting where the predictive variables and responses are allowed to be independent. In this work, we consider linear regression in a semi-supervised learning setting where, beside a small sample of matched data, we have access to a relatively large unmatched sample. Using maximum likelihood estimation, we show that under some mild assumptions the semi-supervised learning empirical maximum likelihood estimator (SSLEMLE) is asymptotically normal and give explicitly its asymptotic covariance matrix as a function of the ratio of the matched/unmatched sample sizes and other parameters. Furthermore, we quantify the statistical gain achieved by having the additional large unmatched sample over having only the small matched sample. To illustrate the theory, we present the results of an extensive simulation study and apply our methodology to the "combined cycle power plant" data set.

While InfoNCE underlies modern contrastive learning, its geometric mechanisms remain under-characterized beyond the canonical alignment–uniformity decomposition. We develop a measure-theoretic framework in which representation measures evolve on a fixed embedding manifold. In the large-batch limit, we prove value and gradient consistency, linking the stochastic objective to explicit deterministic energy landscapes and revealing a geometric bifurcation between unimodal and symmetric multimodal regimes. In the unimodal case, the intrinsic energy is strictly convex and admits a unique Gibbs equilibrium, showing that entropy acts as a tie-breaker within the aligned basin. In the multimodal case, the intrinsic geometry becomes cross-coupled and contains a persistent negative symmetric divergence term: each modality's marginal reshapes the effective landscape of the other, allowing strong pairwise alignment to coexist with a persistent modality gap. Controlled synthetic experiments and analyses of pretrained CLIP representations support these predictions. Overall, our results shift the analytical lens from pointwise discrimination to population geometry, showing that pairwise alignment alone is insufficient to control cross-modal marginal structure.

The deployment of Artificial Intelligence in high-risk domains, such as finance and healthcare, necessitates models that are both fair and transparent. While regulatory frameworks, including the EU's AI Act, mandate bias mitigation, they are deliberately vague about the definition of bias. In line with existing research, we argue that true fairness requires addressing bias at the intersections of protected groups. We propose a unified framework that leverages Mixed-Integer Optimization (MIO) to train intersectionally fair and intrinsically interpretable classifiers. We prove the equivalence of two measures of intersectional fairness (MSD and SPSF) in detecting the most unfair subgroup and empirically demonstrate that our MIO-based algorithm improves performance in finding bias. We train high-performing, interpretable classifiers that bound intersectional bias below an acceptable threshold, offering a robust solution for regulated industries and beyond.

This paper evaluates the performance of a large language model (LLM) based semantic search tool relative to a traditional keyword-based search for data discovery. Using real-world search behaviour, we compare outputs from a bespoke semantic search system applied to UKRI data services with the Consumer Data Research Centre (CDRC) keyword search. Analysis is based on 131 of the most frequently used search terms extracted from CDRC search logs between December 2023 and October 2024. We assess differences in the volume, overlap, ranking, and relevance of returned datasets using descriptive statistics, qualitative inspection, and quantitative similarity measures, including exact dataset overlap, Jaccard similarity, and cosine similarity derived from BERT embeddings. Results show that the semantic search consistently returns a larger number of results than the keyword search and performs particularly well for place based, misspelled, obscure, or complex queries. While the semantic search does not capture all keyword based results, the datasets returned are overwhelmingly semantically similar, with high cosine similarity scores despite lower exact overlap. Rankings of the most relevant results differ substantially between tools, reflecting contrasting prioritisation strategies. Case studies demonstrate that the LLM based tool is robust to spelling errors, interprets geographic and contextual relevance effectively, and supports natural-language queries that keyword search fails to resolve. Overall, the findings suggest that LLM driven semantic search offers a substantial improvement for data discovery, complementing rather than fully replacing traditional keyword-based approaches.

The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack of a reliable bandwidth selector; practitioners currently rely on iterative optimization methods that are computationally expensive and prone to instability. We derive the “Beta Reference Rule,” a fast, closed-form bandwidth selector based on the unweighted Asymptotic Mean Integrated Squared Error (AMISE) of a beta reference distribution. To address boundary integrability issues, we introduce a principled heuristic for U-shaped and J-shaped distributions. By employing a method-of-moments approximation, we reduce the bandwidth selection complexity from iterative optimization to $\mathcal{O}(1)$. Extensive Monte Carlo simulations demonstrate that our rule matches the accuracy of numerical optimization while delivering a speedup of over 35,000 times. Real-world validation on socioeconomic data shows that it avoids the “vanishing boundary” and “shoulder” artifacts common to Gaussian-based methods. We provide a comprehensive, open-source Python package to facilitate the immediate adoption of the Beta kernel as a drop-in replacement for standard density estimation tools.

In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the parameter space, so that the chain has a low autocorrelation length and the sampler has a high acceptance rate, with the goal of optimising the number of near-independent samples for given computational cost. Standard Gaussian momentum distributions allow arbitrarily large velocities, which can lead to inefficient exploration in posteriors with ridges or funnel-like geometries. We investigate alternative momentum distributions based on relativistic and Student's t kinetic energies, which naturally limit particle velocities and may improve robustness. Using Almanac, a sampler for cosmological posterior distributions of sky maps and power spectra on the sphere, we test these alternatives in both low- and high-dimensional settings. We find that the choice of parameterization and momentum distribution can improve convergence and effective sample rate, though the achievable gains are generally modest and strongly problem-dependent, reaching up to an order of magnitude in favorable cases. Among the momentum distributions that we tested, those with moderately heavy tails achieved the best balance between efficiency and stability. These results highlight the importance of sampler design and encourage future work on adaptive and self-tuning strategies for kinetic energy parameter optimization in high-dimensional settings.

In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the unimodality of the likelihood ratio for the comparison in some stochastic orders of two discrete random variables. These results have interest in comparing discrete random variables because the sufficient conditions are easy to check when there are no closed expressions for the survival functions, which occurs in many cases. In addition, the results are applied to compare several parametric families of discrete distributions.

Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated impressive results in replicating dense, real-world contents such as images, musical pieces, or human languages. This work investigates their application to the numerical simulation of incompressible fluid flows, with a view toward incorporating physical constraints such as incompressibility in the probabilistic forecasting framework enabled by generative networks. For that purpose, we explore different conditional, score-based diffusion models where the divergence-free constraint is imposed by the Leray spectral projector, and autoregressive conditioning is aimed at stabilizing the forecasted flow snapshots at distant time horizons. The proposed models are run on a benchmark turbulence problem, namely a Kolmogorov flow, which allows for a fairly detailed analytical and numerical treatment and thus simplifies the evaluation of the numerical methods used to simulate it. Numerical experiments of increasing complexity are performed in order to compare the advantages and limitations of the diffusion models we have implemented and appraise their performances, including: (i) in-distribution assessment over the same time horizons and for similar physical conditions as the ones seen during training; (ii) rollout predictions over time horizons unseen during training; and (iii) out-of-distribution tests for forecasting flows markedly different from those seen during training. In particular, these results illustrate the ability of diffusion models to reproduce the main statistical characteristics of Kolmogorov turbulence in scenarios departing from the ones they were trained on.

It is often asserted in the literature that one should expect positive autocorrelation for random walk Metropolis-Hastings (RWMH), especially if the typical proposal step-size is small relative to the variability in the target density. In this paper, we consider a stationary RWMH chain ${\bf X}$ taking values in $d$-dimensional Euclidean space and (subject only to the existence of densities with respect to Lebesgue measure) with general target distribution having finite second moment and general proposal random walk step-distribution. We prove, for any nonzero vector ${\bf c}$, strict positivity of the autocorrelation function at unit lag for the stochastic process $\langle{\bf c},{\bf X}\rangle$, that is, \[{\operatorname{Corr}}(\langle{\bf c},{\bf X}_0\rangle,\langle{\bf c},{\bf X}_1\rangle)>0,\] and we establish the same result, but with weak inequality (which can in some cases be equality) when the state space for ${\bf X}$ is changed to the integer grid ${\mathbb Z}^d$. Further, for ${\bf c}\neq{\bf 0}$ we establish the sharp lower bound \[{\operatorname{Corr}}(\langle{\bf c},{\bf X}_0\rangle,\langle{\bf c},{\bf X}_1\rangle)>\tfrac19\] on autocorrelation when we assume both that (i) the target density $\pi$ is spherically symmetric and unimodal in the specific sense that $\pi({\bf x})=\hat{\pi}(\|{\bf x}\|)$ for some nonincreasing function $\hat{\pi}$ on $[0,\infty)$ and that (ii) the proposal step-density is symmetric about ${\bf 0}$. We study the autocorrelation indirectly, by considering the incremental variance function (or incremental second-moment function) at unit lag. The same approach allows us also for $r\in[2,\infty)$ to upper-bound the incremental $r$th-absolute-moment function at unit lag. We give also closely related inequalities for the total variation distance between two distributions on ${\mathbb R}^d$ differing only by a location shift.

This paper investigates whether structural econometric models can rival machine learning in forecasting energy–macro dynamics while retaining causal interpretability. Using monthly data from 1999 to 2025, we develop a unified framework that integrates Time-Varying Parameter Structural VARs (TVP-SVAR) with advanced dependence structures, including DCC-GARCH, t-copulas, and mixed Clayton–Frank–Gumbel copulas. These models are empirically evaluated against leading machine learning techniques Gaussian Process Regression (GPR), Artificial Neural Networks, Random Forests, and Support Vector Regression across seven macro-financial and energy variables, with Brent crude oil as the central asset. The findings reveal three major insights. First, TVP-SVAR consistently outperforms standard VAR models, confirming structural instability in energy transmission channels. Second, copula-based extensions capture non-linear and tail dependence more effectively than symmetric DCC models, particularly during periods of macroeconomic stress. Third, despite their methodological differences, copula-enhanced econometric models and GPR achieve statistically equivalent predictive accuracy (t-test p = 0.8444). However, only the econometric approach provides interpretable impulse responses, regime shifts, and tail-risk diagnostics. We conclude that machine learning can replicate predictive performance but cannot substitute the explanatory power of structural econometrics. This synthesis offers a pathway where AI accuracy and economic interpretability jointly inform energy policy and risk management.

The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that computes the optimal SBB transport plan in only a few iterations. The method exploits a dual representation of the SBB objective to obtain analytic expressions for the optimal drift and volatility, and it incorporates a tunable parameter beta greater than zero that interpolates between pure drift (the Schrodinger Bridge) and pure volatility (Bass martingale transport). We show that LightSBB-M achieves the lowest 2-Wasserstein distance on synthetic datasets against state-of-the-art SB and diffusion baselines with up to 32 percent improvement. We also illustrate the generative capability of the framework on an unpaired image-to-image translation task (adult to child faces in FFHQ). These findings demonstrate that LightSBB-M provides a scalable, high-fidelity SBB solver that outperforms existing SB and diffusion baselines across both synthetic and real-world generative tasks. The code is available at https://github.com/alexouadi/LightSBB-M.

Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models (SBMs), recent advancements have extended these models to handle dynamic and weighted networks, allowing for a more accurate representation of temporal variations in structure. Additional developments have introduced methods for detecting structural changes, such as shifts in community membership. However, limited attention has been paid to dynamic networks with variable population sizes, where nodes may enter or exit the network. To address this gap, we propose an extension of dynamic SBMs (dSBMs) that incorporates a birth-death process, enabling the statistical clustering of nodes in dynamic networks with evolving population sizes. This work makes three main contributions: (1) the introduction of a novel model for dSBMs with birth-death processes, (2) a framework for parameter inference and prediction of latent communities in this model, and (3) the development of an adapted Variational Expectation-Maximization (VEM) algorithm for efficient inference within this extended framework.

Covariate-dependent uncertainty quantification in simulation-based inference is crucial for high-stakes decision-making but remains challenging due to the limitations of existing methods such as conformal prediction and classical bootstrap, which struggle with covariate-specific conditioning. We propose Efficient Quantile-Regression-Based Generative Metamodeling (E-QRGMM), a novel framework that accelerates the quantile-regression-based generative metamodeling (QRGMM) approach by integrating cubic Hermite interpolation with gradient estimation. Theoretically, we show that E-QRGMM preserves the convergence rate of the original QRGMM while reducing grid complexity from $O(n^{1/2})$ to $O(n^{1/5})$ for the majority of quantile levels, thereby substantially improving computational efficiency. Empirically, E-QRGMM achieves a superior trade-off between distributional accuracy and training speed compared to both QRGMM and other advanced deep generative models on synthetic and practical datasets. Moreover, by enabling bootstrap-based construction of confidence intervals for arbitrary estimands of interest, E-QRGMM provides a practical solution for covariate-dependent uncertainty quantification.

Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of Lévy processes, particularly when the noise is state-dependent. To bridge this gap, we establish nonlocal Kramers-Moyal formulas, rigorously generalizing the classical Kramers-Moyal relations to SDEs with multiplicative Lévy noise. These formulas provide a direct link between short-time transition probability densities (or sample path statistics) and the underlying SDE coefficients: the drift vector, diffusion matrix, Lévy jump measure kernel, and Lévy noise intensity functions. Leveraging these theoretical foundations, we develop novel data-driven algorithms capable of simultaneously identifying all governing components from data and establish convergence results and error analysis for the algorithms. We validate the framework through extensive numerical experiments on prototypical systems. This work provides a principled and practical toolbox for discovering interpretable SDE models governing complex systems influenced by discontinuous, heavy-tailed, state-dependent fluctuations, with broad applicability in climate science, neuroscience, epidemiology, finance, and biological physics.

Fairness is a central pillar of trustworthy machine learning, especially in domains where accuracy- or profit-driven optimization is insufficient. While most fairness research focuses on supervised learning, fairness in policy learning remains less explored. Because policy learning is interventional, it induces two distinct fairness targets: action fairness (equitable action assignments) and outcome fairness (equitable downstream consequences). Crucially, equalizing actions does not generally equalize outcomes when groups face different constraints or respond differently to the same action. We propose a novel double fairness learning (DFL) framework that explicitly manages the trade-off among three objectives: action fairness, outcome fairness, and value maximization. We integrate fairness directly into a multi-objective optimization problem for policy learning and employ a lexicographic weighted Tchebyshev method that recovers Pareto solutions beyond convex settings, with theoretical guarantees on the regret bounds. Our framework is flexible and accommodates various commonly used fairness notions. Extensive simulations demonstrate improved performance relative to competing methods. In applications to a motor third-party liability insurance dataset and an entrepreneurship training dataset, DFL substantially improves both action and outcome fairness while incurring only a modest reduction in overall value.

Surveys that rely on ordinal polychotomous (Likert-like) items are widely employed to capture individual preferences because they allow respondents to express both the direction and strength of their preferences. Latent factor models traditionally used in this context implicitly assume that the response functions (the cumulative distribution of the ordinal outcome) are monotonic on the latent trait. This assumption can be too restrictive in several application areas, including in political science and marketing. In this work, we propose a novel ordinal probit unfolding model that can accommodate both monotonic and non-monotonic response functions. The advantages of the model are illustrated by analyzing an immigration attitude survey conducted in the United States.

We analyze Muon as originally proposed and used in practice – using the momentum orthogonalization with a few Newton-Schulz steps. The prior theoretical results replace this key step in Muon with an exact SVD-based polar factor. We prove that Muon with Newton-Schulz converges to a stationary point at the same rate as the SVD-polar idealization, up to a constant factor for a given number $q$ of Newton-Schulz steps. We further analyze this constant factor and prove that it converges to 1 doubly exponentially in $q$ and improves with the degree of the polynomial used in Newton-Schulz for approximating the orthogonalization direction. We also prove that Muon removes the typical square-root-of-rank loss compared to its vector-based counterpart, SGD with momentum. Our results explain why Muon with a few low-degree Newton-Schulz steps matches exact-polar (SVD) behavior at a much faster wall-clock time and explain how much momentum matrix orthogonalization via Newton-Schulz benefits over the vector-based optimizer. Overall, our theory justifies the practical Newton-Schulz design of Muon, narrowing its practice-theory gap.

Characterising and distinguishing gamma-ray bursts (GRBs) has interested astronomers for many decades. While some authors have found two or three groups of GRBs by analyzing only a few parameters, recent work identified five ellipsoidally-shaped groups upon considering nine parameters $T_{50}, T_{90}, F_1, F_2, F_3, F_4, P_{64}, P_{256}, P_{1024}$. Yet others suggest sub-classes within the two or three groups found earlier. Using a mixture model of Gaussian factor analysers, we analysed 1150 GRBs, that had nine parameters observed, from the current Burst and Transient Source Experiment (BATSE) catalogue, and again established five ellipsoidal-shaped groups to describe the GRBs. These five groups are characterised in terms of their average duration, fluence and spectrum as shorter-faint-hard, long-intermediate-soft, long-intermediate-intermediate, long-bright-intermediate and short-faint-hard. The use of factor analysers in describing individual group densities allows for a more thorough group-wise characterisation of the parameters in terms of a few latent features. However, given the discrepancy with many other existing studies that advocated for two or three groups, we also performed model-estimated overlap-based syncytial clustering (MOBSynC) that successively merges poorer-separated groups. The five ellipsoidal groups merge into three and then into two groups, one with GRBs of low durations and the other having longer duration GRBs. These groups are also characterised in terms of a few latent factors made up of the nine parameters. Our analysis provides context for all three sets of results, and in doing so, details a multi-layered characterisation of the BATSE GRBs, while also explaining the structure in their variability.

Color quantization represents an image using a fraction of its original number of colors while only minimally losing its visual quality. The $k$-means algorithm is commonly used in this context, but has mostly been applied in the machine-based RGB colorspace composed of the three primary colors. However, some recent studies have indicated its improved performance in human perception-based colorspaces. We investigated the performance of $k$-means color quantization at four quantization levels in the RGB, CIE-XYZ, and CIE-LUV/CIE-HCL colorspaces, on 148 varied digital images spanning a wide range of scenes, subjects and settings. The Visual Information Fidelity (VIF) measure numerically assessed the quality of the quantized images, and showed that in about half of the cases, $k$-means color quantization is best in the RGB space, while at other times, and especially for higher quantization levels ($k$), the CIE-XYZ colorspace is where it usually does better. There are also some cases, especially at lower $k$, where the best performance is obtained in the CIE-LUV colorspace. Further analysis of the performances in terms of the distributions of the hue, chromaticity and luminance in an image presents a nuanced perspective and characterization of the images for which each colorspace is better for $k$-means color quantization.

We consider the parametric estimation of the Ornstein-Uhlenbeck process driven by a non-Gaussian $\alpha$-stable Lévy process with the stable index $\alpha>1$ and possibly skewed jumps, based on a discrete-time sample over a fixed period. By employing a suitable non-diagonal normalizing matrix, we present the following: the parametric family satisfies the local asymptotic mixed normality with a non-degenerate Fisher information matrix; there exists a local maximum of the log-likelihood function which is asymptotically mixed-normal; the local maximum is asymptotically efficient in the sense that it has maximal concentration around the true value over symmetric convex Borel subsets. In the proof, we prove the asymptotic equivalence between the genuine likelihood and the much simpler Euler-type quasi-likelihood. Furthermore, we propose a simple moment-based method to estimate the parameters of the driving stable Lévy process, which serves as an initial estimator for numerical search of the (quasi-)likelihood, reducing the computational burden of the optimization to a large extent. We also present simulation results, which illustrate the theoretical results and highlight the advantages and disadvantages of the genuine and quasi-likelihood approaches.

We study how to fine-tune LLMs using user-edit deployment data consisting of a set of context, an agent's response, and user edits. This deployment data is naturally generated by users in applications such as LLMs-based writing assistants and coding agents. The _natural_ origin of user edits makes it a desired source for adapting and personalizing LLMs. In this setup, there emerges a unification of various feedback types namely preferences, supervised labels, and cost that are typically studied separately in the literature. In this paper, we initiate the theoretical investigation of learning from user edits. We first derive bounds for learning algorithms that learn from each of these feedback types. We prove that these algorithms have different trade-offs depending upon the user, data distribution, and model class. We then propose a simple ensembling procedure to jointly learn from these feedback types. On two domains adapted from Gao et al. 2024, we show our ensembling procedure outperforms these methods that learn from individual feedback. Further, we show that our proposed procedure can robustly adapt to different user-edit distributions at test time.

This paper introduces a class of copula models for spatial data, based on multivariate Pareto-mixture distributions. We explore the tail properties of these models, demonstrating their ability to capture both tail dependence and asymptotic independence, as well as the tail asymmetry frequently observed in real-world data. The proposed models also offer flexibility in accounting for permutation asymmetry and can effectively represent both the bulk and extreme tails of the distribution. We consider special cases of these models with computationally tractable likelihoods and present an extensive simulation study to assess the finite-sample performance of the maximum likelihood estimators. Finally, we apply our models to analyze a temperature dataset, showcasing their practical utility.

A major public health concern in the United States (US) is gun-related deaths. The number of gun injuries largely varies spatially because of county-wise heterogeneity of race, sex, age, and income distributions. But still, a major challenge is to locally identify the influential socio-economic factors behind these firearm fatality incidents. For a diverging number of predictors, a rich literature exists regarding SCAD under the independence framework; however, a vacuum remains when discussing local variable selection for spatially correlated, over-dispersed data. This research presents a two-step localized variable selection and inference framework for spatially indexed gunshot fatality data. In the first step, we select variables locally using the SCAD penalty for specific locations where the number of gunshot incidents exceeds a threshold. For these locations, after selecting the predictors, we proceed to the next step, which involves examining the directional variation in the latent spatial neighborhood structure. We further discuss the theoretical properties of this county-specific local variable selection under infill asymptotics. This method has threefold advantages: (i) this method selects the variables locally, (ii) this method provides inference about directional variation of a selected predictor, and (iii) instead of assuming the spatial neighborhood structure in an ad hoc manner, this method identifies the specific type of spatial neighborhood structure that is most appropriate for modeling the random effects.

Recent advances in Generative Artificial Intelligence (AI), particularly Large Language Models (LLMs), enable scalable extraction of spatial information from unstructured text and offer new methodological opportunities for studying climate geography. This study develops a spatial framework to examine how cumulative climate risk relates to multidimensional human flourishing across U.S. counties. High-resolution climate hazard indicators are integrated with a Human Flourishing Geographic Index (HFGI), an index derived from classification of 2.6 billion geotagged tweets using fine-tuned open-source Large Language Models (LLMs). These indicators are aggregated to the US county-level and mapped to a structural equation model to infer overall climate risk and human flourishing dimensions, including expressed well-being, meaning and purpose, social connectedness, psychological distress, physical condition, economic stability, religiosity, character and virtue, and institutional trust. The results reveal spatially heterogeneous associations between greater cumulative climate risk and lower levels of expressed human flourishing, with coherent spatial patterns corresponding to recurrent exposure to heat, flooding, wind, drought, and wildfire hazards. The study demonstrates how Generative AI can be combined with latent construct modeling for geographical analysis and for spatial knowledge extraction.

Accurate molecular property prediction is central to drug discovery, yet graph neural networks often underperform in data-scarce regimes and fail to surpass traditional fingerprints. We introduce cross-graph inter-message passing (XIMP), which performs message passing both within and across multiple related graph representations. For small molecules, we combine the molecular graph with scaffold-aware junction trees and pharmacophore-encoding extended reduced graphs, integrating complementary abstractions. While prior work is either limited to a single abstraction or non-iterative communication across graphs, XIMP supports an arbitrary number of abstractions and both direct and indirect communication between them in each layer. Across ten diverse molecular property prediction tasks, XIMP outperforms state-of-the-art baselines in most cases, leveraging interpretable abstractions as an inductive bias that guides learning toward established chemical concepts, enhancing generalization in low-data settings.

Off-policy evaluation (OPE) is a fundamental task in reinforcement learning (RL). In the classic setting of linear OPE, finite-sample guarantees often take the form $$ \textrm{Evaluation error} \le \textrm{poly}(C^\pi, d, 1/n,\log(1/\delta)), $$ where $d$ is the dimension of the features and $C^\pi$ is a coverage parameter that characterizes the degree to which the visited features lie in the span of the data distribution. While such guarantees are well-understood for several popular algorithms under stronger assumptions (e.g. Bellman completeness), the understanding is lacking and fragmented in the minimal setting where only the target value function is linearly realizable in the features. Despite recent interest in tight characterizations of the statistical rate in this setting, the right notion of coverage remains unclear, and candidate definitions from prior analyses have undesirable properties and are starkly disconnected from more standard definitions in the literature. We provide a novel finite-sample analysis of a canonical algorithm for this setting, LSTDQ. Inspired by an instrumental-variable view, we develop error bounds that depend on a novel coverage parameter, the feature-dynamics coverage, which can be interpreted as linear coverage in an induced dynamical system for feature evolution. With further assumptions – such as Bellman-completeness – our definition successfully recovers the coverage parameters specialized to those settings, finally yielding a unified understanding for coverage in linear OPE.