Papers

In this study, we consider sequences drawn from time-homogeneous Markov chains and introduce a novel approach for estimating first hitting-time distributions to specified terminal states. Our method- ology is based on the temporal-consistent survival analysis that facilitates the construction of consistent estimators of the distributions from any estimates of the transition rate and transition probabilities. In this line of work, we also discuss the issue of cured individuals with chains that never reach a termi- nal state, and propose an estimator of the cure rate. Furthermore, we derive non-asymptotic theoretical guarantees for our approach and apply our methodology with kernel type estimators. The latter approach is illustrated in a simulation study using generic data and a real-life application involving patients un- dergoing bone marrow transplants.

This paper proposes a novel framework for the approximation and analysis of circular density data using compositional periodic splines within Bayes spaces with the Hilbert space structure. By applying the centered log-ratio transformation, densities are represented in a subspace of the standard $L^2$ space of real-valued functions, which enables the use of functional data analysis tools while preserving the relative nature of distributions and their periodic structure. A coefficient-based construction of periodic splines with a zero-integral constraint is developed, together with matrix formulations for both smoothing splines and penalized splines, allowing efficient estimation and implementation. The methodology is applied to long-term wind direction data, where it provides smooth and interpretable density estimates and supports further statistical analysis, including functional regression. The results demonstrate the practical relevance of the proposed approach and its potential for extensions to more complex density-valued data.

Champion recommendation in multiplayer online battle arena games is usually framed informally as a problem of metagame strength, personal comfort, or global win rate. We formalize champion recommendation in League of Legends as an interpretable, player-conditional ranking problem under sparse, noisy, and non-stationary behavioral data. The proposed framework combines four information sources: a population-strength proxy, player-style similarity, direct and indirect mastery priors, and archetype-level guardrails. The method uses robust median/MAD normalization, logarithmic transforms for skewed event counts, recency-weighted player style vectors, mastery-weighted champion-pool vectors, weighted cosine similarity, rank-scaled score components, and k-means++ clustering for coarse archetype support. The implemented prototype uses a Python/Pandas modeling layer, Supabase-backed storage, and a web-facing recommendation interface. Unlike black-box supervised win-prediction systems, the proposed method returns decomposed recommendation scores that can be inspected as expected-performance proxy, fit, mastery, and archetype compatibility. A single-player case study on a 100-game history for the player identifier DIVINERAINRACCON is included as an end-to-end sanity check. The manuscript is therefore a methods and systems contribution: it specifies a reproducible, modular, and auditable champion recommender and gives a validation protocol for future large-scale evaluation through temporal train-test splits, next-champion recovery, calibration analysis, and ablation studies.

Representation Autoencoders (RAE) replace traditional VAE with pretrained vision encoders. In this paper, we systematically investigate several design choices and find three insights which simplify and improve RAE. First, we study a generalized formulation where the representation is defined as sum of the last k encoder layers rather than solely the final layer. This simple change greatly improves reconstruction without encoder finetuning or specialized data (e.g., text, faces). Second, we study the prevalent assumption that RAE (using pretrained representation as encoder) replaces representation alignment (REPA), which distills the same representation to intermediate layers instead. Through large-scale empirical analysis, we uncover a surprising finding: RAE and REPA exhibit complementary working mechanisms, allowing the same representation to be used as both encoder and target for intermediate diffusion layers. Finally, the original RAE struggles with classifier-free guidance (CFG) and requires training a second, weaker diffusion model for AutoGuidance (AG). We show that REPA itself can be viewed as x-prediction in RAE latent space. By simply re-parameterizing the output of the DiT model, it can provide guidance for "free". Overall, RAEv2 leads to more than 10x faster convergence over the original RAE, achieving a state-of-the-art gFID of 1.06 in just 80 epochs on ImageNet-256. On FDr6, RAEv2 achieves a state-of-the-art 2.17 at just 80 epochs compared to the previous best 3.26 (800 epochs) without any post-training. This motivates EPFID@k (epochs to reach unguided gFID < k) as a measure of training efficiency. RAEv2 attains an EPFID@2 of 35 epochs, versus 177 for the original RAE. We also validate our approach across diverse settings for text-to-image generation and navigation world models, showing consistent improvements. The code is available at https://raev2.github.io.

We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with the principal eigenvectors of the covariance matrix, thereby establishing a direct and explicit connection with PCA. Our analysis covers both finite and infinite prompt regimes. In the infinite-prompt limit, we prove convergence to globally optimal solutions aligned with the leading spectral direction, while in the finiteprompt setting we show that the same behavior emerges up to sampling effects. We further extend the analysis to an in-context setting with spiked Wishart covariances, where attention successfully recovers the underlying signal direction. These results demonstrate that attention inherently performs PCA-like computations under unsupervised objectives, providing a theoretical foundation for its representation-learning capabilities.

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and long-term behavior. However, dynamical operators are typically estimated independently for each system, preventing the discovery of shared structure across related dynamics. To address this limitation, we posit that related dynamical systems lie near a low-dimensional manifold in spectral operator space. Based on this hypothesis, we introduce DOODL (Dynamical OperatOr Dictionary Learning), a framework that learns a dictionary of characteristic spectral dynamics whose combinations approximate this manifold and yield compact, interpretable embeddings of individual systems. Beyond representation learning, DOODL enables fast and interpretable operator estimation from short and partially observed trajectories by constraining the estimation to the learned operator manifold. Experiments on metastable Langevin dynamics and turbulent plasma simulations demonstrate that DOODL scales to highly complex multiscale regimes while capturing characteristic spectral structure governing the dynamics rather than merely fitting trajectories, achieving errors one to two orders of magnitude lower than independent operator estimation methods in challenging low-data regimes.

The tree-structured varying coefficient (TSVC) model is a flexible approach for generalized regression, where the linear effects of the covariates are allowed to vary with the values of effect modifiers. Relevant effect modifiers and interactions are identified using recursive partitioning. In TSVC models, analogously to other semi- and nonparametric regression approaches, one needs to account for the cost of data-driven model building when deriving the model degrees of freedom (DoF). To address this issue, we develop an easy-to-apply formula to approximate the DoF of a TSVC model. This formula is employed for model selection based on the Bayesian information criterion (BIC) and compared to the naive solution, setting the DoF to the number of free model parameters, in a simulation study. To illustrate the proposed DoF method, TSVC models using BIC-based selection were fitted to data from the Survey of Health, Ageing, and Retirement in Europe. Results indicated that calculation of the DoF using the proposed formula resulted in more accurate selection results with improved predictive ability.

Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we propose Forward-Learned Discrete Diffusion (FLDD), which introduces discrete diffusion with a learnable forward (noising) process. Rather than fixing a Markovian forward chain, we adopt a non-Markovian formulation with learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective. Experiments on various benchmarks show that, for a given number of sampling steps, our approach produces a higher quality samples than conventional discrete diffusion models using the same reverse parameterization.

Wide neural networks in the feature-learning regime drive modern deep learning, and yet they remain far less studied than their kernel-regime counterparts. We consider a critical yet under-explored difference between these two regimes: the regulariser and prior implied by gradient flow training. This canonical regularisation property is well-studied in kernel regime networks – of all the infinite global minima, gradient flow selects exactly the vanishing ridge solution – and underpins the celebrated NN-GP correspondence, precisely allowing the modelling of noise during training. However, we prove ridge regularisation biases gradient flow in feature-learning regime networks, even in the infinitesimal limit of vanishing regularisation. Over training, ridge distorts the inductive bias of the network, with a particular damage done to pretrained networks where the implicit prior is informative. We resolve this by axiomatising the canonical regulariser as a regime-agnostic function-space energy and lift, which uniquely identifies ridge in the kernel regime, and crucially generalises to the feature-learning regime. By studying the Riemannian geometry of feature-learning networks, we derive geodesic ridge from our framework, generalising ridge to the feature-learning regime. Correspondingly, we prove the canonical function-space prior is a Riemannian Gibbs Process, generalising the more familiar Gaussian Process. As a practical contribution, we propose arc ridge as a minimax-robust, scalable surrogate to geodesic ridge, revealing a deep relationship between early stopping and canonical regularisation across learning regimes. Finally, we demonstrate the consequences of our theory empirically on both image processing and NLP transfer-learning problems.

Muon has recently emerged as a strong alternative to AdamW for training neural networks, with encouraging large-scale pretraining results and growing evidence that matrix-structured updates can be faster in practice. Yet Muon, and more generally Linear Minimization Oracle (LMO) based methods, are typically used synchronously. This is problematic in heterogeneous distributed systems, where workers complete gradient computations at different speeds and synchronous training must repeatedly wait for slower workers. In this work, we introduce Ringmaster LMO, an asynchronous LMO-based momentum method for unconstrained stochastic nonconvex optimization. Our method builds on the delay-thresholding idea of Ringmaster ASGD. For SGD-type methods, Ringmaster ASGD achieves optimal time complexity by discarding overly stale gradients. Ringmaster LMO extends this mechanism to general LMO-based updates. We establish convergence guarantees under generalized $(L_0, L_1)$-smoothness and further develop a parameter-agnostic variant with decreasing stepsizes and adaptive delay thresholds. Finally, we translate our iteration guarantees into time complexity bounds under heterogeneous worker computation times. In the classical Euclidean smooth setting, these bounds recover the optimal time complexity of Ringmaster ASGD. Experiments on stochastic quadratic problems and NanoChat language-model pretraining show that the advantages of Ringmaster LMO grow with system heterogeneity and that the method outperforms strong synchronous and asynchronous baselines.

As meta-analysis of multiple diagnostic tests impacts clinical decision making and patient health, there is growing interest in statistical models that synthesize evidence from studies comparing multiple diagnostic tests. To compare the accuracy of multiple diagnostic tests in a single study, three designs are commonly used: (i) the multiple test comparison design; (ii) the randomized design, and (iii) the non-comparative design. Generalized linear mixed models (GLMMs) are currently the recommended approach for jointly meta-analyzing data from all three designs, enabling simultaneous inference. In this context, 1-truncated C-vine copula mixed models are proposed as a flexible and powerful alternative. These models generalize the GLMM framework by allowing for arbitrary univariate distributions of the random effects and capturing tail dependencies and asymmetries. We demonstrate the utility of our methods with an extensive simulation study and by insightfully re-analysing a case study on the network meta-analysis of diagnostic tests for deep vein thrombosis. Findings indicate that 1-truncated C-vine copula mixed models can offer improvements over GLMMs, supporting their adoption for network meta-analysis of multiple diagnostic tests.

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend on deterministic point sets tailored to a specific kernel, making them sensitive to misspecification and less robust in practice. In this work, we study randomized quadrature methods with a focus on robustness rather than kernel-specific optimality. We construct an explicit, $n$-dependent sampling distribution that achieves minimax rates for worst-case error over smoothness classes without requiring knowledge of the kernel. This kernel-agnostic design improves robustness while retaining optimal rates. Our analysis includes unbounded sampling measures such as Gaussian and Student-$t$ distributions, extending beyond compact domains. The results provide both theoretical guarantees and a practical recipe for robust, rate-optimal randomized quadrature.

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible update rules consistently improve final validation loss, reduce expert load imbalance in sparse MoE models, and in several cases control final vocabulary-logit growth, improve router stability, and overall training stability over the corresponding AdamW updates.

This article presents a theoretical study of uncertainty functionals on general measurable spaces. These functionals are fundamental in experimental design and global sensitivity analysis, where they are used to quantify variability and information content in probabilistic models. As first articulated in DeGroot's seminal 1962 article, a natural requirement is that uncertainty should decrease on average when additional information is obtained. This requirement is equivalent to the probabilistic form of Jensen's inequality on the space of probability measures. Our main results show that concavity is necessary but not sufficient for Jensen's inequality to hold whenever the underlying measurable space is infinite. We also provide practicable sufficient conditions under which the desired property holds. These results contribute to a clearer mathematical foundation for uncertainty quantification. Several open questions are formulated.

This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad class of variance schedules, including the cosine schedule, we establish sharp upper bounds that are optimal in both the dimension and the number of steps, and recover several sharp error bounds previously obtained in the literature. (ii) We prove that the same Lipschitz-type conditions, which encompass those commonly imposed on the (learned) score, imply a logarithmic Sobolev inequality and hence a quadratic transportation cost inequality for the DDPM. As a consequence, in settings covered by existing work, an optimal Wasserstein bound, up to a logarithmic factor, follows from the recently obtained sharp error bound in the Kullback-Leibler divergence under geometric-type variance schedules. (iii) We show that for general log-concave target distributions, the optimal Wasserstein error bound remains attainable even without a quadratic transportation cost inequality for the target. Our analysis is based on viewing the DDPM sampler as a discretization of the Föllmer process rather than the conventional reverse Ornstein-Uhlenbeck process.

We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among sample complexity, condition number, runtime, and prediction error for efficient algorithms. Our first result is a near-linear-time algorithm that uses $\widetilde{O}(d/\epsilon^4)$ samples, where $d$ is the dimension and $\epsilon$ is the corruption rate, and achieves prediction error $O(\sqrt{\epsilon\kappa})$ under the condition $\epsilon\kappa \lesssim 1$, improving over all prior works. We complement this result with a Statistical Query (SQ) lower bound showing that efficient SQ algorithms achieving error $o(\sqrt{\epsilon\kappa})$ when $\epsilon \kappa \lesssim 1$ require queries that take $\Omega(d^2)$ samples to simulate. Finally, we prove a low-degree polynomial lower bound that gives fine-grained evidence that, without assumptions such as $\epsilon \kappa \lesssim 1$, efficient algorithms may require $\tilde{\Omega}\left(\min\{d\epsilon^{2}\kappa^{2},\ \epsilon^{2}d^{2}\}\right)$ samples to significantly outperform the trivial estimator that always guesses $0$.

The Föllmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an “augmented” time-compressed version of the reverse stochastic differential equation (SDE) corresponding to the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, the connection between direct discretization of the Föllmer process and the DDPM sampler has not yet been fully explored. This paper clarifies this point while surveying relevant results from the literature. We show that discretized Föllmer processes give natural hyper-parameter settings of the DDPM sampler while accommodating a broader class of variance schedules than discretized reverse SDEs. Moreover, this allows us to systematically recover state-of-the-art results on DDPM sampling error bounds, along with slight improvements.

This paper proposes a robust test for assessing isotropy based on the variogram of spatial data on a two-dimensional regular grid. The test is based on the non-robust subsampling test for isotropy of Guan et al. (2004), which uses the idea of comparing variogram estimates in diff erent directions at the same distance. The robust test employs robust variogram esti- mators which are based on estimators of univariate or multivariate scatter and perform well in the presence of isolated or block outliers. Additionally, a diff erent resampling method, called block permutation, is proposed. Compared with the subsampling test, the block per- mutation test maintains the signifi cance level even for strong dependencies in the data and is robust to outliers. The methods are illustrated by an application to Landsat 8 satellite data, where outlier blocks may occur due to, for example, clouds.

Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using modular arithmetic tasks under heavy label noise. Through extensive experiments on two-layer neural networks, we find that larger models tend to generalize better under appropriate optimization and model configurations, while noisy labels are memorized faster than clean data. Over-parameterized models internally form a generalization structure, but its expression in the output is suppressed by the need to fit noisy labels. Remarkably, even with 80% label noise, near-perfect test accuracy can be achieved by extracting this internal structure using frequency-based methods. We further propose a task-agnostic method to partition networks into generalization and memorization components. Although this subnetwork improves generalization, it is limited compared with frequency-based extraction, indicating that the generalization structure is distributed across neurons and motivating the development of new tools to retrieve generalizable knowledge from over-parameterized networks.

We propose a data-driven Fourier-trained neural-network method for estimating fixed-horizon probability densities from empirical characteristic-function (CF) information. The estimator is a positive Gaussian–Laplace mixture with closed-form CF, so training can be performed directly in Fourier space while preserving nonnegativity and unit mass. We consider two sampling settings. In the direct i.i.d. sampling setting, the method is trained against an empirical CF constructed from i.i.d. samples. In the resampling-based pseudo-sampling setting, it is trained against an empirical pseudo-CF constructed from dependent data by resampling. For the direct i.i.d. case, we derive an expected squared $L_2$ density-error bound that separates Fourier truncation, empirical training error, discretization, and CF sampling error, together with a corresponding bound for the expected $L_2$ norm. For the pseudo-sampling case, we obtain conditional counterparts with an additional pseudo-law discrepancy term. We develop a multidimensional extension of the framework and analyze its computational complexity. Numerical experiments show competitive performance relative to Expectation–Maximization on Gaussian-mixture benchmarks and clear gains on heavy-tailed targets. A controlled comparison with exact-CF training quantifies the additional density error introduced by empirical-CF training; further experiments show that the $L_2$ norm decays approximately as the inverse square root of the sample size when the remaining error terms are controlled, and demonstrate the method on a one-year Australian equity return law estimated from resampled dependent data.

Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability for deep learning-based blood pressure (BP) estimation from photoplethysmography (PPG) signals under both in-distribution (ID) and OOD settings. Using an XResNet1D-50 trained on PulseDB and tested on four external datasets, we compared deep ensembles (DE) and Monte Carlo dropout (MCD) with Gaussian negative log-likelihood (GNLL) and mean squared error (MSE) losses, optionally followed by post-hoc recalibration via conformal prediction (CP), temperature scaling (TS), and isotonic regression (IR). The key findings of our study are as follows: (1) DE provides stronger predictive robustness under domain shift than MCD, an advantage that becomes clear primarily under external shift. (2) Recalibrated GNLL-based methods yield the best uncertainty calibration (e.g., GNLL+DE+CP for systolic blood pressure (SBP), GNLL+DE+TS for diastolic blood pressure (DBP)), while MSE-based uncertainty requires recalibration to become practically useful. (3) Across settings, CP and TS offer the most consistent gains, with IR remaining competitive in several cases. Overall, our results identify DE-based methods as most robust for predictive performance under domain shift, GNLL as strongest for native UQ, and recalibration as essential for making MSE-based uncertainty practical. These findings highlight the need to jointly assess predictive accuracy and calibration on external data for trustworthy cuffless BP estimation

Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.

Extending saddle-free Newton methods to Wasserstein space requires controlling Hessian dependent operators along nonlinear transport trajectories and accounting for a Hessian spectrum that may accumulate at zero. We address these challenges through Wasserstein Saddle-Free Newton (WSFN), a second-order method for nonconvex optimization over Wasserstein space that preconditions the Wasserstein gradient by a regularized inverse square root Hessian operator. The dynamics exploit curvature magnitude while maintaining negative curvature repulsion and positive curvature attraction, avoiding key Wasserstein Newton limitations. Whereas previous Wasserstein saddle escape results rely on perturbed first-order dynamics, WSFN uses curvature both to modify the deterministic transport and to construct the perturbation mechanism. Our analysis combines stability estimates for Hessian operators with a perturbative saddle escape argument to establish polynomial time convergence to approximate second-order stationarity under regularity of landscape assumptions. The contribution of the saddle curvature parameter $\delta$ improves from $\tilde O(\delta^{-4})$ for prior perturbed first-order Wasserstein methods to $\tilde O(\delta^{-3})$. For benign landscapes, this implies proximity to global minimizers. The cubic dependence corresponds to the scale of the objective decrease that can be guaranteed from negative curvature under Lipschitz Hessian regularity. Near a minimizer, the possible absence of a uniform spectral gap prevents a uniform contraction result and instead calls for a spectral characterization. We prove geometric contraction of the linearized dynamics on positive curvature spectral bands bounded away from zero and polynomial decay under spectral source conditions. Together, these results connect quantitative saddle escape with the local spectral behavior of second-order Wasserstein dynamics.

Training data attribution (TDA) should enable generative model interpretability and foster a variety of related downstream tasks. Nonetheless, current TDA approaches lack reliability and robustness, preventing their adoption in real-world setups. In this paper, we take a decisive step towards more reliable and robust TDA for diffusion models. We propose to perform TDA with mirrored unlearning and noise-consistent skew (MUCS). The idea is to fine-tune a second model with bounded mirrored gradient ascent, and to measure the normalized skew of this model with respect to the original one using consistent noise samples. We show that, while being conceptually simple and generic, MUCS systematically outperforms existing methods on three different datasets by a large margin. We additionally study the effect that core design choices have on final performance, and analyze novel aspects regarding the overlap of influential instances across generated items and the potential of ensembling TDA approaches. We believe that our findings may have broader implications for more general unlearning setups, as well as for tasks requiring the comparison of diffusion losses.

We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target coverage level, most provide marginal coverage. In practice, conditional predictive inference is often preferred, as it quantifies uncertainty for black-box predictions given observed attributes, thereby accommodating heterogeneity. Although many efforts have pursued efficient conditional coverage, existing methods rely on the i.i.d. or exchangeable assumption, often violated in structured settings such as networks, clusters, and imaging data. Recently, SymmPI introduced a unified approach to predictive inference under group symmetries beyond exchangeability; nevertheless, its guarantees remain marginal and do not account for population heterogeneity. To bridge this gap, we introduce C-SymmPI, a framework that achieves near-conditional coverage under general data structures with group symmetries, extending beyond exchangeability to cover networks, cluster-level data, and related structures. Inspired by relaxed multi-accuracy, our approach reformulates conditional coverage as miscoverage error over a user-specified function class. We establish theoretical guarantees under distributional invariance and distribution shift, and derive convergence rates for linear and RKHS function classes, recovering state-of-the-art results in the exchangeable setting as special cases. For computational efficiency, we develop two variants: a projection-based algorithm for high-dimensional observations, and a sampling-based algorithm for large or infinite groups. We demonstrate effectiveness on hierarchical and network data. Empirical results show that C-SymmPI delivers more informative and stable conditional coverage with improved accuracy compared to existing methods.

Some time series can be hierarchically organized into levels based on certain characteristics, such as geography or other attributes of interest. These series are referred to as hierarchical time series. Typically, forecasts are generated at all levels to ensure coherence, meaning that the forecasts should satisfy the same aggregation constraints as the observed data. Various approaches have been proposed to guarantee this coherence by using a set of base forecasts. The process through which these forecasts are adjusted to become coherent is known as forecast reconciliation. Similar to the univariate case, multivariate time series can also be structured hierarchically. However, all existing approaches are limited to a single variable. As a result, ensuring coherent forecasts requires reconciling each variable separately. However, this process does not account for correlations among multiple variables. To address this limitation, this paper proposes a multivariate reconciliation methodology that ensures coherent forecasts and incorporates relationships among variables. The proposed methodology was tested through numerical simulations, considering distinct scenarios within the series hierarchy and across multiple variables. Additionally, some base forecasting models were evaluated. The methodology was also applied to real employment data of admissions and dismissals in Brazil. The results demonstrated that multivariate reconciliation yielded more accurate outcomes than the other methods considered, both in simulated data and in practical applications.

We propose a double/debiased machine learning framework to estimate average derivative effects in nonparametric panel models with two-way fixed effects. It extends instrumental variable methods to panel settings, handles continuous treatments and various forms of endogeneity, and introduces a cross-fitting scheme to restore independence after eliminating time fixed effects. A penalized GMM debiasing term enables automatic debiased machine learning with endogeneity. Our estimators for contemporaneous, dynamic, and aggregated effects are consistent and asymptotically normal with a valid variance estimator. Simulations show reduced regularization bias and accurate confidence intervals. An application to ECLS-K data reveals rich dynamics in the effect of family SES on childhood BMI.

This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing greater flexibility than Fourier-based approaches. Simulation experiments and real-data applications are used to evaluate the model's performance.

iffusion-based generative models increasingly rely on inference-time guidance, adding a drift term or reweighting mixture of experts, to improve sample quality on task-specific objectives. However, most existing techniques require repeated score or gradient evaluations, introducing bias, high computational overhead, or both. We introduce URGE, Unbiased Resampling via Girsanov Estimation, a derivative-free inference-time scaling algorithm that performs path-wise importance reweighting via a Girsanov change of measure. Instead of computing gradient-based particle weights in previous work, URGE attaches a simple multiplicative weight to each simulated trajectory and periodically resamples. No score, no Hessian, and no PDE evaluation is required. We establish an equivalence between path-wise and particle-wise SMC: the Girsanov path weight admits a backward conditional expectation that recovers the previous particle-level weights, guaranteeing that both schemes produce the same unbiased terminal law. Empirically, URGE outperforms existing inference-time guidance baselines on synthetic tests and diffusion-model benchmarks, achieving better generation quality, while being significantly simpler to implement and fully gradient-free.

Over the past century, basketball analytics has moved from simple box-score rates toward complex context-aware measures that evaluate events by their expected effect on game outcomes. Officiating analysis has not made the same transition: existing work and public discussion still rely heavily on foul rates, foul differentials, reviewed late-game correctness labels, or team/player benefit from calls. This leaves an empirical gap because a low-leverage foul in a decided game should not be treated as equivalent to a whistle that materially shifts win probability in a close game. To address this gap, we introduce the Ref Impact Metric (RIM), a game-level statistic that aggregates the absolute win-probability movement attached to foul events, measuring the impact of each referee for each game. Using ESPN game-summary and win-probability data for NBA seasons 2021-2022 through 2024-2025, we show that RIM is empirically distinct from both foul volume and foul disparity, identify regular-season and postseason referee distributions, and examine home/away, team-side, and referee-team heterogeneity. We then use linear controls intentionally as stress tests: conditioning on home status, team, opponent, season, and postseason series state asks which descriptive outliers persist after basic contextual adjustment. The results show that several team-side and referee-team patterns remain visible after conditioning, but omitted-variable robustness diagnostics indicate that these patterns should be interpreted as observational screening signals rather than evidence of intent, misconduct, or whistle-level responsibility by any single official. Our contribution to the literature is foundational, and we emphasize that this framework should be tested with different win probability models and further causal inference.