Papers

For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the narrow networks or kernel methods analysed until now. We positively answer through the study of the supervised learning of a multi-layer perceptron. Importantly, (i) its width scales as the input dimension, making it more prone to feature learning than ultra wide networks, and more expressive than narrow ones or ones with fixed embedding layers; and (ii) we focus on the challenging interpolation regime where the number of trainable parameters and data are comparable, which forces the model to adapt to the task. We consider the matched teacher-student setting. Therefore, we provide the fundamental limits of learning random deep neural network targets and identify the sufficient statistics describing what is learnt by an optimally trained network as the data budget increases. A rich phenomenology emerges with various learning transitions. With enough data, optimal performance is attained through the model's "specialisation" towards the target, but it can be hard to reach for training algorithms which get attracted by sub-optimal solutions predicted by the theory. Specialisation occurs inhomogeneously across layers, propagating from shallow towards deep ones, but also across neurons in each layer. Furthermore, deeper targets are harder to learn. Despite its simplicity, the Bayes-optimal setting provides insights on how the depth, non-linearity and finite (proportional) width influence neural networks in the feature learning regime that are potentially relevant in much more general settings.

Existing multilevel quasi-Monte Carlo (MLQMC) methods often rely on multiple independent randomizations of a low-discrepancy (LD) sequence to estimate statistical errors on each level. While this approach is standard, it can be less efficient than simply increasing the number of points from a single LD sequence. However, a single LD sequence does not permit statistical error estimates in the current framework. We propose to recast the MLQMC problem in a Bayesian cubature framework, which uses a single LD sequence and quantifies numerical error through the posterior variance of a Gaussian process (GP) model. When paired with certain LD sequences, GP regression and hyperparameter optimization can be carried out at only $\mathcal{O}(n \log n)$ cost, where $n$ is the number of samples. Building on the adaptive sample allocation used in traditional MLQMC, where the number of samples is doubled on the level with the greatest expected benefit, we introduce a new Bayesian utility function that balances the computational cost of doubling against the anticipated reduction in posterior uncertainty. We also propose a new digitally-shift-invariant (DSI) kernel of adaptive smoothness, which combines multiple higher-order DSI kernels through a weighted sum of smoothness parameters, for use with fast digital net GPs. A series of numerical experiments illustrate the performance of our fast Bayesian MLQMC method and error estimates for both single-level problems and multilevel problems with a fixed number of levels. The Bayesian error estimates obtained using digital nets are found to be reliable, although, in some cases, mildly conservative.

Neural networks have become a popular tool in predictive modelling, more commonly associated with machine learning and artificial intelligence than with statistics. Generalised Additive Models (GAMs) are flexible non-linear statistical models that retain interpretability. Both are state-of-the-art in their own right, with their respective advantages and disadvantages. This paper analyses how these two model classes have performed on real-world tabular data. Following PRISMA guidelines, we conducted a systematic review of papers that performed empirical comparisons of GAMs and neural networks. Eligible papers were identified, yielding 143 papers, with 430 datasets. Key attributes at both paper and dataset levels were extracted and reported. Beyond summarising comparisons, we analyse reported performance metrics using mixed-effects modelling to investigate potential characteristics that can explain and quantify observed differences, including application area, study year, sample size, number of predictors, and neural network complexity. Across datasets, no consistent evidence of superiority was found for either GAMs or neural networks when considering the most frequently reported metrics (RMSE, $R^2$, and AUC). Neural networks tended to outperform in larger datasets and in those with more predictors, but this advantage narrowed over time. Conversely, GAMs remained competitive, particularly in smaller data settings, while retaining interpretability. Reporting of dataset characteristics and neural network complexity was incomplete in much of the literature, limiting transparency and reproducibility. This review highlights that GAMs and neural networks should be viewed as complementary approaches rather than competitors. For many tabular applications, the performance trade-off is modest, and interpretability may favour GAMs.

An ongoing challenge in animal ecology is developing movement models that account for the autocorrelation, and often temporal irregularity, in telemetry data. Continuous-time Langevin diffusion models have been proposed to model temporally autocorrelated and irregularly sampled data. However, current estimation techniques obtain increasingly biased parameter estimates as the time between observations increases. In this paper, we propose using Brownian bridges in an importance sampling scheme to improve the likelihood approximation of the Langevin diffusion model. In a series of simulation studies, we showed that our approach effectively removed the bias under various scenarios. We found that the precision of the estimated habitat coefficients increased for data spanning a longer duration at a lower frequency than for shorter, more frequently sampled tracks. This suggests that the model may be well suited for modelling tracking data sampled at a coarser resolution, as is common in datasets collected with older generations of animal tags. We illustrated the application of our model using tracking data from Steller sea lions, Eumetopias jubatus. We found that the coefficient estimates converged to values significantly different than those estimated in previous studies, suggesting that bias in conventional estimation methods may meaningfully affect ecological conclusions about habitat preference. Together, these improvements broaden the applicability of Langevin diffusion models, thereby improving ecological insight into habitat selection.

The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds. It can be used to sample from any probability density which “depends only on distance". The idea is to combine the statistical principle of rejection sampling with the geometric principle of volume comparison. CURS is an exact sampling method and (assuming the underlying Riemannian manifold satisfies certain technical conditions) it has a particularly moderate computational cost. The aim of the present work is to show that there are many applications where CURS should be the user's method of choice for dealing with relatively low-dimensional scenarios.

Feature and trait allocation models are fundamental objects in Bayesian nonparametrics and play a prominent role in several applications. Existing approaches, however, typically assume full exchangeability of the data, which may be restrictive in settings characterized by heterogeneous but related groups. In this paper, we introduce a general and tractable class of Bayesian nonparametric priors for partially exchangeable trait allocation models, relying on completely random vectors. We provide a comprehensive theoretical analysis, including closed-form expressions for marginal and posterior distributions, and illustrate the tractability of our framework in the cases of binary and Poisson-distributed traits. A distinctive aspect of our approach is that the number of traits is a random quantity, thereby allowing us to model and estimate unobserved traits. Building on these results, we also develop a novel mixture model that infers the group partition structure from the data, effectively clustering trait allocations. This extension generalizes Bayesian nonparametric latent class models and avoids the systematic overclustering that arises when the number of traits is assumed to be fixed. We demonstrate the practical usefulness of our methodology through an application to the `Ndrangheta criminal network from the Operazione Infinito investigation, where our model provides insights into the organization of illicit activities.

In multitemporal InSAR, phase linking (PL) refers to the estimation of a single-reference interferometric phase history for distributed scatterers (DS) from the information contained in the sample coherence matrix. Because the phase information in this matrix is typically inconsistent, DS processing needs practical reliability indicators to decide whether a pixel's PL estimate is sufficiently supported by the data for subsequent deformation analysis. For maximum-likelihood estimation, uncertainty can be quantified via Fisher-information-based covariance estimates, but no analogous, generally applicable uncertainty quantification is available for the broad range of non-ML methods. We propose three heuristic quality coefficients within a unified mathematical framework that covers common PL methods: (1) a method-specific goodness-of-fit coefficient that normalizes the achieved PL objective between a method-consistent upper bound and an empirically modeled noise floor level; (2) a closure phase coefficient computed from the sample coherence matrix in advance; and (3) an ambiguity coefficient that compares the obtained PL estimate with the best alternative in its orthogonal complement in the solution space. All coefficients are normalized to the interval $[0,1]$, where 1 indicates maximum reliability and 0 matches the behavior expected under pure noise. Simulations under exponential and seasonal decorrelation models show that the goodness-of-fit coefficient tracks the normalized absolute phase error most consistently, whereas the closure phase coefficient provides an a priori indicator for pre-screening. Experiments on a TerraSAR-X stack over Visp, Switzerland, reveal plausible spatial patterns across urban and vegetated areas and show that the ambiguity coefficient provides complementary information, especially in regions with temporally varying scattering mechanisms.

Various estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the Aalen-Johansen estimator is generally only consistent under the rather restrictive Markov assumption, the landmark Aalen-Johansen estimator can handle non-Markov multi-state models. However, the landmark Aalen-Johansen estimator leads to a strict data reduction and, thus, to an increased variance. The hybrid Aalen-Johansen estimator serves as a compromise by, firstly, checking with a log-rank-based test whether the Markov assumption is satisfied. Secondly, landmarking is only applied if the Markov assumption is rejected. In this work, we propose a new hybrid Aalen-Johansen estimator which uses a Cox model instead of the log-rank-based test to check the Markov assumption in the first step. Furthermore, we compare the four estimators in an extensive simulation study across Markov, semi-Markov, and distinct non-Markov settings. In order to get deep insights into the performance of the estimators, we consider four different measures: bias, variance, root mean squared error, and coverage rate. Additionally, further influential factors on the estimators such as the form and degree of non-Markov behaviour, the different transitions, and the starting time are analysed. The main result of the simulation study is that the hybrid Aalen-Johansen estimators yield favourable results across various measures and settings.

This project introduces the GNAR-HARX model, which combines Generalised Network Autoregressive (GNAR) structure with Heterogeneous Autoregressive (HAR) dynamics and exogenous predictors such as implied volatility. The model is designed for forecasting realised volatility by capturing both temporal persistence and cross-sectional spillovers in financial markets. We apply it to daily realised variance data for ten international stock indices, generating one-step-ahead forecasts in a rolling window over an out-of-sample period of approximately 16 years (2005-2020). Forecast accuracy is evaluated using the Quasi-Likelihood (QLIKE) loss and mean squared error (MSE), and we compare global, standard, and local variants across different network structures and exogenous specifications. The best model found by QLIKE is a local GNAR-HAR without exogenous variables, while the lowest MSE is achieved by a standard GNAR-HARX with implied volatility. Fully connected networks consistently outperform dynamically estimated graphical lasso networks. Overall, local and standard GNAR-HAR(X) models deliver the strongest forecasts, though at the cost of more parameters than the parsimonious global variant, which nevertheless remains competitive. Across all cases, GNAR-HAR(X) models outperform univariate HAR(X) benchmarks, which often require more parameters than the GNAR-based specifications. While the top model found by QLIKE does not use exogenous variables, implied volatility and overnight returns emerge as the most useful predictors when included.

This study proves that Nearest Neighbor (NN) matching can be interpreted as an instance of Riesz regression for automatic debiased machine learning. Lin et al. (2023) shows that NN matching is an instance of density-ratio estimation with their new density-ratio estimator. Chernozhukov et al. (2024) develops Riesz regression for automatic debiased machine learning, which directly estimates the Riesz representer (or equivalently, the bias-correction term) by minimizing the mean squared error. In this study, we first prove that the density-ratio estimation method proposed in Lin et al. (2023) is essentially equivalent to Least-Squares Importance Fitting (LSIF) proposed in Kanamori et al. (2009) for direct density-ratio estimation. Furthermore, we derive Riesz regression using the LSIF framework. Based on these results, we derive NN matching from Riesz regression. This study is based on our work Kato (2025a) and Kato (2025b).

We provide a description of pilot and production experiences to streamline some business functions in the official statistical production process using statistical learning models. Our approach is quality-oriented searching for an improvement on accuracy, cost-efficiency, timeliness, granularity, response burden reduction, and frequency. Pilot experiences have been conducted with data from real surveys in Statistics Spain (INE).

Artificial intelligence in medicine is built to serve the average patient. By minimizing error across large datasets, most systems deliver strong aggregate accuracy yet falter at the margins: patients with rare variants, multimorbidity, or underrepresented demographics. This average patient fallacy erodes both equity and trust. We propose a different design: a multi-agent ecosystem for N-of-1 decision support. In this environment, agents clustered by organ systems, patient populations, and analytic modalities draw on a shared library of models and evidence synthesis tools. Their results converge in a coordination layer that weighs reliability, uncertainty, and data density before presenting the clinician with a decision-support packet: risk estimates bounded by confidence ranges, outlier flags, and linked evidence. Validation shifts from population averages to individual reliability, measured by error in low-density regions, calibration in the small, and risk–coverage trade-offs. Anticipated challenges include computational demands, automation bias, and regulatory fit, addressed through caching strategies, consensus checks, and adaptive trial frameworks. By moving from monolithic models to orchestrated intelligence, this approach seeks to align medical AI with the first principle of medicine: care that is transparent, equitable, and centered on the individual.

We introduce Perception Learning (PeL), a paradigm that optimizes an agent's sensory interface $f_\phi:\mathcal{X}\to\mathcal{Z}$ using task-agnostic signals, decoupled from downstream decision learning $g_\theta:\mathcal{Z}\to\mathcal{Y}$. PeL directly targets label-free perceptual properties, such as stability to nuisances, informativeness without collapse, and controlled geometry, assessed via objective representation-invariant metrics. We formalize the separation of perception and decision, define perceptual properties independent of objectives or reparameterizations, and prove that PeL updates preserving sufficient invariants are orthogonal to Bayes task-risk gradients. Additionally, we provide a suite of task-agnostic evaluation metrics to certify perceptual quality.

We propose a density-free method for frequentist inference on population quantiles, termed Self-Normalized Quantile Empirical Saddlepoint Approximation (SNQESA). The approach builds a self-normalized pivot from the indicator score for a fixed quantile threshold and then employs a constrained empirical saddlepoint approximation to obtain highly accurate tail probabilities. Inverting these tail areas yields confidence intervals and tests without estimating the unknown density at the target quantile, thereby eliminating bandwidth selection and the boundary issues that affect kernel-based Wald/Hall-Sheather intervals. Under mild local regularity, the resulting procedures attain higher-order tail accuracy and second-order coverage after inversion. Because the pivot is anchored in a bounded Bernoulli reduction, the method remains reliable for skewed and heavy-tailed distributions and for extreme quantiles. Extensive Monte Carlo experiments across light, heavy, and multimodal distributions demonstrate that SNQESA delivers stable coverage and competitive interval lengths in small to moderate samples while being orders of magnitude faster than large-B resampling schemes. An empirical study on Value-at-Risk with rolling windows further highlights the gains in tail performance and computational efficiency. The framework naturally extends to two-sample quantile differences and to regression-type settings, offering a practical, analytically transparent alternative to kernel, bootstrap, and empirical-likelihood methods for distribution-free quantile inference.

Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all experiments the design should be chosen such that the model parameters are estimated as efficiently as possible. The design choice for such models involves the known nonlinear models' design difficulties but \cite{gilmour_trinca_2012b} proposed a methodology capable of producing exact designs that makes use of the computing facilities available today. In this paper, we use this methodology to find Bayesian optimal exact designs for several fractional polynomial models. The optimum designs are compared to various standard designs in response surface problems.

Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size, particularly near the boundary between stationarity and nonstationarity. We propose a new, parameter-free testing procedure based on the evaluation of periodograms across multiple epochs. The limiting distributions derived here are obtained under stationarity and nonstationarity assumptions and analytically tractable, expressed as finite sums of weighted independent $\chi^2$ random variables. Simulation studies indicate that the proposed method performs favorably compared to existing approaches.

Decentralized bilevel optimization has garnered significant attention due to its critical role in solving large-scale machine learning problems. However, existing methods often rely on prior knowledge of problem parameters-such as smoothness, convexity, or communication network topologies-to determine appropriate stepsizes. In practice, these problem parameters are typically unavailable, leading to substantial manual effort for hyperparameter tuning. In this paper, we propose AdaSDBO, a fully problem-parameter-free algorithm for decentralized bilevel optimization with a single-loop structure. AdaSDBO leverages adaptive stepsizes based on cumulative gradient norms to update all variables simultaneously, dynamically adjusting its progress and eliminating the need for problem-specific hyperparameter tuning. Through rigorous theoretical analysis, we establish that AdaSDBO achieves a convergence rate of $\widetilde{\mathcal{O}}\left(\frac{1}{T}\right)$, matching the performance of well-tuned state-of-the-art methods up to polylogarithmic factors. Extensive numerical experiments demonstrate that AdaSDBO delivers competitive performance compared to existing decentralized bilevel optimization methods while exhibiting remarkable robustness across diverse stepsize configurations.

We consider the adversarial linear bandits setting and present a unified algorithmic framework that bridges Follow-the-Regularized-Leader (FTRL) and Follow-the-Perturbed-Leader (FTPL) methods, extending the known connection between them from the full-information setting. Within this framework, we introduce self-concordant perturbations, a family of probability distributions that mirror the role of self-concordant barriers previously employed in the FTRL-based SCRiBLe algorithm. Using this idea, we design a novel FTPL-based algorithm that combines self-concordant regularization with efficient stochastic exploration. Our approach achieves a regret of $\mathcal{O}(d\sqrt{n \ln n})$ on both the $d$-dimensional hypercube and the $\ell_2$ ball. On the $\ell_2$ ball, this matches the rate attained by SCRiBLe. For the hypercube, this represents a $\sqrt{d}$ improvement over these methods and matches the optimal bound up to logarithmic factors.

Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's spatial coordinates. First, we propose a new, translation-invariant spreadness index that quantifies spatial balance with a clear interpretation. Second, we develop a clustering method that balances clusters with respect to an auxiliary variable; when the auxiliary variable is the inclusion probability, the procedure yields clusters whose totals are one, so that a single draw per cluster is, in principle, representative and produces units optimally spread along the population coordinates, an attractive feature for finite population sampling. Third, building on the graphical sampling framework, we design an efficient sampling scheme that further enhances spatial balance. At its core lies an intelligent, computationally efficient search layer that adapts to the population's spatial structure and inclusion probabilities, tailoring a design to each specific population to maximize spread. Across diverse spatial patterns and both equal- and unequal-probability regimes, this intelligent coupling consistently outperformed all rival spread-oriented designs on dispersion metrics, while the spreadness index remained informative and the clustering step improved representativeness.

In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller than the dimension. We consider two types of loss function: the empirical $L_1$ distance between the intensity functions of the process and the $L_1$ norm on the parameters (background rates and interaction functions). Our results are the first results to control the $L_1$ norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes.

National statistical institutes are beginning to use non-traditional data sources to produce official statistics. These sources, originally collected for non-statistical purposes, include point-of-sales(POS) data and mobile phone global positioning system(GPS) data. Such data have the potential to significantly enhance the usefulness of official statistics. In the era of big data, many private companies are accumulating vast amounts of transaction data. Exploring how to leverage these data for official statistics is increasingly important. However, progress has been slower than expected, mainly because such data are not collected through sample-based survey methods and therefore exhibit substantial selection bias. If this bias can be properly addressed, these data could become a valuable resource for official statistics, substantially expanding their scope and improving the quality of decision-making, including economic policy. This paper demonstrates that even biased transaction data can be useful for producing official statistics for prompt release, by drawing on the concepts of density ratio estimation and supervised learning under covariate shift, both developed in the field of machine learning. As a case study, we show that preliminary statistics can be produced in a timely manner using biased data from a Japanese private employment agency. This approach enables the early release of a key labor market indicator that would otherwise be delayed by up to a year, thereby making it unavailable for timely decision-making.

It is recommended that measures of between-study effect heterogeneity be reported when conducting individual-participant data meta-analyses (IPD-MA). Methods exist to quantify inconsistency between trials via I^2 (the percentage of variation in the treatment effect due to between-study heterogeneity) when conducting two-stage IPD-MA, and when conducting one-stage IPD-MA with approximately equal numbers of treatment and control group participants. We extend formulae to estimate I^2 when investigating treatment-covariate interactions with unequal numbers of participants across subgroups and/or continuous covariates. A simulation study was conducted to assess the agreement in values of I^2 between those derived from two-stage models using traditional methods and those derived from equivalent one-stage models. Fourteen scenarios differed by the magnitude of between-trial heterogeneity, the number of trials, and the average number of participants in each trial. Bias and precision of I^2 were similar between the one- and two-stage models. The mean difference in I^2 between equivalent models ranged between -1.0 and 0.0 percentage points across scenarios. However, disparities were larger in simulated datasets with smaller samples sizes with up to 19.4 percentage points difference between models. Thus, the estimates of I^2 derived from these extended methods can be interpreted similarly to those from existing formulae for two-stage models.

With the surge of domestic tourism in India and the influence of social media on young tourists, this paper aims to address the research question on how "social return" - responses received on social media sharing - of recent trip details can influence decision-making for short-term future travels. The paper develops a multi-model framework to build a predictive machine learning model that establishes a relationship between a traveler's social return, various social media usage, trip-related factors, and her future trip-planning behavior. The primary data was collected via a survey from Indian tourists. After data cleaning, the imbalance in the data was addressed using a robust oversampling method, and the reliability of the predictive model was ensured by applying a Monte Carlo cross-validation technique. The results suggest at least 75% overall accuracy in predicting the influence of social return on changing the future trip plan. Moreover, the model fit results provide crucial practical implications for the domestic tourism sector in India with future research directions concerning social media, destination marketing, smart tourism, heritage tourism, etc.

Kernel Stein discrepancies (KSDs) are widely used for goodness-of-fit testing, but standard KSDs can be insensitive to higher-order dependence features such as tail dependence. We introduce the Copula-Stein Discrepancy (CSD), which defines a Stein operator directly on the copula density to target dependence geometry rather than the joint score. For Archimedean copulas, CSD admits a closed-form Stein kernel derived from the scalar generator. We prove that CSD metrizes weak convergence of copula distributions, admits an empirical estimator with minimax-optimal rate $O_P(n^{-1/2})$, and is sensitive to differences in tail dependence coefficients. We further extend the framework beyond Archimedean families to general copulas, including elliptical and vine constructions. Computationally, exact CSD kernel evaluation is linear in dimension, and a random-feature approximation reduces the quadratic $O(n^2)$ sample scaling to near-linear $\tilde{O}(n)$; experiments show near-nominal Type~I error, increasing power, and rapid concentration of the approximation toward the exact $\widehat{\mathrm{CSD}}_n^2$ as the number of features grows.

This paper presents Two-Stage LKPLO, a novel multi-stage outlier detection framework that overcomes the coexisting limitations of conventional projection-based methods: their reliance on a fixed statistical metric and their assumption of a single data structure. Our framework uniquely synthesizes three key concepts: (1) a generalized loss-based outlyingness measure (PLO) that replaces the fixed metric with flexible, adaptive loss functions like our proposed SVM-like loss; (2) a global kernel PCA stage to linearize non-linear data structures; and (3) a subsequent local clustering stage to handle multi-modal distributions. Comprehensive 5-fold cross-validation experiments on 10 benchmark datasets, with automated hyperparameter optimization, demonstrate that Two-Stage LKPLO achieves state-of-the-art performance. It significantly outperforms strong baselines on datasets with challenging structures where existing methods fail, most notably on multi-cluster data (Optdigits) and complex, high-dimensional data (Arrhythmia). Furthermore, an ablation study empirically confirms that the synergistic combination of both the kernelization and localization stages is indispensable for its superior performance. This work contributes a powerful new tool for a significant class of outlier detection problems and underscores the importance of hybrid, multi-stage architectures.

In the presence of competing events, many investigators are interested in a direct treatment effect on the event of interest that does not capture treatment effects on competing events. Classical survival analysis methods that treat competing events like censoring events, at best, target a controlled direct effect: the effect of the treatment under a difficult to imagine and typically clinically irrelevant scenario where competing events are somehow eliminated. A separable direct effect, quantifying the effect of a future modified version of the treatment, is an alternative direct effect notion that may better align with an investigator's underlying causal question. In this paper, we provide insights into the implications of naively applying an estimator constructed for a controlled direct effect (i.e., "censoring by competing events") when the actual causal effect of interest is a separable direct effect. We illustrate the degree to which controlled and separable direct effects may take different values, possibly even different signs, and the degree to which these two different effects may be differentially impacted by violation and/or near violation of their respective identifying conditions under a range of data generating scenarios. Finally, we provide an empirical comparison of inverse probability of censoring weighting to an alternative weighted estimator specifically structured for a separable effect using data from a randomized trial of estrogen therapy and prostate cancer mortality.

Combinatorial bandits extend the classical bandit framework to settings where the learner selects multiple arms in each round, motivated by applications such as online recommendation and assortment optimization. While extensions of upper confidence bound (UCB) algorithms arise naturally in this context, adapting arm elimination methods has proved more challenging. We introduce a novel elimination scheme that partitions arms into three categories (confirmed, active, and eliminated), and incorporates explicit exploration to update these sets. We demonstrate the efficacy of our algorithm in two settings: the combinatorial multi-armed bandit with general graph feedback, and the combinatorial linear contextual bandit. In both cases, our approach achieves near-optimal regret, whereas UCB-based methods can provably fail due to insufficient explicit exploration. Matching lower bounds are also provided.

Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative model using kinetic (underdamped) Langevin dynamics with specular reflection of velocity on the boundary defining constraints. This results in piecewise continuously differentiable noising and denoising process where the latter is characterized by a time-reversed dynamics restricted to a domain with boundary due to specular boundary condition. In addition, we also contribute to existing reflected SDEs based constrained generative models, where the stochastic dynamics is restricted through an abstract local time term. By presenting efficient numerical samplers which converge with optimal rate in terms of discretizations step, we provide a comprehensive comparison of models based on confined (specularly reflected kinetic) Langevin diffusion with models based on reflected diffusion with local time.

Using data from the Longyearbyen weather station, quantile gradient boosting ("small AI") is applied to forecast daily temperatures in Svalbard, Norway. Temperatures above 0 degrees Celsius are of special interest because of their impact on ice, snow, and tundra permafrost. To improve forecasting skill for warmer temperatures, the target quantile is 0.60; forecast underestimates are weighted 1.5 times more heavily than forecast overestimates when the quantile loss is computed. Predictors include eight routinely collected indicators of weather conditions, each lagged by 14 days, yielding temperature forecasts with a two-week lead time. Adaptive conformal prediction regions quantify forecasting uncertainty with provably valid coverage. Using a holdout sample, a forecast of 0 degrees Celsius is correct 14 days later at least 80% of the time. Implications for Arctic adaptation policy are discussed.

Understanding the relationship between antibody sequence, structure and function is essential for the design of antibody-based therapeutics and research tools. Recently, machine learning (ML) models mostly based on the application of large language models to sequence information have been developed to predict antibody properties. Yet there are open directions to incorporate structural information, not only to enhance prediction but also to offer insights into the underlying molecular mechanisms. This chapter provides an overview of these approaches and describes two ML frameworks that integrate structural data (via graph representations) with neural networks to predict properties of antibodies: ANTIPASTI predicts binding affinity (a global property) whereas INFUSSE predicts residue flexibility (a local property). We survey the principles underpinning these models; the ways in which they encode structural knowledge; and the strategies that can be used to extract biologically relevant statistical signals that can help discover and disentangle molecular determinants of the properties of interest.