Papers

Non-negative matrix factorization (NMF) approximates a non-negative endogenous data matrix as $Y_1 \approx XB$, with non-negative latent components $X$ and coefficients $B$. Standard covariate-aware NMF is feedforward: $B$ depends only on exogenous variables $Y_2$, with no latent feedback among endogenous variables. We propose NMF-FFB (NMF with feedforward-feedback structure), an exploratory data-fitting framework that embeds the simultaneous equation $B = \Theta_1 Y_1 + \Theta_2 Y_2$ in NMF, where $\Theta_1$ is non-negative latent feedback and $\Theta_2$ non-negative exogenous pathways. NMF-FFB is positioned within data-fitting structural equation modeling (SEM): it fits $Y_1$ directly rather than a model-implied covariance, and is not a confirmatory measurement model or a replacement for maximum-likelihood SEM under standard confirmatory factor analysis assumptions. When $\rho(X\Theta_1)<1$, the reduced form $Y_1 \approx (I-X\Theta_1)^{-1} X\Theta_2 Y_2$ defines a latent Leontief inverse separating direct from cumulative feedback-amplified effects. Estimation uses regularized multiplicative updates with orthogonality and sparsity penalties; an $X$-fixed bootstrap summarizes uncertainty for the feedback spectral radius, the amplification ratio, and path coefficients. Unlike conventional SEM, NMF-FFB requires only the latent rank $Q$ and lets $X$ group endogenous indicators into latent factors. This suits non-negative additive data, automatic loading discovery, Leontief-type cumulative effects, and small samples where covariance-based maximum-likelihood fitting is ill-conditioned. Applications to Holzinger-Swineford, Los Angeles pollution-mortality, and Mississippi county-level health data demonstrate interpretable parts-based representations across distinct latent-feedback regimes.

Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent or associated in some way, such as linear, nonlinear, clustering or anomalies. Here we provide new methods for generating a variety of high-dimensional structures using mathematical functions and statistical distributions organized into the R package cardinalR. Several example data sets are also provided. These will be useful for researchers to better understand how different analytical methods work and can be improved, with a special focus on nonlinear dimension reduction methods. This package enriches the existing toolset of benchmark datasets for evaluating algorithms.

This is the monograph on the theory and applications of copula entropy (CE). This book first introduces the theory of CE, including its background, definition, theorems, properties, and estimation methods. The theoretical applications of CE to structure learning, association discovery, variable selection, causal discovery, system identification, time lag estimation, domain adaptation, multivariate normality test, copula hypothesis test, two-sample test, change point detection, and symmetry test are reviewed. The relationships between the theoretical applications and their connections to correlation and causality are discussed. The framework based on CE for measuring statistical independence and conditional independence is compared to the other similar ones. The advantages of CE based methodologies over the other comparable ones are evaluated with simulations. The mathematical generalizations of CE are reviewed. The real applications of CE to every branch of science and engineering are briefly introduced.

Nonlinear dimension reduction methods provide a low-dimensional representation of high-dimensional data by applying a Nonlinear transformation. However, the complexity of the transformations and data structures can create wildly different representations depending on the method and hyper-parameter choices. It is difficult to determine whether any of these representations are accurate, which one is the best, or whether they have missed important structures. The R package quollr has been developed as a new visual tool to determine which method and which hyper-parameter choices provide the most accurate representation of high-dimensional data. The scurve data from the package is used to illustrate the algorithm. Single-cell RNA sequencing (scRNA-seq) data from mouse limb muscles are used to demonstrate the usability of the package.

Psychological change processes, such as university student dropout in math, often exhibit discrete latent state transitions and can be studied using regime-switching models with intensive longitudinal data (ILD). Recently, regime-switching state-space (RSSS) models have been extended to allow for latent variables and their autoregressive effects. Despite this progress, estimation methods for handling both intra-individual changes and inter-individual differences as predictors of regime-switches need further exploration. Specifically, there's a need for frequentist estimation methods in dynamic latent variable frameworks that allow real-time inferences and forecasts of latent or observed variables during ongoing data collection. Building on Chow and Zhang's (2013) extended Kim filter, we introduce a first frequentist filter for RSSS models which allows hidden Markov(-switching) models to depend on both latent within- and between-individual characteristics. As a counterpart of Kelava et al.'s (2022) Bayesian forecasting filter for nonlinear dynamic latent class structural equation models (NDLC-SEM), our proposed method is the first frequentist approach within this general class of models. In an empirical study, the filter is applied to forecast emotions and behavior related to student dropout in math. Parameter recovery and prediction of regime and dynamic latent variables are evaluated through simulation study.

Large language models (LLMs) have emerged as powerful tools for generating domain-specific multiple-choice questions (MCQs), offering efficiency gains for certification boards but raising new concerns about examination security. This study investigated whether LLM-generated items created with proprietary guidance differ meaningfully from those generated using only publicly available resources. Four representative clinical activities from the American Board of Family Medicine (ABFM) blueprint were mapped to corresponding Entrustable Professional Activities (EPAs), and three LLMs (GPT-4o, Claude 4 Sonnet, Gemini 2.5 Flash) produced items under a naive strategy using only public EPA descriptors, while GPT-4o additionally produced items under a guided strategy that incorporated proprietary blueprints, item-writing guidelines, and exemplar items, yielding 160 total items. Question stems and options were encoded using PubMedBERT and BioBERT, and intra- and inter-strategy cosine similarity coefficients were calculated. Results showed high internal consistency within each prompting strategy, while cross-strategy similarity was lower overall. However, several domain model pairs, particularly in narrowly defined areas such as viral pneumonia and hypertension, exceeded the 0.65 threshold, indicating convergence between naive and guided pipelines. These findings suggest that while proprietary resources impart distinctiveness, LLMs prompted only with public information can still generate items closely resembling guided outputs in constrained clinical domains, thereby heightening risks of item exposure. Safeguarding the integrity of high stakes examinations will require human-first, AI-assisted item development, strict separation of formative and summative item pools, and systematic similarity surveillance to balance innovation with security.

Statistical models often require inputs that are not completely known. This can occur when inputs are measured with error, indirectly, or when they are predicted using another model. In environmental epidemiology, air pollution exposure is a key determinant of health, yet typically must be estimated for each observational unit by a complex model. Bayesian two-stage models combine this stage-one model with a stage-two model for the health outcome given the exposure. However, analysts usually only have access to the stage-one model output without all of its specifications or input data, making joint Bayesian inference apparently intractable. We show that two prominent workarounds-using a point estimate or using the posterior from the stage-one model without feedback from the stage-two model-lead to miscalibrated inference. Instead, we propose efficient algorithms to facilitate joint Bayesian inference and provide more accurate estimates and well-calibrated uncertainties. Comparing different approaches, we investigate the association between PM2.5 exposure and county-level mortality rates in the South-Central USA.

Dynamic programming approaches have long been applied to fit models of univariate and multivariate trait evolution on phylogenetic trees for discrete and continuous traits, and more recently adapted to phylogenetic networks with reticulation. We previously showed that various trait evolution models on a network can be readily cast as probabilistic graphical models, so that likelihood-based estimation can proceed efficiently via belief propagation on an associated clique tree. Even so, exact likelihood inference can grow computationally prohibitive for large complex networks. Loopy belief propagation can similarly be applied to these settings, using non-tree cluster graphs to optimize a factored energy approximation to the log-likelihood, and may provide a more practical trade-off between estimation accuracy and runtime. However, the influence of cluster graph structure on this trade-off is not precisely understood. We conduct a simulation study using the Julia package PhyloGaussianBeliefProp to investigate how varying maximum cluster size affects this trade-off for Gaussian trait evolution models on networks. We discuss recommended choices for maximum cluster size, and prove the equivalence of likelihood-based and factored-energy-based parameter estimates for the homogeneous Brownian motion model.

Survival analysis is a critical tool for modeling time-to-event data. Recent deep learning-based models have reduced various modeling assumptions including proportional hazard and linearity. However, a persistent challenge remains in incorporating longitudinal covariates, with prior work largely focusing on cross-sectional features, and in assessing calibration of these models, with research primarily focusing on discrimination during evaluation. We introduce TraCeR, a transformer-based survival analysis framework for incorporating longitudinal covariates. Based on a factorized self-attention architecture, TraCeR estimates the hazard function from a sequence of measurements, naturally capturing temporal covariate interactions without assumptions about the underlying data-generating process. The framework is inherently designed to handle censored data and competing events. Experiments on multiple real-world datasets demonstrate that TraCeR achieves substantial and statistically significant performance improvements over state-of-the-art methods. Furthermore, our evaluation extends beyond discrimination metrics and assesses model calibration, addressing a key oversight in literature.

Social scientists employ latent Dirichlet allocation (LDA) to find highly specific topics in large corpora, but they often struggle in this task because (1) LDA, in general, takes a significant amount of time to fit on large corpora; (2) unsupervised LDA fragments topics into sub-topics in short documents; (3) semi-supervised LDA fails to identify specific topics defined using seed words. To solve these problems, I have developed a new topic model called distributed asymmetric allocation (DAA) that integrates multiple algorithms for efficiently identifying sentences about important topics in large corpora. I evaluate the ability of DAA to identify politically important topics by fitting it to the transcripts of speeches at the United Nations General Assembly between 1991 and 2017. The results show that DAA can classify sentences significantly more accurately and quickly than LDA thanks to the new algorithms. More generally, the results demonstrate that it is important for social scientists to optimize Dirichlet priors of LDA to perform content analysis accurately.

We study how to select a subset of patients who are unlikely to experience an adverse event within a given time horizon, by calibrating a screening rule based on the output of any survival model. We consider two complementary frameworks. The first extends the classical idea of estimating the event rate among selected patients using a hold-out dataset, integrating it with the Learn-Then-Test method. This provides approximate high-probability guarantees that are comparable to those obtainable from simultaneous confidence bands while being often less conservative. The second takes a different perspective by reformulating the problem in terms of multiple hypotheses testing, enabling false discovery rate (FDR) control via the Benjamini-Hochberg procedure applied to selective conformal p-values. This provides approximate guarantees in expectation. We clarify the theoretical relationship between these approaches, explain how both can handle right-censored data and be made doubly robust via augmented inverse probability of censoring weighting, and compare them empirically using simulations and oncology data from the Flatiron Health Research Database. Our results reveal a practical trade-off: FDR-based screening is typically more powerful, while high-probability calibration is more conservative but offers stronger guarantees, especially when few patients are selected. We also provide practical guidance on implementation and tuning.

Many statistical and econometric problems involve parameters defined by moments of a joint distribution when only marginal distributions are observed, leading naturally to partial identification. We develop a methodology for identification, estimation, and inference in the corresponding partially identified GMM model. We characterize the sharp identified set for the parameter of interest via a support-function/optimal-transport (OT) representation. To estimate the identified set, we employ entropic regularization, which yields a smooth approximation to the classical OT problem that can be computed efficiently using the Sinkhorn algorithm. We also propose a test statistic for hypothesis testing and the construction of confidence regions for the identified set. To derive its asymptotic distribution, we establish a novel central limit theorem for the entropic OT value under general smooth cost functions. We then obtain valid critical values using the bootstrap for directionally differentiable functionals of Fang and Santos (2019). The resulting testing procedure controls size locally uniformly, including at parameter values on the boundary of the identified set. We demonstrate good finite-sample performance of our methodology in Monte Carlo simulations. Finally, as an empirical illustration, we estimate a panel logit model of self-reported happiness with attrition and refreshment, using data from the Understanding America Study.

Standard approaches to causal inference, such as Outcome Regression and Inverse Probability Weighted Regression Adjustment (IPWRA), are typically derived through the lens of missing data imputation and identification theory. In this work, we unify these methods from a Machine Learning perspective, reframing ATE estimation as a domain adaptation problem under distribution shift. We demonstrate that the canonical Hajek estimator is a special case of IPWRA restricted to a constant hypothesis class, and that IPWRA itself is fundamentally Importance-Weighted Empirical Risk Minimization designed to correct for the covariate shift between the treated sub-population and the target population. Leveraging this unified framework, we critically examine the optimization objectives of Doubly Robust estimators. We argue that standard methods enforce sufficient but not necessary conditions for consistency by requiring outcome models to be individually unbiased. We define the true "ATE Risk Function" and show that minimizing it requires only that the biases of the treated and control models structurally cancel out. Exploiting this insight, we propose the Joint Robust Estimator (JRE). Instead of treating propensity estimation and outcome modeling as independent stages, JRE utilizes bootstrap-based uncertainty quantification of the propensity score to train outcome models jointly. By optimizing for the expected ATE risk over the distribution of propensity scores, JRE leverages model degrees of freedom to achieve robustness against propensity misspecification. Simulation studies demonstrate that JRE achieves up to a 15% reduction in MSE compared to standard IPWRA in finite-sample regimes with misspecified outcome models.

A key challenge in estimating causal effects from observational data is handling confounding and is commonly achieved through weighting methods that balance distribution of covariates between treatment and control groups. Weighting approaches can be classified by whether weights are estimated using parametric or nonparametric methods, and by whether the model relies on modeling and inverting the propensity score or directly estimates weights to achieve distributional balance by minimizing a measure of dissimilarity between groups. Parametric methods, both for propensity score modeling and direct balancing, are prone to model misspecification. In addition, balancing approaches often suffer from the curse of dimensionality, as they assign equal importance to all covariates, thus potentially de-emphasizing true confounders. Several methods, such as the outcome adaptive lasso, attempt to mitigate this issue through variable selection, but are parametric and focus on propensity score estimation rather than direct balancing. In this paper, we propose a nonparametric direct balancing approach that uses random forests to adaptively emphasize confounders. Our method jointly models treatment and outcome using random forests, allowing the data to identify covariates that influence both processes. We construct a similarity measure, defined by the proportion of trees in which two observations fall into the same leaf node, yielding a distance between treatment and control distributions that is sensitive to relevant covariates and captures the structure of confounding. Under suitable assumptions, we show that the resulting weights converge to normalized inverse propensity scores in the L2 norm and provide consistent treatment effect estimates. We demonstrate the effectiveness of our approach through extensive simulations and an application to a real dataset.

Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP regression on the warped domain. While this composition of GPs is conceptually straightforward, the functional nature of the multi-dimensional latent warping makes Bayesian posterior inference challenging. Traditional GPs with smooth kernels are naturally suited for the integration of gradient information, but the integration of gradients within a DGP presents new challenges and has yet to be explored. We propose a novel and comprehensive Bayesian framework for DGPs with gradients that facilitates both gradient-enhancement and gradient posterior predictive distributions. Our focus is on surrogate modeling of expensive, deterministic, and nonstationary computer experiments. Gradient-enhancement is most impactful when data is limited, and gradient predictions are most useful for downstream surrogate modeling tasks like optimization and active learning. We benchmark both contributions (gradient-enhanced DGPs and DGP gradient predictions), separately and together, on a variety of nonstationary test functions as well as real quantum mechanics computer experiments that simulate molecular energy and forces as a function of atomic position. On nonstationary surfaces, our gradient-enhanced DGPs outperform gradient-enhanced GPs and non-enhanced DGPs, and our DGP gradient predictions are more effective than GP gradient predictions. We provide open-source software in the "deepgp" package on CRAN, with optional Vecchia approximation to circumvent cubic computational bottlenecks.

This study aims to provide a data-driven approach for empirically tuning and validating rating systems, focusing on the Elo system. Well-known rating frameworks, such as Elo, Glicko, TrueSkill systems, rely on parameters that are usually chosen based on probabilistic assumptions or conventions, and do not utilize game-specific data. To address this issue, we propose a methodology that learns optimal parameter values by maximizing the predictive accuracy of match outcomes. The proposed parameter-tuning framework is a generalizable method that can be extended to any rating system, even for multiplayer setups, through suitable modification of the parameter space. Implementation of the rating system on real and simulated gameplay data demonstrates the suitability of the data-driven rating system in modeling player performance.

Industrial symbiosis fosters circularity by enabling firms to repurpose residual resources, yet its emergence is constrained by socio-spatial frictions that shape costs, matching opportunities, and market efficiency. Existing models often overlook the interaction between spatial structure, market design, and adaptive firm behavior, limiting our understanding of where and how symbiosis arises. We develop an agent-based model where heterogeneous firms trade byproducts through a spatially embedded double-auction market, with prices and quantities emerging endogenously from local interactions. Leveraging reinforcement learning, firms adapt their bidding strategies to maximize profit while accounting for transport costs, disposal penalties, and resource scarcity. Simulation experiments reveal the economic and spatial conditions under which decentralized exchanges converge toward stable and efficient outcomes. Counterfactual regret analysis shows that sellers' strategies approach a near Nash equilibrium, while sensitivity analysis highlights how spatial structures and market parameters jointly govern circularity. Our model provides a basis for exploring policy interventions that seek to align firm incentives with sustainability goals, and more broadly demonstrates how decentralized coordination can emerge from adaptive agents in spatially constrained markets.

Sampling from multimodal distributions is a central challenge in Bayesian inference and machine learning. In light of hardness results for sampling – classical MCMC methods, even with tempering, can suffer from exponential mixing times – a natural question is how to leverage additional information, such as a warm start point for each mode, to enable faster mixing across modes. To address this, we introduce Reweighted ALPS (Re-ALPS), a modified version of the Annealed Leap-Point Sampler (ALPS) that dispenses with the Gaussian approximation assumption. We prove the first polynomial-time bound that works in a general setting, under a natural assumption that each component contains significant mass relative to the others when tilted towards the corresponding warm start point. Similarly to ALPS, we define distributions tilted towards a mixture centered at the warm start points, and at the coldest level, use teleportation between warm start points to enable efficient mixing across modes. In contrast to ALPS, our method does not require Hessian information at the modes, but instead estimates component partition functions via Monte Carlo. This additional estimation step is crucial in allowing the algorithm to handle target distributions with more complex geometries besides approximate Gaussian. For the proof, we show convergence results for Markov processes when only part of the stationary distribution is well-mixing and estimation for partition functions for individual components of a mixture.

Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of Monte Carlo algorithms, focusing on the persistent tension between statistical efficiency and computational cost. We describe the historical development from the foundational Metropolis Hastings algorithm to contemporary methods like Hamiltonian Monte Carlo. A central emphasis of this survey is the rigorous discussion of time and space complexity, including upper, lower, and asymptotic tight bounds for each major algorithm class. We examine the specific motivations for developing these methods and the key theoretical and practical observations such as the introduction of gradient information and adaptive tuning in HMC that led to successively better solutions. Furthermore, we provide a justification framework that discusses explicit situations in which using one algorithm is demonstrably superior to another for the same problem. The paper concludes by assessing the profound significance and impact of these algorithms and detailing major current research challenges.

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically justified approximations that require less training than standard methods. However, they can become computationally prohibitive for large training sets and can be sensitive to noise. We propose a regularized random Fourier feature (RRFF) approach, coupled with a finite element reconstruction map (RRFF-FEM), for learning operators from noisy data. The method uses random features drawn from multivariate Student's $t$ distributions, together with frequency-weighted Tikhonov regularization that suppresses high-frequency noise. We establish high-probability bounds on the extreme singular values of the associated random feature matrix and show that when the number of features $N$ scales like $m \log m$ with the number of training samples $m$, the system is well-conditioned, which yields estimation and generalization guarantees. Detailed numerical experiments on benchmark PDE problems, including advection, Burgers', Darcy flow, Helmholtz, Navier-Stokes, and structural mechanics, demonstrate that RRFF and RRFF-FEM are robust to noise and achieve improved performance with reduced training time compared to the unregularized random feature model, while maintaining competitive accuracy relative to kernel and neural operator tests.

Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein–Uhlenbeck-type stochastic differential equations, in which sampling is driven by a combination of deterministic drift and Brownian diffusion, resulting in continuous particle trajectories in the ambient space. While such dynamics enjoy exponential convergence guarantees for strongly log-concave target distributions, it is well known that their mixing rates deteriorate exponentially in the presence of nonconvex or multimodal landscapes, such as double-well potentials. Since many practical generative modeling tasks involve highly non-log-concave target distributions, considerable recent effort has been devoted to developing sampling schemes that improve exploration beyond classical diffusion dynamics. A promising line of work leverages tools from information geometry to augment diffusion-based samplers with controlled mass reweighting mechanisms. This perspective leads naturally to Wasserstein–Fisher–Rao (WFR) geometries, which couple transport in the sample space with vertical (reaction) dynamics on the space of probability measures. In this work, we formulate such reweighting mechanisms through the introduction of explicit correction terms and show how they can be implemented via weighted stochastic differential equations using the Feynman–Kac representation. Our study provides a preliminary but rigorous investigation of WFR-based sampling dynamics, and aims to clarify their geometric and operator-theoretic structure as a foundation for future theoretical and algorithmic developments.

Slice sampling is a well-established Markov chain Monte Carlo method for approximate sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a superlevel set of the given unnormalized target density (with respect to a reference measure). However, slice sampling algorithms usually require per step multiple evaluations of the target density, and thus can become computationally expensive. This is particularly the case for Bayesian inference with costly likelihoods. In this paper, we exploit deterministic approximations of the target density, which are relatively cheap to evaluate, and propose delayed acceptance versions of several common (hybrid) slice samplers. We show ergodicity of the resulting slice sampling methods, discuss the superiority of delayed acceptance (ideal) slice sampling over delayed acceptance Metropolis-Hastings algorithms, and illustrate the benefits of our novel approach in terms of improved computational efficiency in numerical experiments.

This chapter demonstrates how computational social science (CSS) tools are extending and expanding research on aging. The depth and context from traditionally qualitative methods such as participant observation, in-depth interviews, and historical documents are increasingly employed alongside scalable data management, computational text analysis, and open-science practices. Machine learning (ML) and natural language processing (NLP), provide resources to aggregate and systematically index large volumes of qualitative data, identify patterns, and maintain clear links to in-depth accounts. Drawing on case studies of projects that examine later life–including examples with original data from the DISCERN study (a team-based ethnography of life with dementia) and secondary analyses of the American Voices Project (nationally representative interview)–the chapter highlights both uses and challenges of bringing CSS tools into more meaningful dialogue with qualitative aging research. The chapter argues such work has potential for (1) streamlining and augmenting existing workflows, (2) scaling up samples and projects, and (3) generating multi-method approaches to address important questions in new ways, before turning to practices useful for individuals and teams seeking to understand current possibilities or refine their workflow processes. The chapter concludes that current developments are not without peril, but offer potential for new insights into aging and the life course by broadening–rather than replacing–the methodological foundations of qualitative research.

We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove information-theoretic lower bounds together with matching or near-matching upper bounds, covering both fixed and random designs under Hilbert-valued Gaussian noise and Gaussian white noise errors. The rates are controlled by the spectrum of the covariance operator of the measure that defines the error metric. Our setup is very general and allows for measures with unbounded support. A key implication is a curse of sample complexity, which shows that the minimax risk for generic Lipschitz operators cannot decay at any algebraic rate in the sample size. We obtain sharp characterizations when the covariance spectrum decays exponentially and provide general upper and lower bounds in slower-decay regimes. Finally, we show that assuming higher regularity, i.e., Hölder smoothness, does not improve minimax rates over the Lipschitz case, up to potential constants. Thus, we show that learning operators of any finite regularity necessarily suffers a curse of sample complexity.

We introduce a general, simple, and computationally efficient functional data analysis framework for forecasting day-ahead supply and demand merit-order curves, and the resulting electricity price. We conduct a rigorous empirical comparison on data from the Italian (GME), German (EPEX-DE-LU), and French (EPEX-FR) day-ahead markets over the 2023-2024 period, analyzing curve forecasting performance, price forecasting performance, and the relationship between the two. We find that strong curve forecasting performance does not necessarily translate into strong price forecasting performance, with important implications for curve model evaluation and selection when price forecasting is among the objectives. We also show that this functional data representation approach consistently outperforms the original discretization-based approach of Ziel and Steinert (2016) on price forecasting across all three markets. Finally, the proposed curve-based approach is competitive with state-of-the-art price-based models for two out of three markets (GME and EPEX-FR), and substantially improves accuracy during midday hours (when prices frequently drop due to high renewable generation) with MAE reductions of up to 27% in those windows. For EPEX-DE-LU, however, price-based models retain a clear and significant advantage.

During the height of the hype in late 2021, the Metaverse drew more attention from around the world than ever before. It promised new ways to interact with people in three-dimensional digital spaces. This cross-sectional study investigates the attitudes, perceptions, and predictors of the willingness to engage with the Metaverse among 381 Turkish university students surveyed in December 2021. The study employs Fisher's Exact Tests and binary logistic regression to assess the influence of demographic characteristics, prior digital experience, and perception-based factors. The results demonstrate that demographic factors, such as gender, educational attainment, faculty association, social media engagement, and previous virtual reality exposure, do not significantly forecast the propensity to participate in the Metaverse. Instead, the main things that affect people's intentions to adopt are how they see things. Belief in the Metaverse's capacity to revolutionize societal frameworks, especially human rights, surfaced as the most significant positive predictor of willingness. Conversely, apprehensions regarding psychological harm, framed as a possible 'cyber syndrome' represented a significant obstacle to participation. Perceptions of technical compatibility and ethical considerations showed complex effects, showing that optimism, uncertainty, and indifference affect willingness in different ways. In general, the results show that early adoption of the Metaverse is based on how people see it, not on their demographics. The research establishes a historically informed benchmark of user skepticism and prudent assessment during the advent of Web 3.0, underscoring the necessity of addressing collective psychological, ethical, and normative issues to promote future engagement.

In this paper, a method for recursively computing approximate modal paths is developed. A recursive formulation of the modal path can be obtained either by backward or forward dynamic programming. By combining both methods, a “two-filter” formula is demonstrated. Both method involves a recursion over a so-called value function, which is intractable in general. This problem is overcome by quadratic approximation of the value function in the forward dynamic programming paradigm, resulting in both a filtering and smoothing method. The merit of the approach is verified in a simulation experiments, where it is shown to be on par or better than other modern algorithms.

Parameter-efficient fine-tuning methods, such as Low-Rank Adaptation (LoRA), enable fast specialization of large pre-trained models to different downstream applications. However, this process often leads to catastrophic forgetting of the model's prior domain knowledge. We address this issue with LaLoRA, a weight-space regularization technique that applies a Laplace approximation to Low-Rank Adaptation. Our approach estimates the model's confidence in each parameter and constrains updates in high-curvature directions, preserving prior knowledge while enabling efficient target-domain learning. By applying the Laplace approximation only to the LoRA weights, the method remains lightweight. We evaluate LaLoRA by fine-tuning a Llama model for mathematical reasoning and demonstrate an improved learning-forgetting trade-off, which can be directly controlled via the method's regularization strength. We further explore different loss landscape curvature approximations for estimating parameter confidence, analyze the effect of the data used for the Laplace approximation, and study robustness across hyperparameters.

We introduce a flexible framework for modeling dependent feature allocations. Our approach addresses limitations in traditional nonparametric methods by directly modeling the logit-probability surface of the feature paintbox, enabling the explicit incorporation of covariates and complex but tractable dependence structures. The core of our model is a Gaussian Markov Random Field (GMRF), which we use to robustly decompose the latent field, separating a structural component based on the baseline covariates from intrinsic, unstructured heterogeneity. This structure is not a rigid grid but a sparse k-nearest neighbors graph derived from the latent geometry in the data, ensuring high-dimensional tractability. We extend this framework to a dynamic spatio-temporal process, allowing item effects to evolve via an Ornstein-Uhlenbeck process. Feature correlations are captured using a low-rank factorization of their joint prior. We demonstrate our model's utility by applying it to a polypharmacy dataset, successfully inferring latent health conditions from patient drug profiles.

The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian processes offer theoretical consistency and exact uncertainty quantification, their prohibitive computational scaling renders them impractical for massive sensor networks. Conversely, modern transformer architectures excel at sequence modeling but inherently lack a geometric inductive bias, treating spatial sensors as permutation-invariant tokens without a native understanding of distance. In this work, we propose a spatially-informed transformer, a hybrid architecture that injects a geostatistical inductive bias directly into the self-attention mechanism via a learnable covariance kernel. By formally decomposing the attention structure into a stationary physical prior and a non-stationary data-driven residual, we impose a soft topological constraint that favors spatially proximal interactions while retaining the capacity to model complex dynamics. We demonstrate the phenomenon of “Deep Variography”, where the network successfully recovers the true spatial decay parameters of the underlying process end-to-end via backpropagation. Extensive experiments on synthetic Gaussian random fields and real-world traffic benchmarks confirm that our method outperforms state-of-the-art graph neural networks. Furthermore, rigorous statistical validation confirms that the proposed method delivers not only superior predictive accuracy but also well-calibrated probabilistic forecasts, effectively bridging the gap between physics-aware modeling and data-driven learning.