Papers

Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially-structured data. The concept has been interpreted in various ways but is broadly defined as bias in estimates arising from unmeasured spatial variation. In this paper we review definitions, classical spatial models, and recent methodological advances, including approaches from spatial statistics and causal inference. We provide an unified view of the many available approaches for areal as well as geostatistical data and discuss their relative merits both theoretically and empirically with a head-to-head comparison on real datasets. Finally, we leverage the results of the empirical comparisons to discuss directions for future research.

We consider the landscape of empirical risk minimization for high-dimensional Gaussian single-index models (generalized linear models). The objective is to recover an unknown signal $\boldsymbol{\theta}^\star \in \mathbb{R}^d$ (where $d \gg 1$) from a loss function $\hat{R}(\boldsymbol{\theta})$ that depends on pairs of labels $(\mathbf{x}_i \cdot \boldsymbol{\theta}, \mathbf{x}_i \cdot \boldsymbol{\theta}^\star)_{i=1}^n$, with $\mathbf{x}_i \sim \mathcal{N}(0, I_d)$, in the proportional asymptotic regime $n \asymp d$. Using the Kac-Rice formula, we analyze different complexities of the landscape – defined as the expected number of critical points – corresponding to various types of critical points, including local minima. We first show that some variational formulas previously established in the literature for these complexities can be drastically simplified, reducing to explicit variational problems over a finite number of scalar parameters that we can efficiently solve numerically. Our framework also provides detailed predictions for properties of the critical points, including the spectral properties of the Hessian and the joint distribution of labels. We apply our analysis to the real phase retrieval problem for which we derive complete topological phase diagrams of the loss landscape, characterizing notably BBP-type transitions where the Hessian at local minima (as predicted by the Kac-Rice formula) becomes unstable in the direction of the signal. We test the predictive power of our analysis to characterize gradient flow dynamics, finding excellent agreement with finite-size simulations of local optimization algorithms, and capturing fine-grained details such as the empirical distribution of labels. Overall, our results open new avenues for the asymptotic study of loss landscapes and topological trivialization phenomena in high-dimensional statistical models.

Electroencephalography (EEG)-based P300 brain-computer interfaces (BCIs) enable communication without physical movement by detecting stimulus-evoked neural responses. Accurate and efficient decoding remains challenging due to high dimensionality, temporal dependence, and complex interactions across EEG channels. Existing approaches often treat channels independently or rely on black-box models, limiting interpretability and personalization. We propose a sparse Bayesian time-varying regression framework that explicitly models pairwise EEG channel interactions while performing temporal feature selection, where a relaxed-thresholded Gaussian process prior induces structured sparsity in both channel-specific and interaction effects, enabling interpretable identification of task-relevant channels and channel pairs. Applied to a public P300 speller dataset of 55 participants, our method achieves a 96.4% median character-level accuracy using all sequence repetitions and attains the best overall decoding performance among competing statistical and deep learning approaches. Incorporating channel interactions yields subgroup-specific gains in character-level accuracy, particularly among participants abstained from alcohol (median 7%, up to 14%). Importantly, our approach improves median BCI-Utility by more than 10% at its optimal operating point, achieving peak throughput after only six sequence repetitions. These results demonstrate that explicitly modeling structured EEG channel interactions within a principled Bayesian framework enhances accuracy and user-centric throughput, and supports personalization in P300 BCI systems.

We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL). Unlike interpretations framing Transformers as performing implicit gradient descent, we formalize ICL as meta-learning over latent sequence tasks. For tasks governed by Linear Gaussian State Space Models (LG-SSMs), we prove a meta-trained selective SSM asymptotically implements the Bayes-optimal predictor, converging to the posterior predictive mean. We further establish a statistical separation from gradient descent, constructing tasks with temporally correlated noise where the optimal Bayesian predictor strictly outperforms any empirical risk minimization (ERM) estimator. Since Transformers can be seen as performing implicit ERM, this demonstrates selective SSMs achieve lower asymptotic risk due to superior statistical efficiency. Experiments on synthetic LG-SSM tasks and a character-level Markov benchmark confirm selective SSMs converge faster to Bayes-optimal risk, show superior sample efficiency with longer contexts in structured-noise settings, and track latent states more robustly than linear Transformers. This reframes ICL from "implicit optimization" to "optimal inference," explaining the efficiency of selective SSMs and offering a principled basis for architecture design.

In-context learning (ICL) allows large language models to adapt to new tasks from a few examples without updating their parameters. Existing theories explain ICL by assuming the test task distribution matches pretraining – an assumption that breaks down under adversarial distribution shifts. We introduce a distributionally robust meta-learning framework that provides worst-case guarantees for ICL under Wasserstein-based distribution shifts. Focusing on linear self-attention Transformers, we derive a non-asymptotic bound connecting adversarial perturbation strength ($\rho$), model capacity ($m$), and the number of in-context examples ($N$). The analysis reveals that the maximum safe perturbation radius scales as $\rho_{\max} \propto \sqrt{m}$, while maintaining performance under adversarial shift requires additional in-context examples with $N_\rho - N_0 \propto \rho^2$. Experiments on synthetic tasks confirm these scaling laws, and experiments on 21 real pretrained models (0.1B–7B parameters, 5 families) provide qualitative evidence consistent with the theory's predictions, while revealing that ICL capability is a prerequisite for robustness. These findings advance the theoretical understanding of ICL under adversarial conditions and formalize the sense in which larger models are safer under distributional shift.

Market area models, such as the Huff Model and its extensions, are used to estimate regional market shares and customer flows of retail and service locations. In health geography, market area and accessibility models are applied for the analysis of catchment areas and spatial accessibility of healthcare locations. The huff Python package provides a complete workflow for market area and spatial accessibility analysis, including data import, construction of origin-destination interaction matrices, basic model analysis, parameter estimation from empirical data, calculation of distance or travel time matrices, and map visualization. The package is modular and object-oriented. It is intended for researchers in economic geography, regional economics, marketing, geoinformation science, and health geography. The software is openly available via the Python Package Index (PyPI) (https://pypi.org/project/huff/). Its development and version history are managed in a public GitHub Repository (https://github.com/geowieland/huff_official) and archived at Zenodo (https://doi.org/10.5281/zenodo.18639559). A methodological handbook is also available on GitHub Pages (https://geowieland.github.io/huff_official/).

Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through weak–strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier.

The proliferation of Large Language Models (LLMs) necessitates efficient mechanisms to distinguish machine-generated content from human text. While statistical watermarking has emerged as a promising solution, existing methods suffer from two critical limitations: the lack of a principled approach for selecting sampling distributions and the reliance on fixed-horizon hypothesis testing, which precludes valid early stopping. In this paper, we bridge this gap by developing the first e-value-based watermarking framework, Anchored E-Watermarking, that unifies optimal sampling with anytime-valid inference. Unlike traditional approaches where optional stopping invalidates Type-I error guarantees, our framework enables valid, anytime-inference by constructing a test supermartingale for the detection process. By leveraging an anchor distribution to approximate the target model, we characterize the optimal e-value with respect to the worst-case log-growth rate and derive the optimal expected stopping time. Our theoretical claims are substantiated by simulations and evaluations on established benchmarks, showing that our framework can significantly enhance sample efficiency, reducing the average token budget required for detection by 13-15% relative to state-of-the-art baselines.

Cryo-electron microscopy (cryo-EM) has emerged as a powerful technique for resolving the three-dimensional structures of macromolecules. A key challenge in cryo-EM is characterizing continuous heterogeneity, where molecules adopt a continuum of conformational states. Covariance-based methods offer a principled approach to modeling structural variability. However, estimating the covariance matrix efficiently remains a challenging computational task. In this paper, we present SOLVAR (Stochastic Optimization for Low-rank Variability Analysis), which leverages a low-rank assumption on the covariance matrix to provide a tractable estimator for its principal components, despite the apparently prohibitive large size of the covariance matrix. Under this low-rank assumption, our estimator can be formulated as an optimization problem that can be solved quickly and accurately. Moreover, our framework enables refinement of the poses of the input particle images, a capability absent from most heterogeneity-analysis methods, and all covariance-based methods. Numerical experiments on both synthetic and experimental datasets demonstrate that the algorithm accurately captures dominant components of variability while maintaining computational efficiency. SOLVAR achieves state-of-the-art performance across multiple datasets in a recent heterogeneity benchmark. The code of the algorithm is freely available at https://github.com/RoeyYadgar/SOLVAR.

The win ratio (WR) statistic is increasingly used to evaluate treatment effects based on prioritized composite endpoints, yet existing Bayesian adaptive designs are not directly applicable because the WR is a summary statistic derived from pairwise comparisons and does not correspond to a unique data-generating mechanism. We propose a Bayesian model-assisted adaptive design for randomized phase II clinical trials based on the WR statistic, referred to as the BMW design. The proposed design uses the joint asymptotic distribution of WR test statistics across interim and final analyses to compute posterior probabilities without specifying the underlying outcome distribution. The BMW design allows flexible interim monitoring with early stopping for futility or superiority and is extended to jointly evaluate efficacy and toxicity using a graphical testing procedure that controls the family-wise error rate (FWER). Simulation studies demonstrate that the BMW design maintains valid type I error and FWER control, achieves power comparable to conventional methods, and substantially reduces expected sample size. An R Shiny application is provided to facilitate practical implementation.

We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the alternative corresponds to a disjoint set $Q$. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the alternative, which is asymptotically tight. Our novel analysis improves the existing lower bounds, which are either asymptotic or provably sub-optimal in this setting. Our lower bound incorporates both the stationary distribution and the transition structure induced by the unknown Markov chain. We further propose an optimal test whose expected stopping time matches this lower bound asymptotically as $\alpha \to 0$. We illustrate the usefulness of our framework through applications to sequential detection of model misspecification in Markov Chain Monte Carlo and to testing structural properties, such as the linearity of transition dynamics, in Markov decision processes. Our findings yield a sharp and general characterization of optimal sequential testing procedures under Markovian dependence.

Omniprediction is a learning problem that requires suboptimality bounds for each of a family of losses $\mathcal{L}$ against a family of comparator predictors $\mathcal{C}$. We initiate the study of omniprediction in a multiclass setting, where the comparator family $\mathcal{C}$ may be infinite. Our main result is an extension of the recent binary omniprediction algorithm of [OKK25] to the multiclass setting, with sample complexity (in statistical settings) or regret horizon (in online settings) $\approx \varepsilon^{-(k+1)}$, for $\varepsilon$-omniprediction in a $k$-class prediction problem. En route to proving this result, we design a framework of potential broader interest for solving Blackwell approachability problems where multiple sets must simultaneously be approached via coupled actions.

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression in unconstrained setting in which the mixing weight $\xi$ may be outside the unit interval. Conditioned on the training data and without any distributional assumptions, we prove that for any squared prediction risk (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher for every regularization level $\lambda > 0$ at which the teacher ridge risk $R(\lambda)$ is nonstationary (i.e., $R'(\lambda) \neq 0$). We obtain a closed-form expression for the optimal mixing weight $\xi^\star(\lambda)$ for any value of $\lambda$ and show that it obeys the sign rule: $\operatorname{sign}(\xi^\star(\lambda))=-\operatorname{sign}(R'(\lambda))$. In particular, $\xi^\star(\lambda)$ can be negative, which is the case in over-regularized regimes. To quantify the risk improvement due to SD, we derive exact deterministic equivalents for the optimal SD risk in the proportional asymptotics regime (where the sample and feature sizes $n$ and $p$ both diverge but their aspect ratio $p/n$ converges) under general anisotropic covariance and deterministic signals. Our asymptotic analysis extends standard second-order ridge deterministic equivalents to their fourth-order analogs using block linearization, which may be of independent interest. From a practical standpoint, we propose a consistent one-shot tuning method to estimate $\xi^\star$ without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

Training large-scale generative models is resource-intensive and relies heavily on heuristic dataset weighting. We address two fundamental questions: Can we train Large Language Models (LLMs) modularly, combining small, domain-specific experts to match monolithic performance, and can we do so robustly for any data mixture, eliminating heuristic tuning? We present a theoretical framework for modular generative modeling where a set of pre-trained experts are combined via a gating mechanism. We define the space of normalized gating functions $\mathcal{G}_{1}$ and formulate the problem as a minimax game to find a single robust gate that minimizes divergence to the worst-case data mixture. We prove the existence of such a robust gate using Kakutani's fixed-point theorem and show that modularity acts as a strong regularizer, with generalization bounds scaling with the lightweight gate's complexity. Furthermore, we prove that this modular approach can theoretically outperform models retrained on aggregate data, with the gap characterized by the Jensen-Shannon Divergence. Finally, we introduce a scalable Stochastic Primal-Dual algorithm and a Structural Distillation method for efficient inference. Empirical results on synthetic and real-world datasets confirm that our modular architecture effectively mitigates gradient conflict and can robustly outperform monolithic baselines.

Efficient estimation of causal and structural parameters can be automated using the Riesz representation theorem and debiased machine learning (DML). We present genriesz, an open-source Python package that implements automatic DML and generalized Riesz regression, a unified framework for estimating Riesz representers by minimizing empirical Bregman divergences. This framework includes covariate balancing, nearest-neighbor matching, calibrated estimation, and density ratio estimation as special cases. A key design principle of the package is automatic regressor balancing (ARB): given a Bregman generator $g$ and a representer model class, genriesz} automatically constructs a compatible link function so that the generalized Riesz regression estimator satisfies balancing (moment-matching) optimality conditions in a user-chosen basis. The package provides a modulr interface for specifying (i) the target linear functional via a black-box evaluation oracle, (ii) the representer model via basis functions (polynomial, RKHS approximations, random forest leaf encodings, neural embeddings, and a nearest-neighbor catchment basis), and (iii) the Bregman generator, with optional user-supplied derivatives. It returns regression adjustment (RA), Riesz weighting (RW), augmented Riesz weighting (ARW), and TMLE-style estimators with cross-fitting, confidence intervals, and $p$-values. We highlight representative workflows for estimation problems such as the average treatment effect (ATE), ATE on treated (ATT), and average marginal effect estimation. The Python package is available at https://github.com/MasaKat0/genriesz and on PyPI.

In variational inference (VI), the practitioner approximates a high-dimensional distribution $\pi$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions might not capture the correct radial profile of $\pi$, resulting in poor coverage. In this work, we approach the VI problem from the perspective of optimizing over these radial profiles. Our algorithm radVI is a cheap, effective add-on to many existing VI schemes, such as Gaussian (mean-field) VI and Laplace approximation. We provide theoretical convergence guarantees for our algorithm, owing to recent developments in optimization over the Wasserstein space–the space of probability distributions endowed with the Wasserstein distance–and new regularity properties of radial transport maps in the style of Caffarelli (2000).

Detecting brief changes in time-series data remains a major challenge in fields where short-lived states carry meaning. In single-molecule localisation microscopy, this problem is particularly acute as fluorescent molecules used to tag protein oligomers display heterogenous photophysical behaviour that can complicate photobleach step analysis; a key step in resolving nanoscale protein organisation. Existing methods often require extensive filtering or prior calibration, and can fail to accurately account for blinking or reversible dark states that may contaminate downstream analysis. In this paper, an extension to RJMCMC is proposed for change point detection with heterogeneous temporal dynamics. This approach is applied to the problem of estimating per-frame active fluorophore counts from one-dimensional integrated intensity traces derived from Fluorescence Localisation Imaging with Photobleaching (FLImP), where compound change point pair moves are introduced to better account for short-lived events known as blinking and dark states. The approach is validated using simulated and experimental data, demonstrating improved accuracy and robustness when compared with current photobleach step analysis methods and with the existing analysis approach for FLImP data. This Compound RJMCMC (CRJMCMC) algorithm performs reliably across a wide range of fluorophore counts and signal-to-noise conditions, with signal-to-noise ratio (SNR) down to 0.001 and counts as high as nineteen fluorophores, while also effectively estimating low counts observed when studying EGFR oligomerisation. Beyond single molecule imaging, this work has applications for a variety of time series change point detection problems with heterogeneous state persistence. For example, electrocorticography brain-state segmentation, fault detection in industrial process monitoring and realised volatility in financial time series.

The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties of weakly convex–concave regularized estimators in high-dimensional quadratic measurements models. By employing a weakly convex–concave penalized least squares approach, we establish support recovery and $\ell_2$-error bounds for the local minimizer. To solve the corresponding optimization problem, we adopt two proximal gradient strategies, where the proximal step is computed either in closed form or via a weighted $\ell_1$ approximation, depending on the regularization function. Numerical examples demonstrate the efficacy of the proposed method.

We present Nested Sampling with Slice-within-Gibbs (NS-SwiG), an algorithm for Bayesian inference and evidence estimation in high-dimensional models whose likelihood admits a factorization, such as hierarchical Bayesian models. We construct a procedure to sample from the likelihood-constrained prior using a Slice-within-Gibbs kernel: an outer update of hyperparameters followed by inner block updates over local parameters. A likelihood-budget decomposition caches per-block contributions so that each local update checks feasibility in constant time rather than recomputing the global constraint at linearly growing cost. This reduces the per-replacement cost from quadratic to linear in the number of groups, and the overall algorithmic complexity from cubic to quadratic under standard assumptions. The decomposition extends naturally beyond independent observations, and we demonstrate this on Markov-structured latent variables. We evaluate NS-SwiG on challenging benchmarks, demonstrating scalability to thousands of dimensions and accurate evidence estimates even on posterior geometries where state-of-the-art gradient-based samplers can struggle.

In imaging inverse problems with Poisson-distributed measurements, it is common to use objectives derived from the Poisson likelihood. But performance is often evaluated by mean squared error (MSE), which raises a practical question: how much does a Poisson objective matter for MSE, even at low dose? We analyze the MSE of Poisson and Gaussian surrogate reconstruction objectives under Poisson noise. In a stylized diagonal model, we show that the unregularized Poisson maximum-likelihood estimator can incur large MSE at low dose, while Poisson MAP mitigates this instability through regularization. We then study two Gaussian surrogate objectives: a heteroscedastic quadratic objective motivated by the normal approximation of Poisson data, and a homoscedastic quadratic objective that yields a simple linear estimator. We show that both surrogates can achieve MSE comparable to Poisson MAP in the low-dose regime, despite departing from the Poisson likelihood. Numerical computed tomography experiments indicate that these conclusions extend beyond the stylized setting of our theoretical analysis.

Statistical boosting algorithms are renowned for their intrinsic variable selection and enhanced predictive performance compared to classical statistical methods, making them especially useful for complex models such as generalized additive models for location scale and shape (GAMLSS). Boosting this model class can suffer from imbalanced updates across the distribution parameters as well as long computation times. Shrunk optimal step lengths have been shown to address these issues. To examine the influence of socio-economic factors on the distribution of the number of antenatal care visits in Nigeria, we generalize boosting of GAMLSS with shrunk optimal step lengths to base-learners beyond simple linear models and to a more complex response variable distribution. In an extensive simulation study and in the application we demonstrate that shrunk optimal step lengths yield a more balanced regularization of the overall model and enhance computational efficiency across diverse settings, in particular in the presence of base-learners penalizing the size of the fit.

Human self-report questionnaires are increasingly used in NLP to benchmark and audit large language models (LLMs), from persona consistency to safety and bias assessments. Yet these instruments presume honest responding; in evaluative contexts, LLMs can instead gravitate toward socially preferred answers-a form of socially desirable responding (SDR)-biasing questionnaire-derived scores and downstream conclusions. We propose a psychometric framework to quantify and mitigate SDR in questionnaire-based evaluation of LLMs. To quantify SDR, the same inventory is administered under HONEST versus FAKE-GOOD instructions, and SDR is computed as a direction-corrected standardized effect size from item response theory (IRT)-estimated latent scores. This enables comparisons across constructs and response formats, as well as against human instructed-faking benchmarks. For mitigation, we construct a graded forced-choice (GFC) Big Five inventory by selecting 30 cross-domain pairs from an item pool via constrained optimization to match desirability. Across nine instruction-following LLMs evaluated on synthetic personas with known target profiles, Likert-style questionnaires show consistently large SDR, whereas desirability-matched GFC substantially attenuates SDR while largely preserving the recovery of the intended persona profiles. These results highlight a model-dependent SDR-recovery trade-off and motivate SDR-aware reporting practices for questionnaire-based benchmarking and auditing of LLMs.

We seek to narrow the gap between parametric and nonparametric modelling of stationary time series processes. The approach is inspired by recent advances in focused inference and model selection techniques. The paper generalises and extends recent work by developing a new version of the focused information criterion (FIC), directly comparing the performance of parametric time series models with a nonparametric alternative. For a pre-specified focused parameter, for which scrutiny is considered valuable, this is achieved by comparing the mean squared error of the model-based estimators of this quantity. In particular, this yields FIC formulae for covariances or correlations at specified lags, for the probability of reaching a threshold, etc. Suitable weighted average versions, the AFIC, also lead to model selection strategies for finding the best model for the purpose of estimating e.g.~a sequence of correlations.

This methodological note investigates and discuss possible selection and collider restriction bias due to predictor availability in prognostic models.

The combinatorial approach applied to functional oxides has enabled the production of material libraries that formally contain infinite compositions. A complete ternary diagram can be obtained by pulsed laser deposition (PLD) on 100 mm silicon wafers. However, interest in such materials libraries is only meaningful if high-throughput characterization enables the information extraction from the as-deposited library in a reasonable time. While much commercial equipment allows for XY-resolved characterization at room temperature, very few sample holders have been made available to investigate structural, chemical, and functional properties at high temperatures in controlled atmospheres. In the present work, we present a furnace that enables the study of 100 mm wafers as a function of temperature. This furnace has a dome to control the atmosphere, typically varying from nitrogen gas to pure oxygen atmosphere with external control. We present the design of such a furnace and an example of X-ray diffraction (XRD) and fluorescence (XRF) measurements performed at the DiffAbs beamline of the SOLEIL synchrotron. We apply this high-throughput approach to a combinatorial library up to 735 {\textdegree}C in nitrogen and calculate the thermal expansion coefficients (TEC) of the ternary system using custom-made MATLAB codes. The TEC analysis revealed the potential limitations of Vegard's law in predicting lattice variations for high-entropy materials.

Generating samples from limited information is a fundamental problem across scientific domains. Classical maximum entropy methods provide principled uncertainty quantification from moment constraints but require sampling via MCMC or Langevin dynamics, which typically exhibit exponential slowdown in high dimensions. In contrast, generative models based on diffusion and flow matching efficiently transport noise to data but offer limited theoretical guarantees and can overfit when data is scarce. We introduce Moment Guided Diffusion (MGD), which combines elements of both approaches. Building on the stochastic interpolant framework, MGD samples maximum entropy distributions by solving a stochastic differential equation that guides moments toward prescribed values in finite time, thereby avoiding slow mixing in equilibrium-based methods. We formally obtain, in the large-volatility limit, convergence of MGD to the maximum entropy distribution and derive a tractable estimator of the resulting entropy computed directly from the dynamics. Applications to financial time series, turbulent flows, and cosmological fields using wavelet scattering moments yield estimates of negentropy for high-dimensional multiscale processes.

The problem of domain generalization concerns learning predictive models that are robust to distribution shifts when deployed in new, previously unseen environments. Existing methods typically require labeled data from multiple training environments, limiting their applicability when labeled data are scarce. In this work, we study domain generalization in an anti-causal setting, where the outcome causes the observed covariates. Under this structure, environment perturbations that affect the covariates do not propagate to the outcome, which motivates regularizing the model's sensitivity to these perturbations. Crucially, estimating these perturbation directions does not require labels, enabling us to leverage unlabeled data from multiple environments. We propose two methods that penalize the model's sensitivity to variations in the mean and covariance of the covariates across environments, respectively, and prove that these methods have worst-case optimality guarantees under certain classes of environments. Finally, we demonstrate the empirical performance of our approach on a controlled physical system and a physiological signal dataset.

The best known methods for estimating hazard rate functions in survival analysis models are either purely parametric or purely nonparametric. The parametric ones are sometimes too biased while the nonparametric ones are sometimes too variable. In the present paper a certain semiparametric approach to hazard rate estimation, proposed in Hjort (1991), is developed further, aiming to combine parametric and nonparametric features. It uses a dynamic local likelihood approach to fit the locally most suitable member in a given parametric class of hazard rates, and amounts to a version of nonparametric parameter smoothing within the parametric class. Thus the parametric hazard rate estimate at time $s$ inserts a parameter estimate that also depends on $s$. We study bias and variance properties of the resulting estimator and methods for choosing the local smoothing parameter. It is shown that dynamic likelihood estimation often leads to better performance than the purely nonparametric methods, while also having capacity for not losing much to the parametric methods in cases where the model being smoothed is adequate.

Learning to Defer (L2D) enables a classifier to abstain from predictions and defer to an expert, and has recently been extended to multi-expert settings. In this work, we show that multi-expert L2D is fundamentally more challenging than the single-expert case. With multiple experts, the classifier's underfitting becomes inherent, which seriously degrades prediction performance, whereas in the single-expert setting it arises only under specific conditions. We theoretically reveal that this stems from an intrinsic expert identifiability issue: learning which expert to trust from a diverse pool, a problem absent in the single-expert case and renders existing underfitting remedies failed. To tackle this issue, we propose PiCCE (Pick the Confident and Correct Expert), a surrogate-based method that adaptively identifies a reliable expert based on empirical evidence. PiCCE effectively reduces multi-expert L2D to a single-expert-like learning problem, thereby resolving multi expert underfitting. We further prove its statistical consistency and ability to recover class probabilities and expert accuracies. Extensive experiments across diverse settings, including real-world expert scenarios, validate our theoretical results and demonstrate improved performance.

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses several common message passing architectures: node features are first propagated over the graph then mapped to responses via a nonlinear function. For least-squares estimation over GNNs with linear graph convolutions and a deep ReLU readout, we prove a sharp non-asymptotic risk bound that separates approximation, stochastic, and optimization errors. The bound makes explicit how performance scales with the fraction of labeled nodes and graph-induced dependence. Approximation guarantees are further derived for graph-smoothing followed by smooth nonlinear readouts, yielding convergence rates that recover classical nonparametric behavior under full supervision while characterizing performance when labels are scarce. Numerical experiments validate our theory, providing a systematic framework for understanding GNN performance and limitations.